Lightweight Robotic Excavation

Krzysztof Skonieczny

April 17, 2013

School of Computer ScienceCarnegie Mellon University

Pittsburgh, PA 15213

Thesis Committee:David Wettergreen, Co-Chair

William (Red) L. Whittaker, Co-ChairDimitrios Apostolopoulos

Karl Iagnemma, MIT

Submitted in partial fulfillment of the requirementsfor the degree of Doctor of Philosophy.

Copyright c© 2013 Krzysztof Skonieczny

Abstract

Planetary excavators face unique and extreme engineering constraints relative toterrestrial counterparts. In space missions mass is alwaysat a premium because itis the main driver behind launch costs. Lightweight operation, due to low mass andreduced gravity, hinders excavation and mobility by reducing the forces a robot caneffect on its environment.

This thesis shows that there is a quantifiable, non-dimensional threshold thatdistinguishes the regimes of lightweight and heavy excavation. This threshold iscrossed at lower weights for continuous excavators (bucket-wheels, bucket chains,etc.) than discrete excavators (loaders, scrapers, etc.).The lightweight thresholdrelates payload ratio (weight of regolith payload collected to empty robot weight),excavation resistance (force imparted on an excavator by cutting and collecting soil),and excavation thrust (force supplied by an excavator that is available for cuttingsoil).

Experiments and simulation herein show that payload ratio governs productivityof lightweight excavators. Reducing weight (due to low mass,reduced gravity, orboth) decreases an excavator’s thrust to resistance ratio,especially in cohesive soils.There is a predictable regime in the operating space where this ratio is low enoughthat it limits an excavator’s payload ratio and, ultimately, productivity. Discreteexcavators cross into this regime more readily than continuous excavators, becausesoil accumulation on their blades increases their excavation resistance.

This research introduces novel experimentation that for the first time subjectsexcavators to gravity offload (a cable pulls up on the robot with 5/6 its weight, tosimulate lunar gravity) while they dig. A 300 kg excavator offloaded to 1/6 g suc-cessfully collects 0.5 kg/s using a bucket-wheel, with no discernable effect on mobil-ity. For a discrete excavator of the same weight, productionrapidly declines as risingexcavation resistance stalls the robot; in total the discrete bucket collects less than20 kg of regolith. These experiments demonstrate that discrete excavation crossesthe lightweight threshold under conditions where continuous excavation does not.They also suggest caution in interpreting low gravity performance predictions basedsolely on testing in Earth gravity.

This work develops a novel robotic bucket-wheel excavator.It features uniquedirect transfer from a bucket-wheel to a high payload ratio dump bed, as well as ahigh traction and high speed mobility system. Past lightweight excavator prototypeswere too slow or carried too little regolith payload. Some used bucket-wheels orbucket-ladders to dig continuously, but transported regolith using exposed chains orconveyors that would not withstand harsh lunar conditions.

Future research on lightweight excavation would benefit from testing in reducedgravity flights. These provide the most representative testenvironment short of ac-tually operating on a planetary surface, as excavator and regolith are both subjectto reduced gravity. Another important direction for futurestudy is deep excavationin the presence of submerged rocks, which pose challenges for lighweight continu-ous and discrete excavators alike. Experiments to confirm the generality of results

herein are recommended, including studying the scaling of excavation resistance incohesive soils, and comparing a broad variety of discrete and continuous excavatortools.

iv

Contents

1 Introduction 11.1 Motivation for planetary excavation . . . . . . . . . . . . . . . .. . . . . . . . 11.2 The Load-Haul-Dump cycle at the core of excavation tasks. . . . . . . . . . . . 21.3 Lightweight is low mass in low gravity . . . . . . . . . . . . . . . .. . . . . . . 41.4 Definitions of important terms and concepts . . . . . . . . . . .. . . . . . . . . 6

1.4.1 Continuous vs. discrete excavators . . . . . . . . . . . . . . . .. . . . . 61.4.2 Payload ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4.3 Excavation thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91.4.4 Excavation resistance . . . . . . . . . . . . . . . . . . . . . . . . . .. . 10

1.5 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.6 The problem of distinguishing productive lightweight excavator configurations . 111.7 Thesis Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 111.8 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Background and Related Work 132.1 Fundamental mechanics of excavation . . . . . . . . . . . . . . . .. . . . . . . 13

2.1.1 Gravity and cohesion forces included in all excavation models . . . . . . 142.1.2 Adhesion and inertial forces can usually be neglected. . . . . . . . . . . 152.1.3 Surcharge forces arise due to soil accumulation . . . . .. . . . . . . . . 162.1.4 Discrete Element Models for excavation . . . . . . . . . . . .. . . . . . 16

2.2 Experimentation for Lunar and Planetary Excavation . . .. . . . . . . . . . . . 172.2.1 The large impact of soil accumulation on discrete excavation . . . . . . . 172.2.2 Soil properties and gravity are important conditionsto control . . . . . . 18

2.3 Applicability of excavation resistance models to planetary excavation . . . . . . 192.4 Lunar excavation trade studies . . . . . . . . . . . . . . . . . . . . .. . . . . . 192.5 Lightweight excavator prototypes . . . . . . . . . . . . . . . . . .. . . . . . . . 212.6 Soil loosening methods and mechanisms . . . . . . . . . . . . . . .. . . . . . . 232.7 Autonomous Earthmoving and Tele-Operation . . . . . . . . . .. . . . . . . . . 232.8 Conclusions Based on Related Work . . . . . . . . . . . . . . . . . . . . . .. . 24

3 Hauling and Payload Ratio 273.1 Task-level site work modeling . . . . . . . . . . . . . . . . . . . . . .. . . . . 27

3.1.1 Traction modeling (wheels) . . . . . . . . . . . . . . . . . . . . . .. . 283.1.2 Excavation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

v

3.1.3 Operations modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . .333.1.4 Power modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.1.5 Parametric sensitivity analysis . . . . . . . . . . . . . . . . .. . . . . . 35

3.2 Experiments with a small robotic excavator . . . . . . . . . . .. . . . . . . . . 363.2.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .393.2.2 Predicted sensitivity of experimental parameters . .. . . . . . . . . . . 413.2.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43

3.3 Comparison of simulated and experimental results . . . . . .. . . . . . . . . . . 453.4 Hauling dominates task productivity . . . . . . . . . . . . . . . .. . . . . . . . 483.5 Conclusions from sensitivy experiments and simulations. . . . . . . . . . . . . 49

4 Thrust and resistance in lightweight excavation 514.1 Relationship of mass and scale . . . . . . . . . . . . . . . . . . . . . . .. . . . 514.2 Light weight reduces excavation thrust coefficient . . . .. . . . . . . . . . . . . 534.3 Predicted effects of light weight on excavation resistance coefficient . . . . . . . 55

4.3.1 Effects of light weight operation on surcharge . . . . . .. . . . . . . . . 594.4 Excavation scaling experiments . . . . . . . . . . . . . . . . . . . .. . . . . . . 61

4.4.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .624.4.2 Preliminary investigation of soil preparation . . . . .. . . . . . . . . . . 634.4.3 Soil preparation and force measurement . . . . . . . . . . . .. . . . . . 644.4.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . .. 67

4.5 Conclusions regarding thrust and resistance for lightweight resistance . . . . . . 71

5 The ‘lightweight threshold’ 755.1 A non-dimensional ‘Lightweight number’ . . . . . . . . . . . . .. . . . . . . . 75

5.1.1 L for continuous and discrete excavation . . . . . . . . . . . . . . . . .775.2 Gravity offloaded excavation experiments . . . . . . . . . . . .. . . . . . . . . 79

5.2.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .805.2.2 Predicted lightweight numbers . . . . . . . . . . . . . . . . . . .. . . . 825.2.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84

5.3 Conclusions regarding the lightweight threshold . . . . . .. . . . . . . . . . . . 86

6 Lightweight excavator development 896.1 Excavation tooling configuration . . . . . . . . . . . . . . . . . . .. . . . . . . 89

6.1.1 Testing transverse bucket-wheels . . . . . . . . . . . . . . . .. . . . . . 926.2 Excavator mobility system . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 966.3 Conclusions regarding lightweight robotic excavator development . . . . . . . . 96

7 Conclusions and future work 997.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103

7.2.1 Bringing planetary excavation missions forward . . . . .. . . . . . . . . 1037.2.2 Establishing resources and direction for future work. . . . . . . . . . . 104

7.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

vi

8 Bibliography 109

A Extensions 119A.1 Regolith shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119A.2 Non-tractive excavation thrust . . . . . . . . . . . . . . . . . . . .. . . . . . . 120

B Soil flow imaging and grouser spacing 123

vii

viii

1 Introduction

1.1 Motivation for planetary excavation

Excavation of regolith enablesin situ resource utilization(ISRU) on the Moon and Mars. ISRU

reduces the cost of exploration by producing consumables (including oxygen, water, and fuel)

from native regolith and building earthwork infrastructure (such as trenches as berms). NASA

highlights five motivations for excavation:

(1) excavation for oxygen production, (2) excavation and material handling for land-

ing pad and berm fabrication, (3) excavation for habitat protection (e.g., radiation

and micrometeoroids), (4) excavation for mission element emplacement (e.g., nu-

clear reactor burial), and (5) excavation for science (e.g., trenching for stratigraphy

evaluation). The most important task identified to date is regolith excavation and

transport for oxygen production [58].

China intends to build a lunar base for taikonauts. Russia and Japan plan to extablish robotic

lunar outposts. Early ISRU missions will be fully robotic, demonstrating ISRU and excava-

tion technology while carrying out scientific inquiry. Regolith excavation and processing will

continue to be performed robotically as the technology matures, even when supporting human

exploration.

Excavation can expose buried ice by removing overburden. Figure 1.1 shows multiple regions

at the Lunar South Pole that may harbor buried deposits of water ice. Studies suggest ice could

1

Figure 1.1: The Lunar south pole has areas cold enough to sustain water ice (shown redthrough blue) even in accessible areas well outside of permanently shadowed craters (outlined inwhite) [23]. Excavating down to these resources can uncoverthem for direct scientific measure-ment, characterization, or mining.

be found in accessible areas (outside crater rims) at depthsof only tens of centimeters [23, 59].

Excavating down to these deposits can uncover them for direct scientific measurement, charac-

terization, or mining. Characterizing and mapping these iceresources is another important goal

for ISRU [58], and Astrobotic Technology Inc. and Shackleton Energy Company intend to mine

these resources. Moon Express aims to mine platinum on the lunar surface.

The tasks requiring excavation on the Moon and Mars thus spanmining, earthworking for

infrastructure, as well as direct scientific inquiry. Figure 1.2 and Figure 1.3 show visualizations

of some of these various excavation tasks.

1.2 The Load-Haul-Dump cycle at the core of excavation tasks

Regolith requires varying degrees of processing depending on the application. Three classes of

task are distinguished here based on this degree of processing.

2

Figure 1.2: Conceptual discrete excavation robot (with a front-loading bucket) building outpostinfrastructure on the Moon

Figure 1.3: Conceptual continuous excavation robot (with a bucket-wheel) digging a trench onthe Moon, while collecting regolith

3

1. Displacement. For some tasks the only requirement is moving the regolith out of the

way. These tasks (or sub-tasks) include removing overburden from buried ice, trenching

to expose stratigraphy, and digging holes to emplace mission elements.

2. Shaping. For another class of tasks - which includes building berms,covering habitats,

burying emplaced assets - the regolith is the desired material. Once moved into place, addi-

tional processing consists merely of physically shaping, molding, and perhaps compacting

or sintering the regolith.

3. Refinement. For some tasks, the desired resource makes up only a fraction of the re-

golith, and processing is required to refine and extract the resource. This includes oxygen

extraction as well as mining for ice or platinum.

Moving regolith from one place to another, in a load-haul-dump cycle, is central to the first

two of these task classes. The degree to which load-haul-dump is also central to the third depends

on where processing occurs. Options include a central processing plant designed to accept raw

regolith, a central plant that accepts beneficiated regolith (i.e. pre-processed to increase the

concentration of the desired resource), or a plant that runsentirely on the excavator. Onboard

processing introduces significant mass and extreme thermalrequirements; oxygen extraction, for

example, requires heating regolith to between900◦C and1600◦C [58]. It is assumed that, for

these reasons, onboard processing will not be incorporatedinto excavators themselves during

prototypical excavation missions. Load-haul-dump is thusa paradigm that encompasses the key

aspects of all relevant regolith excavation tasks.

1.3 Lightweight is low mass in low gravity

Light weight can be attributed to low robot mass, reduced gravity, or both. In any space mission,

mass is always at a premium because it is the main driver behind launch costs. Small excavators

that can achieve mission goals are preferable to larger ones. Low mass machines operating in

4

Figure 1.4: Contraints of planetary excavation impose unique engineering challenges

reduced gravity (1/6 of Earth gravity on the Moon, 1/3 on Marsor Mercury) have limited weight

available to produce traction or plunge tools into regolith. Traction and plunge force are limited

to a fraction of robot weight. Figure 1.4 expresses how low mass and reduced gravity leads to low

traction and plunge force. Engineering challenges associated with lightweight excavation neces-

sitate a rethink of excavation configurations, possibly beyond the dozers, loaders, and excavators

typical in terrestrial applications [12].

Excavation missions started small. For example, the Surveyor, Viking, and Phoenix landers

gathered samples of a few cubic centimeters at depths of a fewcentimeters with scoops mounted

to relatively heavy landers (see Figure 1.5). Next missionswill likely escalate to excavating cubic

meters worth of regolith at depths of 10’s of cm’s using lightweight mobile robots (e.g. digging

down to expose and collect water-ice in polar regions of the Moon). Finally, excavation will scale

up to production machines for ISRU. Having a configuration that scales well with increasing size

and mass allows subsequent missions to re-use existing technology, learn from past difficulties,

and reduce risk. This principle is exemplified in the similarities between Mars Sojourner, the

subsequent MERs, and now the Mars Science Laboratory (MSL), as seen in Fig. 1.6. Robotic

5

Figure 1.5: Lunar and Martian landers to date have gathered only small samples with scoopsmounted to relatively heavy landers. Surveyor (top left) onthe Moon with scoop extending righton scissor arm; Viking (top center) model with excavation boom deployed; Phoenix (top right)artists concept; Trenches dug by each (bottom row), respectively [NASA].

excavators with high productivity across a range of light weights are essential.

1.4 Definitions of important terms and concepts

Before addressing the problem posed by lightweight robotic excavation, a few additional con-

cepts and terms are defined.

1.4.1 Continuous vs. discrete excavators

Excavators can be classified as continuous or discrete, describing interactions with the soil while

taking multiple cuts.

Continuous excavatorsstay continually in contact with the soil as they take multiple cuts.

This necessitates having multiple cutting surfaces; by thetime each surface or bucket has ac-

6

Figure 1.6: Configurations that scale well from small initialmissions reduce risks in subsequentmissions. Sojourner (center), MER (left), and MSL (right) share a common suspension configu-ration for this reason [NASA JPL].

cumulated an appreciable amount of soil it clears the groundand the next, soil-free, bucket has

already started cutting. Continuous excavators include bucket-wheels, bucket-chains, and elevat-

ing scrapers.

Discrete excavatorsare those that must break contact with the soil before starting a new cut;

between cuts, the excavator may need to dump its load or clearthe cutting surface, for example.

These excavators fill one large bucket with a single cut; the cutting edge has an ever-growing

accumulation of soil as the bucket is filled. Discrete excavators include front-end loaders, dozers,

mining shovels, and open bowl scrapers.

Figure 1.7 shows examples of both continuous (left box) and discrete (right box) mobile

excavators. The taxonomy lines in the figure also note another way of subdividing the excavators,

namely into trenchers, scrapers, and front-end loaders/pushers.

In this work, a discrete excavator’s blade or bucket (filled directly by the act of cutting)

is assumed to be the excavator’s only vessel for collecting and transporting regolith. Discrete

excavators that transfer load to a secondary collection bin(i.e. a dump-bed) are considered

separately in Appendix A.

7

Figure 1.7: Taxonomy of mobile excavators, with continuousexcavators shown in the blue box (left), and discrete in the yellow(right). The upper and lower rows show parallels between terrestrial and planetary machines, respectively.

8

1.4.2 Payload ratio

Payload ratio is the ratio of weight of regolith payload collected to emptyrobot weight; it is a

measure of pound-for-pound regolith moving capacity that turns out to govern the productivity

of lightweight robotic excavators. Terrestrial loaders and scrapers attain payload ratios as high as

80% to 100% [35]. Space systems are subject to additional constraints that make it challenging

to attain payload values that high; a payload ratio of 50% is considered relatively high in this

context. In this thesis, the non-dimensional quantity payload ratio is denotedP .

1.4.3 Excavation thrust

Excavation thrust is the force supplied by an excavator that is available for cutting soil. In

this work, excavation thrust is assumed to be provided by traction, as excavator configurations

typically considered for space applications cut by drivingforward. Alternate modes of providing

excavation thrust, such as resisting articulation forces using a static base or using excavator

weight directly to cut vertically down, are considered separately as extensions to this work, in

Appendix A.

A vehicle’s drawbar pull is the net traction available for doing work, and is dependent upon

slip (or travel reduction, a caveat explained in Chapter 4). Drawbar pull at 20% slip is a good

measure of tractive performance, as pull begins to plateau around 20% slip for many wheels (or

tracks) while negative effects such as sinkage increase [68]. A non-dimensional quantity,P20/W

(Drawbar pull at 20% slip, normalized by weight), has been used as a benchmark metric for lunar

wheel performance from the times of Apollo [24] to today [70,80].

In this thesis, excavation thrust refers to drawbar pull at 20% slip, because of the assumption

of tractive thrust; it is denotedP20. The non-dimensional ratio of excavation thrust to weight

is defined as theexcavation thrust coefficient, and is denotedT . Under the tractive thrust

assumption,T = P20/W .

9

1.4.4 Excavation resistance

Excavation resistanceis the force imparted on an excavator by cutting and collecting soil. Only

the forces during the cut (once the excavation blade is already in the ground) are treated explicitly.

Penetration forces are neglected but, as Blouin assumes these forces are of the same nature as

the cutting forces [11], they can be treated as analagous to cutting forces and subsumed by them.

Crucially, resistance introduced by soil accumulation at a bucket’s cutting edge (which increases

the force required to move additional soil into the bucket) is accounted for as part of excavation

resistance.

Excavation resistance force is denotedFex in this work. The non-dimensional ratio of exca-

vation resistance to empty excavator weight is defined as theexcavation resistance coefficient,

and is denotedF = Fex/Wrobot.

1.5 Scope

This thesis considers excavation tasks that involve load-haul-dump, with some additional pro-

cessing such as shaping, compaction, and beneficiation treated as extensions to this central task.

Mining robots that fully process resources onboard are outside the scope of this work.

This work deals primarily with excavators that produce thrust for cutting by developing trac-

tion, with other sources of excavation thrust treated as extensions in Appendix A.

Excavation in gravity between 1 and 1/6 that of Earth is considered, to cover a range that

includes Earth, Mars, Mercury, and the Moon. Digging on asteroids is outside the scope of

this work. The range of robot mass considered in this work spans from 30 kg to approximately

300 kg. Larger, more massive, machines are unlikely to satisfy mass budgets of near-future

excavation missions. As machines get smaller than 30 kg or so, baseline components that do not

scale well (like computing and communications) take up an ever larger proportion of the mass,

leaving little room for productive excavation tooling. Thescope of this work covers a range of

10

weights that is relevant across multiple space mission scenarios.

1.6 The problem of distinguishing productive lightweight ex-

cavator configurations

Excavation using lightweight machines is problematic because light weight puts severe limits on

forces an excavator can effect for traction and plunging tools into soil. Excavators for building

infrastructure and mining resources on the Moon and Mars will necessarily be lightweight, be-

cause they will be low mass machines (in space missions mass is always at a premium) operating

in reduced gravity.

No prior methodology exists for developing or even evaluating robotic configurations that are

lightweight and yet still productive.

1.7 Thesis Statement

This thesis substantiates that continuous excavators maintain high productivity at light weights,

where productivity for discrete excavators declines. All excavators have a ‘lightweight threshold’

in the operating space, below which their productivity is limited. This threshold is crossed at

lower weights for continuous excavators than discrete excavators. The lightweight threshold is

described by a non-dimensional quantity that relates payload ratio, excavation resistance, and

excavation thrust.

1.8 Overview

The remainder of this document is organized as follows:

Chapter 2 presents related work in lightweight excavation. This includes excavator config-

uration trade studies and a variety of prototypes. Proposedmethods for reducing excavation

11

resistance, including percussion and raking, are discussed. The utility and limitations of ana-

lytical models and experimental techniques commonly used for lunar excavation research are

explored.

Chapter 3 shows that the haul stage of load-haul-dump cycles governs excavator productivity,

based on experiments and simulations. The resulting importance of payload ratio is discussed, as

are underlying assumptions regarding excavation thrust and resistance that underpin these results.

Excavation thrust, excavation resistance, and the relation of these terms, are the subject of

Chapter 4. This chapter also discusses how excavation resistance varies during excavation de-

pending on excavator configuration (i.e. continuous vs. discrete excavation). Excavation resis-

tance due to soil accumulation is explored. Analytical models are used to extend results to low

gravity environments, and these results are compared to thelimited low gravity experimental

data available.

Chapter 5 develops the ‘lightweight threshold’, combining the concepts from the previous

chapters. Experimental results of excavation operations below and above this threshold are pre-

sented. The limitations of performing lightweight excavation experiments on Earth are discussed.

Chapter 6 presents practical considerations for implementing continuous excavation in space.

This is done in the context of the development of a prototype for a novel lightweight bucket-wheel

excavator robot.

Chapter 7 summarizes the major conclusions and contributions of this thesis, and proposes

relevant future work.

12

2 Background and Related Work

Literature related to lightweight robotic excavation research includes the principles of excavation

and attempts to model its mechanics, experimentation in analogue lunar and planetary conditions,

trade studies and prototypes of lunar excavator configurations, soil loosening methods, and au-

tomation of earthmoving and mining equipment.

2.1 Fundamental mechanics of excavation

The mechanics of excavation are based on the principles of passive earth pressure, adapted from

the design of retaining walls, as shown in Figure 2.1. Reece presents the following as the funda-

mental equation of earthmoving mechanics [32]:

PEx = Nγγgd2 +Nccd+Nqqd+NaCad (2.1)

wherePEx is excavation resistance force per unit width, and the four terms of the summation

represent (in order) forces due to frictional shearing (i.e. gravity), cohesion, surcharge, and soil-

tool adhesion. Inertial forces are explicitly ignored, as low cutting speed is assumed. TheNi are

non-dimensional coefficients pertaining to each of the foursources of force, respectively. Grav-

itational acceleration is denotedg, γ is soil density,d is cut depth,c is cohesion,q is surcharge

pressure, andCa is soil-tool adhesion. The equation is for cutting with a flatplate. As this is

a two-dimensional formulation, a first order estimate of excavation resistance force for a cut of

13

Figure 2.1: Mechanics of excavation based on passive earth pressure [32]

finite width can be made by multipyling by said width,w:

FEx = wPEx (2.2)

A wide variety of models have been investigated for their potential applicability to planetary

excavation [26, 39, 73, 74]. However, at their root, they areall just variations of Reece’s funda-

mental equation (with the possible exception of Luth & Wismer). Models vary in which force

terms they do and don’t include. Several models omit tool-soil adhesion and/or surcharge forces.

Some include inertial forces, which Reece explicitly omitted. Table 2.1 lists the array of models

and shows which force terms they include. Additionally, themodels vary in their definitions of

theNi coefficients.

2.1.1 Gravity and cohesion forces included in all excavation models

Excavation shears soil, and a soil’s shear strength is governed by its internal friction angle and

cohesion. These shear strength contributions are modelledfor excavation resistance by gravity

and cohesion terms, respectively. All the models listed in Table 2.1 include at least some form

14

Model Gravity Cohesion Surcharge Adhesion Inertia

Reece X X X X

Osman X X X X

Gill X X X

Luth & Wismer X ∼1 ∼1

Godwin X X X X

Balovnev2 X X X

McKyes / Swick X X X X X

Qinsen X X X3

X

Willman X X

Zeng X X X ∼4

Table 2.1: Models vary in which force terms they include, butgravity and cohesion are alwaysconsidered.1In Luth & Wismer, cohesion and inertia terms are multiplied by gravity terms,rather than added to them.2Balovnev includes additional terms to account for sidewallsand ablunt cutting edge.3Qinsen models a curved bulldozer blade, and explicitly models surchargedue to soil accumulation.4Zeng treats acceleration directly, rather than inertia.

of these two terms, implying that their contribution to total excavation resistance is of primary

importance. In fact, Wilkinson and DeGennaro show that, forthe McKyes / Swick model (which

includes all five typical terms), the gravity term (referredto as the depth term in their paper)

and/or cohesion are the dominant contributions to total excavation resistance force over a very

broad range of operating conditions [73].

2.1.2 Adhesion and inertial forces can usually be neglected

Compared to gravity and cohesion, adhesion and inertial forces tend to have minimal contribution

to excavation resistance force. Hettiaratchi and Reece notethat theNa coefficient (for adhesion)

is small compared to the otherNi and that soil-tool adhesion is almost always smaller than

cohesion; they neglect inertial forces outright, arguing that cutting speeds are typically low [32].

Table 2.1 shows that adhesion and inertial terms are the two most often omitted from excavation

resistance force models.

15

2.1.3 Surcharge forces arise due to soil accumulation

The surcharge term can be used to account for soil that accumulates at the front edge of the bucket

during cutting. The surcharge increases as cutting proceeds. To account for this, Shmulevich [61]

models surcharge as:

q ∝ γgx (2.3)

wherex is cut advance distance (andγ is soil density). Kobayashi [42], making different as-

sumptions about the shape of the accumulating pile, proposes: q ∝ γg√dx whered is cut depth.

In both cases, surcharge increases with cut advance distance, linearly in the former and as the

square root in the latter. In both cases, the surcharge forceis assumed to be only due to the

additional weight causing increased frictional shearing.

Qinsen [57], when modeling excavation with a bulldozer blade, accounts for soil accumula-

tion directly. They model forces at steady state once soil accumulation has reached maximum

extent. The model considers not only the weight and frictional shearing of the cut soil, but also

its cohesion.

As discussed in Section 1.4.1, soil accumulation is particularly notable for discrete excava-

tors such as front-end loaders and bulldozers. Section 2.2.1 discusses experimental results that

demonstrate how excavation resistance increases during discrete excavation, and relates these

results to the models discussed above.

2.1.4 Discrete Element Models for excavation

Discrete Element Modeling (DEM) provides greater promise for high fidelity modeling of exca-

vation. This approach explicitly models interactions between particles, and produces resultant

flow fields and stresses for these soil particles. DEM could therefore model how soil flows and

accumulates in a bucket. The goal of current research in DEM [9, 69] is to produce excavation

flow fields as well as calibrated resultant forces. Experiments providing quantified visualizations

16

of excavation will drive development and validation of DEM.Bui et al [14] have performed soil

footing failure experiments in reduced gravity to provide data for tuning their DEM model for

excavation.

This modern approach is still being developed, and is not ready to incorporate into system

development optimizations, let alone online prediction and control. DEM development is a field

of research in its own right, and is outside the scope of this work.

2.2 Experimentation for Lunar and Planetary Excavation

Classical excavation experiments pull blades and buckets through soil bins, measuring how exca-

vation resistance and other variables are affected by changes in excavation parameters; a recent

example is work at NASA Glenn Research Center [2]. Controlled soil bin experiments have also

been conducted with bucket-wheels [36].

2.2.1 The large impact of soil accumulation on discrete excavation

Agui shows that horizontal excavation resistance rises approximately linearly with cut distance,

as soil accumulates in a bucket [2]. These results agree withthe general modeling assumptions

of Shmulevich presented in Section 2.1.3. Agui also showed though, that the shape and location

of a pile accumulating in a bucket is non trivially dependentupon time as well as cut depth, cut

angle, and possibly other parameters. Modeling soil accumulation in a bucket by a continuously

changing surcharge distribution is therefore difficult, and ideally would depend on knowing how

the soil flows as it enters the bucket.

A bulldozer blade also exhibits significant increase in horizontal force as surcharge increases

with cut distance, as demonstrated by King [39]. Comparing a variety of excavation models to

their data, they conclude that Qinsen’s model provides the best fit. This is not entirely unex-

pected, as Qinsen’s model was developed specifically for bulldozing (though one of the other

17

Figure 2.2: Gravity offload: a cable pulls up on an excavator with 5/6 its weight to simulate lunargravity

models compared against was specific to bulldozing as well).

2.2.2 Soil properties and gravity are important conditions to control

Controlled planetary excavation experiments make use of simulants that mimic the geotechnical

properties of Lunar or Martian soils. GRC-1 and GRC-3 are lunar simulants with properties

relevant for excavation [56]. JSC-1 is another lunar simulant often used for excavation experi-

ments [18, 74]. JSC-1 has a particle size distribution that issimilar enough to lunar regolith to

duplicate its compaction and relative density [83].

Simulating low gravity conditions is another important consideration for lightweight exca-

vation experiments. Boles [13] showed that excavation resistance in 1/6 of Earth gravity (expe-

rienced during reduced gravity flights) could be anywhere between 1/6 and 1 of the resistance

experienced in full Earth gravity. Sample data shows excavation forces in 1/6 g that average 1/3

of the resistance in full Earth gravity.

Another way to simulate low gravity conditions (at least forthe excavator if not the soil) is to

use a gravity offload mechanism. No excavator testing with gravity offload has been reported in

the literature to date.

18

2.3 Applicability of excavation resistance models to planetary

excavation

A common result from literature that attempts to compare excavation forces predicted by various

models (e.g. [39, 73, 74]) is that the models yield disparatepredictions. This makes it inprudent

to rely on any one model for estimating excavation forces. AsSection 2.1 showed, however, the

models share common fundamentals that are instructive wheninvestigating planetary excavation.

Any estimate of excavation resistance must take into account soil weight (and thus friction) and

cohesion. Surcharge is also very important, particularly for discrete excavation; the weight, and

perhaps cohesion, of the accumulating soil comprise this surcharge.

Muff [53] reports that the Luth & Wismer model was tested against Martian telemetry from

the Viking sampling digs (a claim seemingly based on personal correspondance with those who

performed the analysis), giving this model flight heritage in a sense. The lack of published

quantitative comparisons, however, compels caution in interpreting this claim.

2.4 Lunar excavation trade studies

Trade studies have examined the applicability of various excavation robot options, specifically

for lunar outpost site work. However, these studies assume several metric tons are available for

excavation equipment; this is unlikely to be the case in the short or even medium term. The trade

studies also restrict themselves to predefined configuration options, potentially missing novel

designs that could fare better than those considered.

Boles et al. [12] compares the probable required launch mass of several construction ma-

chine suites. The study concludes that typical terrestrialexcavation machines would not be as

effective as tripod cranes, sweeper leveler/excavators, and other innovative vehicles. Abu El

Samid’s work [1] continues along the lines of Boles’, concentrating on tradeoffs between au-

tonomous and tele-operated operation and between single vehicle and team configurations. A

19

Configuration options Metrics Selected option Ref.

Boom cranes, trackdozers, haulers, drills,clamshell diggers,sweeper excava-tor/levelers

Launch mass All-purpose supercranes with drilling,excavating, level-ing, and haulingcapabilities

[12]

Same as Boles (con-trolled manually), orteams of autonomousbulldozers, bucketloaders, or bucketwheels

Launch mass Team of autonomousbulldozers

[1]

Multipurpose exca-vator, auger, bucketladder, bucket wheel,dragline, overshotloader, pneumaticvacuum, scraper

Productivity, reliabil-ity, dust generation,power efficiency,maintainability

Multipurpose excava-tor

[51]

Table 2.2: Trade studies examining options for large-scalelunar excavation (using several metrictons of equipment) arrive at different conclusions, demonstrating the weakness of approachingsuch a complex problem with a predefined set of solutions to choose from.

team of autonomous bulldozers is recommended for the task ofberm building. Mueller and

King’s study [51] scores excavator designs on a number of quantitative and qualitative metrics

and decides a multi-purpose machine with bulldozing blade and excavator arm is most appropri-

ate for lunar site work. The results of these trade studies are summarized in Table 2.2.

The aforementioned trade studies restrict themselves to predefined configuration options and

compare their relative merit for lunar operations; in that sense, they espouse a top-down approach

to configuration analysis. Each of the studies arrives at different conclusions regarding robot

designs. The varying results highlight effects of differing assumptions, models, and metrics

when approaching such a complex problem with a predefined setof solutions to choose from.

Assumptions of high mass machinery, as well as wide variability of the results, limit the

relevance of past trade studies to the development of lightweight robotic excavators. Metrics for

comparison of configurations in these studies are useful to consider, but the top-down approach

20

of studying a predefined set of solutions is not as useful.

2.5 Lightweight excavator prototypes

In recent years, several robot prototypes have been developed specifically for lunar excavation

and ISRU. There are tested, however, in full Earth gravity, so principles of lightweight excavation

are obscured. The taxonomy of mobile excavators introducedin Section 1.4.1 can be applied to

these robots as well, as seen in Figure 1.7. The figure shows samples of each of the following: a

bucket-wheel excavator, a bucket-ladder scraper, an open bowl scraper, as well as a loader and a

dozer.

Bucket-wheel excavators produce low resistance forces suitable for lightweight operation [36].

A past lunar bucket-wheel excavator prototype [52] has beenconfigured like a trencher (see Fig-

ure 1.7). However, the small scale intended for the lightweight excavator made material handling

and tranfer prohibitively challenging [37]. A novel lightweight bucket-wheel excavator, with a

simplified material transfer approach, has been developed as part of this work and will be dis-

cussed in detail in Chapter 6. A Bucket-Drum Excavator, which is an adaptation of a bucket

wheel [17], has a novel regolith collection system with cutting buckets mounted directly around

the outside of the collection drum. Regolith Advanced Surface Systems Operations Robot (RAS-

SOR) has counter-rotating front and rear bucket drums, making it possible to balance horizontal

excavation forces [50]. Figure 2.3 shows a Bucket Drum Excavator as well as RASSOR.

Due to past difficulties encountered transferring regolithfrom bucket-wheel to collection

bin, bucket-ladders have gained favor [37]. Bucket-laddersuse chains to move buckets along

shapeable paths, easing transfer to a collection bin. Winners of the NASA Regolith Excavation

Challenge and subsequent Lunabotics mining competitions (competitions where lightweight ex-

cavators must collect as much regolith simulant as possiblein 15 to 30 minutes) have all em-

ployed bucket-ladder trenchers driven by exposed chains orflexible conveyors. However, ex-

posed chains and conveyors fare poorly in harsh lunar regolith and vacuum, making them inap-

21

Figure 2.3: Adaptations of bucket-wheel excavation: BucketDrum Excavator (left) and RAS-SOR (right)

Figure 2.4: Juno rover with a small load-haul-dump scoop that achieves only low payload ratio.

propriate for operation on the Moon.

Cratos [16] is an open bowl scraper with a central bucket between its tracks, as seen in

Figure 1.7. It can carry a payload ratio of approximately 30%(in Earth gravity). Although

terrestrial scrapers’ buckets extend laterally beyond theoutside of the wheel track, the central

bucket mounting is a key feature that leads to Cratos being classified as a scraper here. Juno

rovers [67] can be equipped with front-end load-haul-dump scoops, though these scoops can

carry only a small fraction of the rover’s mass in regolith (see Figure 2.4).

Other lunar and planetary excavator prototypes include NASA’s Chariot with LANCE bull-

dozer blade and Centaur II with front-loader bucket. These machines are very high mass (on the

order of tonnes) and low payload ratio, making their relevance to lightweight excavation mis-

22

sions limited. Robots that excavate by filling up with regolith as they burrow into the ground

have also been proposed [44].

2.6 Soil loosening methods and mechanisms

Lunar regolith is very strong below the top few centimeters from the surface [30]. The presence

of ice only makes this dense mass harder and more cohesive [27]. This has led researchers to

develop several methods to loosen regolith either prior to or during excavation.

Sture et al [40, 66] as well as Zacny et al [18] have shown that percussive/vibratory actuation

of diggins implements reduces excavation resistance forces. Specifically, percussion reduces

the shear strength of dry soil by removing the effects of soildilatancy from the internal friction

angle along the shear failure boundary layer [28]. To date, the advantages of percussion have

been studied for bulldozers, small narrow scoops, and helical augers.

Gertsch et al. [29] have studied the applicability of cutterhead wheels and rippers for loosen-

ing frozen and compacted regolith in preparation for excavation. Iai showed that adding ripping

reduces total excavation energy (ripping + excavation) in soils with high density and low gravel

content [34]. An important contribution of Iai’s work is raising awareness of the often overlooked

contribution of gravel and rock content to excavation forces.

Bernold has suggesting using small explosive charges to loosen compacted regolith [8]. The

fact that these explosives are a consumable that cannot be manufactured in situ, though, limits

their applicability to ISRU missions.

2.7 Autonomous Earthmoving and Tele-Operation

The automation and tele-operation of earthmoving machinesis a research field in its own right.

Singh [62] lists a taxonomy of the field’s inter-related aspects: sensing, kinematic and dynamic

modeling, soil-tool interaction modeling [45], tool trajectory planning and control, and tele-

23

operation.

Dunbabin [22] investigates operating large-scale excavation machines in extra-terrestrial en-

vironments, and discusses operating modes ranging from manual, through various levels of ab-

stracted tele-operation (remote, fly-by-wire, and copilot), to autonomous. Autonomous dig and

dump cycles are demonstrated (on Earth), with the goal of shifting as much control as possible

to the robotic excavator to avoid tele-operation challenges such as dealing with latency.

A theoretical lower bound on the round trip time of communications between the Earth and

the Moon, based on the speed of light and lunar perigee, is approximately 2.5 s. Even this amount

of latency makes direct remote control a psychologically tiring task for any expert operator,

which can greatly hamper the productivity of even the most capable machines [60].

The Lunokhod rovers were commanded directly via remote tele-operation from Earth. De-

spite the taxing effects of latency, the rovers regularly drove at speeds of 1 km/hr [38]. Of course,

the remote operators did not deal with any excavation tasks as the Lunokhods were not equipped

for them.

This work investigates aspects that arise when tele-operating bucket-wheel excavators. One

of the guiding principles is that continuous excavator configurations should lead to simpler con-

trol than discrete wide bucket excavators. A generalized investigation of autonomy for earth-

moving equipment, beyond reviewing the literature, is outside the scope of this work.

2.8 Conclusions Based on Related Work

Review of literature related to lightweight robotic excavation leads to the following conclusions:

There is no consensus on appropriate excavation force modeling for lunar excavation. How-

ever, it is instructive to rise above the fray of contrastingmodels and focus on their commonly

shared features. Any estimate of excavation resistance must take into account soil weight (and

thus friction) and cohesion. Surcharge is also very important, particularly for discrete excava-

tion; the weight, and perhaps cohesion, of the accumulatingsoil comprise this surcharge. These

24

common features provide a theoretical framework for broadly predicting dependence on key

variables such as soil density and cohesion as well as gravity and cut depth.

Excavation resistance varies significantly during a cut as soil accumulates in the bucket, and

classical models can only approximate this effect. They fail to capture excavation soil flows.

Modern Discrete Element Modeling (DEM) shows promise in modeling excavation soil flows.

Past experiments have studied the effects of many excavation parameters, and have shown

that bucket-wheel excavators produce low resistance forces suitable for lightweight operation.

Only preliminary efforts have been made to study excavationforces in reduced gravity. Exper-

iments with excavator prototypes simulating low gravity constitute a novel contribution to the

field of study.

The wide variability in configurations resulting from lunarexcavation trade studies and proto-

type developments highlight the lack of consensus on appropriate configurations for lightweight

excavators. An anecdotal consensus is the fact that bucket-ladder trenchers have won the Regolith

Excavation Challenge and Lunabotics mining competitions each of the 4 times such competitions

were held [49].

25

26

3 Hauling and Payload Ratio

The load-haul-dump cycle is central to lightweight roboticexcavation tasks, as described in Sec-

tion 1.2. This chapter will show that, for a nominally capable excavator, hauling productivity

dominates overall task performance. Payload ratio directly influences hauling productivity, mak-

ing it an important design parameter.

Section 2.4 showed how excavator configuration trade studies utilizing a top-down approach

(i.e. comparing a predefined set of solutions) have producedwidely varying results, limiting their

usefulness.

This work explores configurations for lightweight robotic excavators from the bottom up,

starting with system parameters that figure into analyticalmodels of excavating and driving,

synthesizing them for analysis of task-level performance metrics. This approach distinguishes

design parameters (such as driving speed, payload ratio, ornumber of wheels) of appropriate

excavator configurations instead of picking between configurations themselves.

3.1 Task-level site work modeling

Regolith-moving machines are commonly characterized for elemental actions like digging or

driving [73], but it is also important to measure comprehensive performance combining digging

and driving. A task model is developed here for excavation tasksthat includes digging, trans-

porting, dumping, and shuttling for recharge (See Fig. 3.1).

The REMOTE (Regolith Excavation, MObility & Tooling Environment) task simulator [65]

27

Figure 3.1: Comprehensive task modeling for lunar site work that combines elemental actions ofdigging and driving

, computes metrics including task completion time, production ratio (weight of regolith moved

per hour, normalized by robot weight), and production efficiency (weight of regolith moved per

unit of energy spent, normalized by robot weight), based on parameters describing the task, the

robotic system, and the environment. The novelty of comprehensive task simulation, combined

with sensitivity analysis, is that it identifies system parameters that are important for overall task

success. This determines what matters most for system design and tradeoffs.

Traction and excavation forces are modeled to determine admissible bucket geometries, and

transport and recharge times are estimated based on drivingspeed and power draw. Excavation

is assumed to occur on approximately flat ground (i.e. not digging on a large uphill or downhill

slope).

3.1.1 Traction modeling (wheels)

The underlying traction model is that of Bekker [7] and Wong [76], based on their empirical and

theoretical work. Net traction, also known as drawbar pull (DP), is obtained by calculating wheel

resistance and thrust.

28

Wheel resistance is assumed due to soil compaction. Gravitational resistance is ignored

because of the assumption of excavating on relatively flat ground. Bulldozing resistance is also

ignored; wheel bulldozing can be avoided with careful grouser design, as shown in Appendix B.

Following Bekker, compaction resistance of a single wheel,Ri, is estimated as:

Ri = b

[(

kcb+ kφ

)

zn+1i

n+ 1

]

Soil pressure-sinkage parameter values are based on estimates made for lunar regolith [30]:

kc = 1.4 kN/mn+1, kφ = 820 kN/mn+2, andn = 1. Wheel width is denotedb, and sinkage,

zi, is estimated as:

zi =

[

3Ni

b(3− n)(kc/b+ kφ)√2r

]2/(2n+1)

whereNi is the normal load on a given wheel, andr is wheel radius. Slip sinkage is ignored,

for the sake of simplicity. New work in terramechanics [20] is developing modeling techniques

for slip sinkage which could be incorporated into future modeling work.

Wheel thrust,Hi, is estimated based on equations (and assumptions) presented by Bekker

and Wong:

Hi = rb

θ0∫

0

(c+ ((kc/b+ kφ)(r(cos θ − cos θ0))n) tanφ)

×(1− exp(−r/K[θ0 − θ − (1− j)(sin θ0 − sin θ)])) cos θdθ

wherec andφ are soil cohesion and internal friction angle, respectively, K is a shear defor-

mation constant,j is wheel slip, andθ0 = cos−1(1 − z/r) is the angle from vertical to where

the wheel rim contacts level terrain, as shown in Fig. 3.2.

Within REMOTE, vehicle load is assumed to be evenly distributed between all wheels, so

drawbar pull is calculated as:

29

Figure 3.2: Wheel geometry terms. Wheel width,b, is into the page.

DP = Nw(Hi −Ri)

whereNw is the number of wheels.

3.1.2 Excavation models

There is no consensus excavation resistance force model forlunar excavation, as discussed in

Chapter 2. REMOTE offers a choice of two underlying excavationmodels, Balovnev and Luth-

Wismer. Balovnev’s [4] is a 3-D bucket model developed from theory. It is of the fundamental

form proposed by Reece (discussed in Section 2.1). Luth-Wismer [46, 75] was developed em-

pirically from separate experiments in cohesive clay and cohesionless sand. The Luth-Wismer

model represents an excavating bucket by a single plate, andmay have been tested under Martian

conditions during the Viking missions [53]. The same parameters govern productivity, indepen-

dent of the choice of model, as will be shown in Section 3.1.5.

Horizontal excavation resistances modeled by Luth and Wismer for (cohesionless) sand and

(cohesive) clay are:

FH,sand = γgwl1.5β1.73√d

(

d

l sin β

)0.77

×[

1.05

(

d

w

)1.1

+ 1.26v2

gl+ 3.91

]

30

Figure 3.3: Excavation geometry terms. Bucket/plate width,w, is into the page.

FH,clay = γgwl1.5β1.15√d

(

d

l sin β

)1.21

×[

(

11.5c

γgd

)1.21(2v

3w

)0.121(

0.055

(

d

w

)0.78

+ 0.065

)

+ 0.64v2

gl

]

Bucket width is denotedw, cut depth isd, β is the angle of the bucket’s cutting face (relative

to horizontal), andl is the length of cutting face interacting with the soil, as seen in Fig. 3.3. In

REMOTE, l is defined byd/ sin β to avoid overconstrained geometry. The bucket’s horizontal

cut velocity is denotedv, and gravitational acceleration isg. Soil density is denotedγ, andc is

soil cohesion. Luth-Wismer does not explicitly include soil friction angle or external (soil-tool)

friction.

Balovnev’s model includes typical force terms due to weight/friction, cohesion, and sur-

charge. It also includes additional terms: external friction contributes resistance on the bucket

sidewalls, and cutting edge thickness is also taken into account. The horizontal component of

excavation resistance is given by:

31

FH = wd(1 + cot β tan δ)A1

[

dgγ

2+ c cotφ+ gq + B ∗ (d− l sin β)

(

gγ1− sinφ

1 + sinφ

)]

+ web(1 + tanδ cotαβ)A2

[

ebgγ

2+ c cotφ+ gq + d

(

gγ1− sinφ

1 + sinφ

)]

+ 2sdA3

[

dgγ

2+ c cotφ+ gq + B ∗ (d− ls sin β)

(

gγ1− sinφ

1 + sinφ

)]

+ 4 tan δA4lsd

[

dgγ

2+ c cotφ+ gq +B ∗ (d− ls sin β)

(

gγ1− sinφ

1 + sinφ

)]

Common parameters are denoted the same as on page 31. The soil internal friction angle is

denotedφ, andδ is the external (soil-tool) friction angle. Surcharge is denotedq. Bucket side

thickness iss, side length isls, eb is blunt edge thickness, andαb is blunt edge angle.Ai are

non-dimensional coefficients specific to the model [4], andB is a boolean flag indicating if the

bucket is fully buried below soil level.

Within REMOTE, excavation is assumed to occur over a short distance, so that cut depth and

cutting face length do not change substantially. By this sameassumption, traction parameters

that might in reality vary with time, such as slip, also remain constant for the duration of an

excavation cut. For longer cuts, one could account for soil accumulation by making surcharge

and/or cut depth depenedent on horizontal cut progress (andthus time).

Excavation with a forward-facing bucket is assumed, meaning the excavator can generate and

sustain an excavation force no greater than its net traction, or drawbar pull. Excavation at this

stall condition is subject to:

FH = DP

This equation is solved, by defining all parameters but one (for example, bucket width), to

find an admissable bucket geometry. The bucket is assumed to be of equilateral triangular prism

shape, as seen in Fig. 3.4. Combining this assumption with a bucket filling efficiency,ηb, gives

32

Figure 3.4: Bucket geometry with equilateral triangular prism shape

the volume of soil that can be excavated in a single cut:

V = ηb1

2wl2 sin(π/3)

To account for excavators that have secondary collection/dump beds, an overall payload ca-

pacity can be defined. In that case, several cuts may be required to reach capacity, and REMOTE

accounts for the time required for all of these cuts as well asthe time for transfers from primary

bucket to collection bed.

3.1.3 Operations modeling

Traction and excavation modeling describe the ‘dig’ portion of a task, but as Fig. 3.1 shows,

a general task also includes transporting and dumping regolith. To account for these aspects

of tasks, REMOTE includes operational parameters such as average distance between dig and

dump, driving speed, area and depth of the desired excavation, and operational efficiency (per-

centage of time spent actually performing work, as opposed to waiting for commands or per-

forming computations).

The number of robots performing a task, and the mass of each robot, are further system

design parameters.

33

3.1.4 Power modeling

Energy is expended by both driving and excavating. There is also baseline power that is always

being dissipated in communication, computation, and otheravionics tasks, even when not per-

forming physical work. Over the class of small vehicles studied (100 kg to 300 kg), this baseline

power is assumed to be the same for each vehicle. Only steady state power is considered during

each phase of a task.

Power expended during driving is modeled by:

Pdrive = KPdmgvd

Wherem is vehicle mass,g is gravitational acceleration,vd is driving velocity, andKPd is a

driving power coefficient. TheKPd coefficient captures and sums several sources of power dissi-

pation. Power required to overcome wheel rolling resistance can be estimated as a percentage of

vehicle weight [55]. Internal machine losses (in bearings,for example) are also proportional to

weight (acting as a radial load). Even undulations in the terrain can be captured by multiplying

weight by the sine of a representative terrain angle.KPd can thus be used to account for rolling

resistance, internal losses, and terrain losses.

Excavation power draw is modeled by:

Pexcav = KPexFHvex

WhereFH is excavation resistance force,vex is excavation velocity, andKPex is an excavation

power coefficient that is nominally 1. Driving power is also expended (withvd = vex) during

excavation.

Dumping power is ignored, as dumping comprises a very small portion of the overall task.

Batteries are assumed to be the primary power source for excavation robots. Each vehicle

is assumed to have a constant fraction of mass budget for batteries, meaning larger vehicles are

34

able to store more energy than smaller ones. A battery charging time is included in the model.

This charge time does not include the time required to shuttle to and from the power plant, which

is accounted for separately in the same way that shuttling toand from a digging site is.

Batteries can potentially be charged during operation by additional power sources such as

onboard solar panels. Such an additional power source is modeled as a negative power draw, and

denoted within REMOTE as trickle power.

3.1.5 Parametric sensitivity analysis

As the preceding sections show, modeling excavation tasks involves a large number of parameters

(over 25). A particularly instructive application of REMOTEis in performing sensitivity analyses

that compare the relative impact of variations in these parameters on output metrics. Here it is

not so much the values themselves of the calculated metrics that are paramount, but rather how

sensitive these calculations are to changes in system, concept of operations, and environmental

parameters.

Parameters for sensitivity analysis include system parameters (such as individual robot mass,

payload ratio, wheel radius, etc.) and concept of operations parameters (operational efficiency,

distance to recharge station, etc.) that could be variablesin system/mission design. Sensitivity

analysis also includes regolith parameters (bulk density,cohesion, etc.) whose values are esti-

mated within bounds. Each parameter is varied individuallyfrom its expected baseline value to

maximum and minimum values in turn. The resulting values of the metrics are calculated at each

variation. Although some parameters are not fully independent in reality, isolating each param-

eter’s individual contribution to productivity in this wayis still a very useful guide for focusing

attention within such a broad design and operational space.

Sensitivity of production ratio to relevant parameters foran example berm building task is

presented in Figure 3.5 and Figure 3.6. The task involves shallow digging, to a total depth of

20 cm, over a large area (50 m diameter circle). Excavated material is moved to an arc along the

35

circle and dumped in a berm. Average distance between dig anddump is 25 m.

Figure 3.5 shows REMOTE sensitivity analysis results for theberm building task, with Luth-

Wismer as the underlying excavation resistance model. Production ratio (mass of regolith moved

per hour, normalized by rover mass) is shown on the x-axis, while parameters that can affect it

are shown on the y-axis. Changing driving speed, from its baseline value of 20 cm/s to 50 cm/s,

for example, is predicted to increase production ratio fromjust over 2 to a little under 4. Driving

speed, payload ratio, and operational efficiency are predicted to have the strongest effects on

productivity. Other parameters, such as number of wheels and battery characteristics, have little

effect.

Figure 3.6 shows results for the same sensitivity analysis,but with the Balovnev excavation

model. Results broadly agree between the two models. Drivingspeed, payload ratio, and opera-

tional efficiency govern productivity. The next three most important parameters in the Balovnev

analysis are external friction angle, cohesion, and robot mass. Luth-Wismer also predicst cohe-

sion and robot mass as the next two most important parameters(Luth-Wismer does not include

external friction angle).

These results demonstrate that task-level sensitivity analyses are not particularly dependent

on the choice of underlying excavation model. In both versions of the analysis, productivity

is governed by payload ratio, driving speed, and operational efficiency. These three parameters

figure prominently in the hauling part of excavation tasks, as will be discussed in Section 3.4. Co-

hesion and robot mass are also important parameters, and have been discussed in prior work [63].

In upcoming sections, additional sensitivity analysis is performed on parameters relevant to

a small robotic excavator, Lysander, and simulated resultsare compared to experimental data.

3.2 Experiments with a small robotic excavator

To develop effective lightweight robotic excavators, it isimportant to identify which design pa-

rameters have a significant effect on productivity. As described in the previous section, REMOTE

36

Figure 3.5: Sensitivity analysis using Luth-Wismer excavation model shows productivity governed by driving speed, payload ratio,and operational efficiency

37

Figure 3.6: Sensitivity analysis using Balovnev excavationmodel shows productivity governed by driving speed, payload ratio, andoperational efficiency

38

Figure 3.7: Lysander is a robotic platform for sitework experimentation - shown here carryingexcavated lunar regolith simulant

simulations and analyses show that payload ratio (ratio of regolith payload mass to robot mass)

and driving speed govern the productivity of small robotic excavators; operational efficiency

also significantly affects productivity. The analysis alsoshows that other parameters, including

number of wheels, have little effect on productivity.

A prototype excavator, Lysander, enables experimental validation of sensitivity analyses as

well as of the simulator more broadly. Lysander is a low center-of-gravity scraper, and is shown

in Fig. 3.7 transporting excavated lunar regolith simulant.

3.2.1 Experimental setup

Load-haul-dump experiments measure productivity of the lightweight robotic excavator, Lysander,

in controlled conditions. A sandbox was set up with an excavation area, a dump area, and ob-

stacles, as seen in Fig. 3.8. The entire experimental area was on flat ground, with a board in the

dump area to keep dumped soil separate for measurement. The setup represents a general load-

haul-dump task, and the layout provided an efficient way to incorporate all major elements of the

task, including driving approx. 6 m (roundtrip), and makingturns to avoid obstacles and align

39

Figure 3.8: Experimental setup for a comprehensive excavation task including digging, dumping,and shuttling between the two

for dig and dump. The soil used in the experiments is a mixtureof general-purpose play sand and

a uniformly fine silica sand. This soil is not a lunar simulant, but its granular nature allows it to

be modeled similarly to regolith. Furthermore, the soil hasan internal friction angle between 39

and 42 degrees, and cohesion up to approximately 3 kPa; the values of these strength parameters

lie within the ranges measured for lunar regolith [30]. Internal friction angle and cohesion are

measured using direct shear tests (ASTM D3080). Results of these tests are shown in Fig. 3.9.

The experimental setup fixes some of the parameters studied in the REMOTE simulations.

Some physical robot parameters, such as wheel radius and mass, are fixed. Battery and recharge

parameters are omitted because tethered power enables rapid repetition of experiments. Strength

parameters, i.e. internal friction angle and cohesion, areknown within confidence bounds (as

described above). Soil strength parameters are kept withintight bounds with consistent soil

preparation. Between each test run, the soil conditions werereset using a technique developed

40

0 50 100 1500

50

100

150

Normal Stress (kPa)

She

ar S

tres

s (k

Pa)

Figure 3.9: Direct shear test results for soil used in Lysander experiments: Internal friction angleof 39 to 42 degrees, cohesion of 0 to 3 kPa

at NASA Glenn Research Center. First, the soil is fully loosened by plunging a shovel approx-

imately 30 cm deep and then levering the shovel to fluff the soil to the surface; this is repeated

every 15-20 cm in overlapping rows. Next, the soil is leveledwith a sand rake (first with tines,

then the flat back edge). The soil is then compacted by dropping a 10 kg tamper from a height

of approximately 15 cm; each spot of soil is tamped 3 times. Finally, the soil is lightly leveled

again for a smooth flat finish.

3.2.2 Predicted sensitivity of experimental parameters

Parameters that either varied during experiments, or were known only within bounds, are listed

on the y axis in Fig. 3.10. Aside from parameters already discussed (payload ratio, driving speed,

operational efficiency, number of wheels, and soil strengthparameters: cohesion and friction

angle), cutting speed, slip, and shear deformation (K) could also potentially vary. While digging,

41

0 10 15 27

Number of wheels

Soil friction angle

Slip

Shear deformation

Cutting speed

Soil cohesion

Operational efficiency

Driving speed

Payload ratio

Production ratio (hr−1)

6

42 deg

90 %

2.5 cm

30 cm/s

0

80 %

28 cm/s

50 %

4

39 deg

60 %

1 cm

10 cm/s

3 kPa

65 %

18 cm/s

25 %

0 10 15 27

Number of wheels

Soil friction angle

Slip

Shear deformation

Cutting speed

Soil cohesion

Operational efficiency

Driving speed

Payload ratio

Production ratio (hr−1)

Figure 3.10: Predicted sensitivity of Lysander’s productivity to candidate experimental vari-ables [65]. Payload ratio, driving speed, and operational efficiency govern productivity. Parame-ters that cannot be varied within experiments, such as fixed wheel radius, etc., are excluded.

soil accumulation increased excavation resistance. This higher resistance slowed progress (i.e.

cutting speed) due to increased slip. The ranges of values incutting speed and slip account for

this variation. Shear deformation is a soil-specific parameter, which could not be measured for

these experiments. A range of possible values from 1 cm to 2.5cm is considered, based on values

presented in literature for similar soils [33, 76].

Load-haul-dump task productivity is also dependent on driving distance between dig and

dump. This distance was kept the same for all experiments, at3 m. This is at the low end

of distances that would be required for any long-term task (e.g. mining, trenching). Longer

distances would be expected to further increase the importance of payload ratio and driving

speed, as an even higher percentage of the task would be devoted to driving and transporting

regolith, as opposed to digging or dumping.

42

Figure 3.10 shows REMOTE sensitivity analysis results for parameters relevent to the ex-

perimentation campaign using Lysander. Production ratio (mass of regolith moved per hour,

normalized by rover mass) is shown on the x-axis, while parameters that can affect it are shown

on the y-axis. Changing Lysander’s payload ratio in simulation, from its baseline value of 25% to

50%, for example, is predicted to increase production ratiofrom 15 to 27. As in earlier REMOTE

simulations for general lightweight excavators, payload ratio and driving speed are predicted to

have a strong effect on productivity while other parameters, such as number of wheels, are not.

3.2.3 Experimental results

The experimental campaign tested sensitivity of two high sensitivity parameters (payload ratio

and driving speed) and one low sensitivity parameter (number of wheels - on Lysander, the

two middle wheels can be removed with relative ease). Payload ratio was modified by simply

changing the amount of payload carried by the robot; this wasimplemented in practice by taking

either 1 or 2 cuts of soil to collect a payload ratio of 25% or 50%, respectively. Before taking a

second cut of soil, the soil from the first cut was shifted out of the way to the back of Lysander’s

large bucket by tilting the bucket back. The large surface ofthe bucket and relatively shallow cut

angle,β, kept the collected soil from sliding back to the front of thebucket during the second

cut. Clearing the cutting edge of the bucket in this fashion ensured similar excavation during

both cuts.

As operational efficiency was also predicted to be a relatively high sensitivity parameter, it

was monitored during each test. By maintaing operational efficiency within a range of 65%

and 80%, the expected effects of its variability were kept smaller than the expected effects of

varying payload ratio and driving speed, as Fig. 3.10 shows.Production ratio was measured

as the output for each test. Experimental test sets at each parameter setting were performed in

triplicate. Photos from a sample experiment are shown in Fig. 3.11, and results from all the tests

are summarized in Table 3.1.

43

Figure 3.11: Lysander at start location (top) and excavation area (bottom) during an experiment

44

Table 3.1: Experimental data from 4 sets of tests (each set intriplicate)

Test set Speed(cm/s)

Payloadratio

No. of wheels Operationalefficiency

Productionratio (hr−1)

Baseline

29 25% 6 73% 17.9

28 23% 6 66% 14.3

30 19% 6 72% 12.4

Low speed

18 22% 6 75% 8.7

18 25% 6 77% 10.3

18 16% 6 80% 11.0

High payloadratio

29 51% 6 76% 28.7

28 51% 6 72% 29.3

28 51% 6 72% 26.6

4 wheels

26 26% 4 77% 14.0

24 27% 4 79% 15.2

37 25% 4 74% 13.1

High payload ratio and low speed result in statistically significant differences in production

ratio relative to the baseline test set. Applying t-tests tothe test sets, high payload ratio and

low speed results in p-values of 0.002 and 0.049, respectively. Both these parameters thus affect

productivity with 95% confidence of statistical significance (meaning there is less than 5% prob-

ability of the observed difference in productivity arisingby chance, as opposed to there being a

real difference). Comparison of the 4 wheel tests with the baseline (6 wheels), on the other hand,

results in a p-value of 0.679, meaning no statistically significant difference in productivity was

observed.

3.3 Comparison of simulated and experimental results

Figure 3.12 (top) shows experimental results graphically,with error bars at each setting indicating

the standard error. The top bar extends from the mean production ratio value measured during

baseline tests (which had payload ratio at 25%), on the left,to the mean production ratio value

measured during tests with 50% payload ratio, on the right. The error bar around the right edge

45

represents the error in the tests with 50% payload ratio, while the error bar around the left edge

represents the error in the baseline tests. Similarly, the next bar extends from the mean production

ratio value measured during baseline tests (which had a driving speed of 28 cm/s), this time on

the right, to the mean production ratio value measured during tests with 18 cm/s driving speed,

on the left. The error bar around the baseline edge is the sameas the bar above, because there

is only one set of baseline tests; these tests act as the baseline for each parameter change. For

the final parameter variation, the plot shows that not only isthe mean production ratio achieved

with 4 wheels within the error for production with 6 wheels, but also the mean production ratio

achieved with 6 wheels is within the error for production with 4 wheels. This provides a visual

representation of the statistical results described in theprevious section. For changes in payload

ratio and driving speed the error bars do not overlap, highlighting a stastistically significant

difference between these tests and the baseline. For changes in the number of wheels, the error

bars overlap fully and no statistically significant difference is observed.

The bottom of Fig. 3.12 shows simulated results for the same conditions as those tested

experimentally. This plot is a subsampling of Fig. 3.10, showing only payload ratio, driving

speed, and number of wheels.

The sensitivity to payload ratio, driving speed, and numberof wheels observed experimen-

tally aligns consistently with the simulated results. For each of the 4 test cases, the simulated

production ratio is within the error of the corresponding experimental case.

As described in previous sections, some modeling simplifications were introduced that do

not correspond exactly with all the details of the excavation tasks. Specifically, slip sinkage

is ignored, as is the time dependency of slip, cut depth (d) and cutting face length (l) during

digging. This makes it impossible to model the observed phenomenon of soil accumulation

(which increases effectived andl), and the subsequent increase in slip (which causes increased

sinkage and thus rolling resistance), using the current implementation of REMOTE.

The good correspondence between simulated and experimental results suggests that this mod-

46

0 10 15 27

Number of wheels

Driving speed

Payload ratio

Production ratio (hr−1)

64

28 cm/s18 cm/s

50 %25 %

0 10 15 27

Number of wheels

Driving speed

Payload ratio

Production ratio (hr−1)

0 10 15 27

Number of wheels

Driving speed

Payload ratio

Production ratio (hr−1)

64

28 cm/s18 cm/s

50 %25 %

0 10 15 27

Number of wheels

Driving speed

Payload ratio

Production ratio (hr−1)

Figure 3.12: Top: Measured production ratio sensitivity toexperimental variables. Bottom:Production ratio sensitivity to experimental variables predicted by simulation. Experiments andmodel show good correspondence. In both cases, payload ratio and driving speed have a signifi-cant effect on productivity, while number of wheels does not[65].

47

eling simplification did not diminish REMOTE’s ability to predict excavator productivity for the

load-haul-dump task described in this work. Figure 3.10 shows that the effects of varying slip

are negligible for this specific task.

The effects of cut depth and slip on prodcutivity are somewhat more significant for trench

excavation, as simulations in prior work show [63]. This suggests that neglecting soil accumu-

lation and slip sinkage may not be appropriate for all tasks,particularly ones involving deep

digging. Before applying REMOTE’s modeling framework specifically to a deep excavation

task, additional experiments and possibly additional modeling are recommended.

A significant source of variability in the experimental results was the inability, in practice,

to keep operational efficiency precisely constant. A human tele-operator cannot replicate per-

formance exactly between test runs. Errors were low enough to make clear observations, as

described above. Tighter error bounds, though, could increase the potential statistical power of

experiments. If such tighter bounds were to be required for future investigations, better control

over operational efficiency could be achieved with increased autonomy for the tests.

3.4 Hauling dominates task productivity

Experiments and simulations all show that payload ratio, driving speed, and operational effi-

ciency govern the production ratio for lightweight roboticexcavators. These parameters direcly

comprise the terms for hauling productivity:

Production ratio (hauling only)= ηopP v/d

whereηop is operational efficiency,P is payload ratio,v is driving speed, andd is hauling

distance. Note that hauling distance is not included as a parameter in above sensitivity analyses,

as it is dictated directly by a given task.

The prominence of the three hauling productivity parameters shows that hauling is the im-

portant part of load-haul-dump excavation tasks, in terms of productivity. In fact, hauling takes

up the vast majority of time in any of the tasks investigated,which is why improvements in this

48

area translate into the largest overall gains. An importantunderlying assumption leading to this

result is that the excavators in question can achieve a nominal level of excavation capability.

If an excavator gets stuck while digging, or must regularly correct and adjust its cuts, the time

spent digging would grow relative to time spent hauling. REMOTE does not model such poten-

tial problems, and they were not encountered in the experiments performed. Ensuring that basic

excavation capability is maintained is the subject of the next chapter.

3.5 Conclusions from sensitivy experiments and simulations

Payload ratio, driving speed, and operational efficiency govern productivity of excavation tasks

by small robots. This has been shown using simulation and sensitivity analysis. Experiments us-

ing Lysander validate these sensitivity analysis results quantitatively, by varying driving speed,

payload ratio, and number of wheels and measuring output productivity. The task had a rela-

tively short travel distance (3 m) between dig and dump. Longer distances would be expected

to only further increase the importance of payload ratio anddriving speed, as an even higher

percentage of the task would be devoted to hauling regolith,as opposed to digging or dumping.

The overarching importance of payload ratio and driving speed is also consistent with simulated

berm building tasks.

The prominence of the three hauling productivity parameters shows that hauling is the impor-

tant part of load-haul-dump excavation tasks, in terms of productivity. An important underlying

assumption in this result is that the excavators in questioncan achieve a basic level of excavation

capability. If an excavator gets stuck while digging, or must regularly correct and adjust its cuts,

the time spent digging would grow relative to time spent hauling. Ensuring that basic excavation

capability is maintained is the subject of the next chapter.

Experiments lend credence to simulated results and highlight the reality of some potentially

counter-intuitive findings. It may not be surprising that payload ratio and driving speed should

govern productivity, as making each load-haul-dump cycle faster and carrying more load each

49

time directly speed up the task. The relatively negligible effect of changing the number of wheels

is not necessarily obvious though; one might have thought that added traction could significantly

speed up the digging process and thus overall task productivity. Both experiment and simulation

suggest that optimizing a traction system is not the best place to expend efforts that should rather

be used maximizing speed and payload ratio.

These results suggest that high payload ratio and high driving speed be included as key fea-

tures of any future lightweight robotic excavators.

REMOTE endevours to strike an appropriate balance between complexity and fidelity for

task-level modeling. Some aspects of excavation tasks are ignored, including wheel slip sinkage

and soil accumulation at the bucket cutting edge. The good correspondence between simulated

and experimental results suggests that these modeling simplifications are acceptable for for high

level analysis of load-haul-dump tasks.

50

4 Thrust and resistance in lightweight

excavation

The previous chapter assumed a nominal level of excavation performance; namely, that exca-

vators could dig without stalling or impeding mobility. Forthis assumption to hold, excavation

resistance must be kept below excavation thrust. This chapter will show that resistance exceeding

excavation thrust can quickly lead to high slip and sinkage.

This chapter investigates the effects of light weight (bothin terms of lower mass and re-

duced gravity) on excavation thrust and resistance. It demonstrates how soil cohesion has the

detrimental effect of increasing excavation resistance coefficient.

4.1 Relationship of mass and scale

Excavator mass scales approximately as the cube of linear dimension. This is because mass is

related to a machine’s three-dimensional volume, while length, width, and height are each single-

dimensional. Fitting data for many terrestrial excavatorsof many scales [35] to a power law of

the form:

m = awα

one expects thatα ≈ 3. The fit yields exponents of 2.92 and 2.98 for the sample of terrestrial

loaders and scrapers, respectively (withR2 = 0.99 in both cases). In the formulation,m is

excavator mass,w is bucket width (treated as a characteristic length),α anda are the power law

51

Figure 4.1: Excavator mass scales with the cube of bucket width, shown by the fact that the ratioof these two quantities equals approximately 1.

exponent and coefficient, respectively. This approaches the idealizedα = 3 very closely. This

relationship is also illustrated by directly comparing theratio of excavator mass to the cube of

bucket width in Figure 4.1. Each of the ratio values is normalized by the median value for easier

comparison. All values are within 15% of the median, with no obvious bias.

In this thesis, any changes in excavator mass are assumed to have corresponding changes in

scale according to the cubic relationship described here. This assumption does not hold for all

possible comparisons, particularly between terrestrial and planetary. Mass optimization may lead

to a planetary excavator with the same scale as a terrestrialone but with lower mass. However, the

more pertinent comparison in this work is instead between two or more planetary excavators. In

this case, all excavators being compared are already mass optimized, so the scaling relationship

is assumed to hold between them.

52

4.2 Light weight reduces excavation thrust coefficient

A vehicle’s drawbar pull is the net traction available for doing work, and is dependent upon slip

(or travel reduction). Slip is defined as:

Slip(%)= 100%× 1− vrω

wherev is the vehicle’s forward velocity,ω is the wheel angular speed, andr is the effective

wheel radius. In granular soils, effective radius is an equivalent radius where shear occurs be-

tween moving soil and static soil [21], which may not be well defined a priori. Compliant wheels

also introduce the possibility of time-varying wheel radius, further confounding measurement of

r and thus slip. For these reasons, an approximately equivalent parameter - travel reduction - is

used in the context of experimental wheel results, instead of slip. Travel reduction is defined as:

Travel reduction(%)= 100%× 1− vv0

wherev0 is a baseline vehicle speed on flat ground, with no drawbar load applied. In any

comparisons of travel reduction, the same wheel angular speed is applied throughout.

Drawbar pull at 20% slip (or 20% travel reduction) is a good measure of tractive performance,

as pull begins to plateau around 20% slip for many wheels (or tracks) while negative effects

such as sinkage increase [68]. A non-dimensional quantity,P20/W (Drawbar pull at 20% slip,

normalized by vehicle weight), has been used as a benchmark metric for lunar wheel performance

from the times of Apollo [24] to today [70, 80]. In this thesis, excavation thrust coefficient is

denotedT ; under an assumption of tractive thrust,T = P20/W .

The ratioP20/W for any given wheel is approximately constant with changingload (i.e. W

changing but scale and gravity constant), up to a critical loading [24]. It is assumed that excavator

wheels are designed to ensure an excavator with full regolith payload loads the wheels less than

this critical point, so thatT remains constant throughout a load-haul-dump excavation task.

Figure 4.2 shows the relationship between normalized drawbar pull (DP/W) and travel reduc-

tion for a set of compliant lunar-relevant tires at two different wheel loadings (980 N and 1790 N

per wheel). The value at which the curves cross 20% travel reduction, i.e. the excavation thrust

53

Figure 4.2: It is safest to keep wheel slip at or below 20%. ‘Spring tires’, for example, exhibitvery gradually rising travel reduction with increasing load until crossing above 20%, where travelreduction jumps suddenly [NASA GRC].

coefficientT , is approximately the same in both cases (within 10% of one another). These tires

exhibit strongly nonlinear performance. Travel reductionincreases very gradually with increas-

ing load until it crosses above 20%, at which point it rapidlyincreases to unsafe conditions of

approximately 80% travel reduction. Other wheels experience similar non-linearities at approxi-

mately 20% to 30% slip [24]. To prevent unsafe slip and sinkage, drawbar pull should not exceed

T . The tires themselves are shown in Figure 4.3.

Reductions inT are predicted for both reduced gravity as well as reduced scale (and thus,

correspondingly, reduced mass). Figure 4.4 shows such predictions for a rigid wheel. Drawbar

pull vs. slip is calculated according to Bekker’s equations,using the same procedure and assump-

tions described in Section 3.1.1. The baseline wheel (plotted in black) has a radius of 30 cm and

width of 15 cm, and is assumed to be for a 200 kg rover; the baseline condition is Earth gravity.

The same wheel and rover are used in the reduced gravity case (blue). The reduced mass case

(red) assumes a 33 kg rover, with wheel radius and width scaled to 17 cm and 8 cm, respectively,

according to the relationship presented in Section 4.1. In all cases, the internal friction angle is

54

Figure 4.3: Compliant, lunar-relevant ‘spring tires’ on theScarab robot [NASA GRC]

45 degrees. Results are plotted for cohesionless soil as wellas soil with c = 3.8 kPa (at the high

end of estimates for lunar regolith).

Figure 4.4 shows that reduced gravity and reduced mass & scale are both predicted to de-

creaseT (though the effect of gravity onT is somewhat mitigated in highly cohesive soil). In

other words, mobility performance decreases by more than just the decrease in weight when

either gravity or mass is reduced.

Kobayashi’s experiments with a rigid wheel in reduced-gravity flights also demonstrate that

lower gravity diminishes relative mobility performance [43]. Higher slip was observed in lower

gravity for otherwise identical test conditions.

4.3 Predicted effects of light weight on excavation resistance

coefficient

An excavator’s requirements for drawbar pull are driven by the excavation resistance it expe-

riences while cutting soil. Chapter 2 showed that excavationresistance can be modeled in the

form:

55

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60

70

80

90

100

DP/W

slip

(%

)

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60

70

80

90

100

DP/W

slip

(%

)

Figure 4.4: Reducing gravity or wheel scale decreases the excavation thrust coefficient,T . Pre-dictedT in cohesionless soil (left) and soil with c = 3.8 kPa (right),for a baseline rigid wheel(black), the same wheel in 1/6 gravity (blue), and a 1/6 mass scaled wheel (red). The circles onthe slip-DP/W curves indicateT (on the DP/W axis) for each case.

Fex = Nγγgwd2 +Nccwd

where gravitational acceleration is denotedg, γ is soil density,d is cut depth,w is cut width,

andc is cohesion. TheNi are non-dimensional coefficients pertaining to each of the sources of

force. Soil-tool adhesion and inertial forces are ignored due to their insignificant contributions.

Surcharge is treated separately in Section 4.3.1.

Of interest is howFex andF (excavation resistance coefficient,Fex/W ) vary in light weight

operation. If we first consider cohesionless soil (c = 0), the simple excavation resistance model

above predicts constant excavation resistance coefficient. F simplifies to:

F =Nγγgwd

2

mg

=Nγγwd

2

m

In this caseF is no longer dependent ong, so it remains unchanged by a reduction in gravity.

Section 4.1 showed that mass varies as the cube of scale for excavators; reducing mass to a

fraction of the original (X) is equivalent to shortening linear dimensions to the cube root of that

fraction ( 3√X). Mass reduction thus also results in an unchangedF for cohesionless soil:

56

F =Nγγgwd

2

mg

=Nγγwd

2

m

=Nγγ(

3√Xw0)(

3√Xd0)

2

Xm0

=Nγγ(

3√X)3w0(d0)

2

Xm0

=Nγγw0(d0)

2

m0

= F0

where the subscript 0 denotes original (pre-reduction) parameter values.

On the other hand, in a purely cohesive soil (Nγ = 0) F is sensitive to changes in weight. In

this caseFex is independent ofg:

Fex = Nccwd

In reduced gravity,Fex remains unchanged while weight reduces proportionally. Inother

words, a reduction in gravity to 1/6 results in a six-fold increase inF in purely cohesive soil.

Reducing mass has a slightly more complex effect onF due to the relationship with length

scaling:

F =Nccwd

mg

=Ncc(

3√Xw0)(

3√Xd0)

Xm0g

=Nccw0d03√Xm0g

=F0

3√X

57

Figure 4.5: Reducing gravity to 1/6 or mass to 1/6 does not decrease excavation force to 1/6 ifthe soil is cohesive. Effects of reduced weight onFex andF depend on the proportion of originalexcavation force from cohesion.

Soils with both frictional and cohesive properties exhibita mix of the weight effects described

above, depending on the proportion ofFex due to cohesion. Figure 4.5 shows the effects of

reducing gravity to 1/6 or mass to 1/6, with dependence on cohesion. Effects onFex and F

are both plotted, on the left and right y-axis, respectively, as each of these related metrics is

convenient to discuss in certain contexts. What is apparent from the figure is that reducing

weight (either by reducing gravity, mass, or both) increases F in any soil with cohesion.

Another important observation is that reducing an excavator’s scale magnifies the effects of

cohesion. Because the ‘gravity’ term inFex includes a product of 3 lengths (wd2) while the

‘cohesion’ term just 2 (wd), reductions in scale lower the ‘gravity’ contribution more than they

lower the ‘cohesion’ contribution. A related analysis withsimilar conclusions was put forward

by Zacny et al [81].

This analysis also provides a potential explanation for results observed by Boles et al [13].

When they compared excavation resistance forces measured inEarth gravity to resistance forces

measured during 1/6 gravity parabolic flights (for otherwise identical experiments), they were

58

puzzled that excavation forces reduced to an average of 1/3 the original force, rather than 1/6.

Figure 4.5 suggests that this simply implies that cohesion contributed approximately 20% of the

resistance force in the Earth gravity experiments. As the soil used in these tests was JSC-1 lunar

simulant, with a documented cohesion as high as 14.4 kPa [41], this is not a surprising result.

4.3.1 Effects of light weight operation on surcharge

Agui shows that longitudinal excavation resistance rises approximately linearly with cut distance,

as soil accumulates in a discrete bucket [2]. This agrees with the general modeling assumptions

of Shmulevich [61], as discussed in Sections 2.1.3 and 2.2.1. Experiments conducted as part of

this research also show approximately linearly increase inF with payload accumulation, as will

be shown in Section 4.4.4.

It is pertinent here to consider how the slope of this linear increase inF with increasing

payload is affected by reductions in gravity or mass. This slope is denoteddF /dP . Shmulevich

and Kobayashi both assume surcharge is caused only by the weight of the accumulating soil (see

Section 2.1.3). Plugging Shmulevich’s surcharge model (Equation 2.3) into Reece’s fundamental

earthmoving equation (2.1 and 2.2) results in a surcharge contribution of the form:

Fex,q = Nγgwdx (4.1)

wherex is the cut distance andN is a dimensionless coefficient. Payload also increases

with cut distance according to the density and volume of cut soil (γgwdx), leading to adF /dP

independent ofg or length scaling:

59

dF

dP=

dF /dt

dP /dt

=Wrobot

−1dFex/dt

Wrobot−1γgwdx

=dFex,q/dt

γgwdx

=Nγgwdx

γgwdx

= N

However, this conclusion hinges on the form ofFex,q proposed by Shmulevich, which as-

sumes that surcharge force depends only on the weight of accumulated soil, and not its cohesion.

Meanwhile, there are in fact reasons to believe cohesion plays a part in surcharge force.

Qinsen [57] demonstrates a precedent for considering cohesive surcharge. They model ex-

cavation for a bulldozer blade, accounting for soil accumulation directly. The model considers

not only the weight of accumulating surcharge, but also its cohesion. The model’s other aspects

relating it specifically to a curved bulldozer blade make it more complex than is expedient for

direct analysis here.

Surcharge models such as Shmulevich’s and Kobayashi’s assume all surcharge force is due

to pressure applied (by accumulating soil) from above original ground level. Soil shearing below

ground level, accounted for by the ‘gravity’ (frictional) and cohesive shear, is assumed to be un-

affected by soil accumulation above. In reality, though, the two are not independent. Figure 4.6,

with photos by Shmulevich [61], shows how the shear plane failure angle (which can be mea-

sured from the photos) changes as soil accumulates. Early inthe cut (displacement 5 mm, left),

the failure angle is just under 30 degrees; later (displacement 70 mm, center) it is approximately

25 degrees; finally (displacement 140 mm, right) it is less than 20 degrees. As cut depth is kept

constant, this shallower angle results in a final shear planeover 50% larger than at the start of the

cut. As shearing along the failure plane is both frictional and cohesive, it stands to reason that

60

Figure 4.6: Soil accumulation not only adds pressure from the weight of the soil, but also in-creases the size of the shear failure plane below the surface, as measured in a photo by Shmule-vich [61]

Cohesionless (c = 0) Cohesive (c 6= 0)

Reduced gravity Constant Large increase

Reduced mass / scale Constant Small increase

Table 4.1: Predicted effects of light weight on bothF anddF /dP , depending on soil properties

cohesive forces thus arise at least indirectly with increasing surcharge.

Analyses analagous to those conducted in the previous section for cohesive soils suggest that

cohesive contributions to surcharge would lead to the slopedF /dP increasing with decreasing

gravity and/or mass. Testing this cohesive surcharge hypothesis experimentally is suggested as

future work.

4.4 Excavation scaling experiments

Table 4.1 summarizes the predicted effects of light weight on both F anddF /dP , based on

analyses presented above. The top-right quadrant describes conditions during experiments by

Boles et al [13]. Although they were not explicitly testing the hypothesis presented here, their

results qualitatively agree. Experiments in conditions shown in the bottom-left quadrant are the

subject of this section. Experiments covering the remaining two quadrants are recommended as

future work.

61

Figure 4.7: Bucket-wheel dimensions: wheel diameterD (A), blade widthw (B), and bladetangent extensione (C)

4.4.1 Experimental setup

Experiments with bucket-wheels (BWs) and flat-plates (FPs) ofvarious scales were conducted

in cohesionless soil, GRC-1 [56], studying the effects of scaling on continuous and discrete ex-

cavation, respectively. The bucket-wheel experiments were conducted jointly with Diaz Lanke-

nau [19].

To study the effects of length scaling (and thus the related mass scaling), 4 sizes each of

bucket-wheels and flat-plates were tested. All aspects of the test implements with a length di-

mension were scaled proportionally. For BWs this includes: wheel diameterD (A), blade width

w (B), blade tangent extensione (C), cut depth, and advance speed. Angular speed, number of

blades, and blade thickness were kept constant. A, B, and C areshown in Figure 4.7. For FP

tests, scaled parameters include: plate width, plate length l, and advance speed (blade thickness

again kept constant). Dimensions for bucket-wheels and flat-plates are summarized in Table 4.2.

Note that production rate, which can be approximated byγwdv (whereγ is soil density,w

is cut width,d is cut depth, andv is advance speed), is consistent between bucket-wheels and

flat-plates of the same scale. In fact, the scaling ensures that production ratio (production rate

normalized by a representative excavator mass) is constantbetween all tests.

62

Scale v BW D BW w BW d BW e FPw FPd FPl Wrobot

1.0 0.07 cm/s 27.6 cm 5.7 cm 2.0 cm 4.6 cm 11.4 cm 1.0 cm 5.8 cm 54 N

1.3 0.10 cm/s 36.8 cm 7.4 cm 2.7 cm 6.2 cm 14.8 cm 1.3 cm 7.5 cm 124 N

1.7 0.13 cm/s 48 cm 9.8 cm 3.5 cm 8.2 cm 19.6 cm 1.7 cm 9.8 cm 283 N

2.3 0.17 cm/s 63 cm 13 cm 4.7 cm 10.9 cm 26 cm 2.3 cm 13.2 cm 645 N

Table 4.2: Scaled dimensions of bucket-wheel (BW) and flat-plate (FP) test implements

Figure 4.8: The four scales of bucket-wheel tested

All bucket-wheels share the same dodecagon-shaped hub designed to hold one L-shaped

blade extending out on each of its 12 sides, as shown in Figure4.8. Each blade is cut and bent

from 1.6mm (1/16 in.) thick aluminum. Flat plates are cut from the same thickness aluminum,

and are bent to a cutting angle of 10 degrees below horizontal.

The scaling of advance speed and bucket-wheel diameter, with angular rate kept constant,

results in a tangential bucket-wheel cutting speed 5 times the advance speed during each test.

Cutting speeds were low enough that no dynamic effects need beconsidered. These values never

exceeded 1 cm/s (measured as the sum of advance speed plus tangential speed).

4.4.2 Preliminary investigation of soil preparation

Soil density is an important parameter of lunar regolith [15]. It also influences tool-soil interac-

tion and must be controlled for repeatable experimental results [3]. There is direct interdepen-

dence of density with state of compaction and stress history[31], both of which can be modified

63

during soil preparation. Resistive forces encountered during penetration and cutting of soil are

of similar nature [82]. It is common to use a penetrating device to estimate cutting resistance in

the field; soil parameters can be determined from such experiments if tools are selected appro-

priately [3].

Penetration tests were done on GRC-1 prepared to different densities to determine the nec-

essary level of compaction. GRC-1 that is too loose may have unpredictable behavior due to the

random localization of large voids in the soil. The test consisted of slowly increasing the vertical

load on a 3.8 cm diameter cylinder penetrating the soil surface until a depth of 7.5 cm is reached.

Throughout the movement of the cylinder load vs. sinkage data was collected and analyzed.

GRC-1 is expected to have a soil constant n of approximately 1.2[56], which means that pene-

tration pressure should increase almost linearly with depth. Linear behavior was observed during

experimentation when compaction was done by ten tamps or more with a 20 x 20 cm 6.7 kg steel

plate.

Not only are the pressure-sinkage results for the compacted(with 10 tamps) soil more linear,

they are also more consistent. Linear regression on each test with ten tamps gives anR2 value

of at least 0.987. The average soil stiffness constant is 2778 kPa/m with a standard deviation of

157 kPa/m; for loose soil those same values are 1625 kPa/m and418 kPa/m respectively. For

these slopes an n soil constant of 1 was used. Plots for five penetration tests each in loose soil

(Figure 4.9) and compacted soil (Figure 4.10) are shown. A vertical offset between experiments

is due to preload sinkage and is not the main concern in testing. Obtaining similar slopes between

experimental runs was the main objective.

4.4.3 Soil preparation and force measurement

All tests were done on GRC-1 lunar regolith simulant containedin a 115 x 68 x 27 cm soil bin.

A consistent soil preparation procedure was followed before each test. First, soil was loos-

ened using a gardening spade. The loose soil surface was madeflat by dragging a straight-edged

64

Figure 4.9: Penetration curves for loosened soil showing wide variability. Each line is oneexperimental run.

Figure 4.10: Penetration curves for compacted soil showingconsistent linear response. Each lineis one experimental run.

65

tool across it. To check if the soil surface was horizontal a digital level was placed length-wise

on it. To be accepted as flat horizontal soil the measured angle must be less than 0.5 and the level

flush with the soil surface all through its 61 cm length. The soil was modified as necessary until

it lay in a satisfactory way, by leveling with the straight-edged tool. The entire surface of the soil

was compacted by tamping with a 20 x 20 6.7 kg steel plate with ahandle attached to it. Each

tamp is achieved by dropping the steel plate from a 5-6 cm height; subsequent tamps overlap

each previous one with approximately 30%.

The steel plate is roughly one third of the width of the soil bin so three side-by-side lanes

were tamped, for a total width of 60 cm. By executing the compaction procedure along these

lanes ten times it was guaranteed each part of the soil surface would be compacted by at least ten

tamps.

Each bucket-wheel and flat-plate test implement was tested at least 3 times, measuring the

force and torque generated during excavation. Test implements were advanced for a distance of

25 cm, using an actuated axis on the soil bin. Before starting each test the test implement was

raised above the prepared soil and the load cell was biased. Load cell data collected commenced

once test implements were set to the correct depth.

Bucket-wheels advanced perpendicularly to the axis of rotation at a fixed depth and speed

through the center of the soil bin. Reaction loads were measured using a 6-DOF Force/Torque

load cell to which the BW motor was mounted. The BW was then set torotate and gradually

lowered into the soil until the desired depth had been reached. To measure depth a ruler was

fixed to the arm holding the BW (as seen in Figure 4.11, left) andvertical distance from the BW

axle to a 3 mm thick clear plastic plate resting on the soil wasmeasured. Once the BW was set to

the right depth, the BW set to rotate and advance. As the BWs do nothave side-walls to contain

the soil they excavate a shop vacuum cleaner was used to remove soil from each blade just as it

fully cleared the soil surface.

Flat plates were also advanced through the center of the soilbin (Figure 4.11, right). Reaction

66

Figure 4.11: Experimental setup for measuring excavation resistance forces of bucket-wheels(left) and flat-plates (right)

loads were again measured using a 6-DOF Force/Torque load cell to which the angled plate was

mounted. The plate was lowered in a space where soil was cleared away to the required depth.

Depth was measured similarly to the procedure for BWs. Once theFP was set to the right depth,

it was advanced through the soil.

4.4.4 Experimental results

Theory developed above suggestsF anddF /dP stay constant when excavation implements are

scaled in cohesionless soil. Bucket-wheel and flat plate excavation resistance was measured at

4 separate scales, with these scales defined in Table 4.2. Each BW and FP was tested at least

3 times, measuring the force and torque generated during excavation. Non-dimensionalized test

data enables the comparison ofF anddF /dP at each scale. To non-dimensionalize,Fex test data

was normalized by an assumedWrobot for each scale, as listed in Table 4.2. The absolute values

67

of these weights are somewhat arbitrary, but are estimated to be reasonable for the given lengths;

the most important thing to note is that the weights are scaled according to the cube of length

dimensions, as described in Section 4.1. The time scale is also non-dimensionalized in the test

data to correspond to a payload ratio accumulation (again normalized by the assumedWrobot for

each scale).

Figure 4.12 shows experimental results from bucket-wheel and flat-plate tests at each of the

4 scales. Raw data from multiple runs at the same scale are overlaid with a linear regression of

combined test data. The data shows how bucket-wheel excavation resistance is bounded, while

it rises approximately linearly with accumulating payloadfor flat-plate excavation. Variability

around this linear rise also tends to increase as a flat-platecut proceeds. Figure 4.13 shows the

same linear regressions all plotted on the same non-dimensionalized axes. Qualitatively, it shows

no obvious trend inF or dF /dP with changes in scale for either bucket-wheels or flat-plates.

Excavation resistance force scaling is also analyzed quantitatively by fitting raw (unnormal-

ized) force data to a power law vs. scale:

Fex = aSα

whereS is scale anda andα are the power law coefficient and exponent, respectively. For

constantF anddF /dP , one expectsα ≈ 3, asFex needs to scale cubically to keep pace with

cubically increasing weight.

For bucket-wheels, mean force from each test is used for the fit. Figure 4.14 shows the mean

force data and the power law modeled to fit them. The best fit predictsα = 2.73, with a 95%

confidence interval forα of [2.5, 3.0]. For flat-plates, two seperate fits are calculated for the

excavation resistance force at the start of a cut, denotedF0 and shown in Figure 4.15, and for

the rate of force increase,dF/dt (Figure 4.16). The best fit forF0 is α = 2.36 (95% confidence

[1.9, 2.9]), and fordF/dt it is 3.05 (95% confidence [2.7, 3.4]). The fits for bucket-wheelF and

flat-platedF/dt are close to 3. For flat-plateF0, α is somewhat low and has a wide confidence

interval; this may be due to experimental procedure. As described in Section 4.4.3, soil was

68

0 0.02 0.04 0.060

0.02

0.04

0.06

0.08

0.1

Payload ratio

Fex

/W

0 0.02 0.04 0.060

0.02

0.04

0.06

0.08

0.1

Payload ratio

Fex

/W

0 0.02 0.04 0.060

0.02

0.04

0.06

0.08

0.1

Payload ratio

Fex

/W

0 0.02 0.04 0.060

0.02

0.04

0.06

0.08

0.1

Payload ratio

Fex

/W

Figure 4.12: Discrete flat-plate excavation resistance (blue) increases without bound, while con-tinuous bucket-wheel excavation resistance (red) remainslow and bounded. Plots show excava-tion resistance coefficient,F , vs. payload ratio accumulated,P , in cohesionless soil at 4 differentscales: 1.0 (top-left), 1.3 (top-right), 1.7 (bottom-left), and 2.3 (bottom-right). Raw data and lin-ear regression shown.

69

0 0.02 0.04 0.060

0.02

0.04

0.06

0.08

0.1

Payload ratio

Fex

/W

Figure 4.13: Discrete flat-plate excavation resistance (blue) increases without bound, while con-tinuous bucket-wheel excavation resistance (red) remainslow and bounded. The trends in ex-cavation resistance coefficient,F , vs. payload ratio accumulated,P , are unaffected by scaling(ranging from 1.0 up to 2.3) in cohesionless soil. Linear regressions shown.

70

1 1.2 1.4 1.6 1.8 2 2.20

2

4

6

8

10

12

Length scale

F

Figure 4.14: Scaling of mean bucket-wheel excavation resistance force. Best fit power lawexponent = 2.73 (compared to a predicted value of approximately 3)

cleared away to enable lowering the flat-plate to the required depth. Variability in this clearing

could lead to the plate first engaging soil at slightly different times between tests, and this shift

in data along the time axis introduces error into measurement of the intercept,F0.

4.5 Conclusions regarding thrust and resistance for lightweight

resistance

Excavation is more difficult on planetary surfaces, especially on the Moon, than it is on Earth.

Lightweight operation with small robots and/or in reduced gravity disproportionately reduces

excavation thrust while also increasing excavation resistance disproportionately in cohesive lunar

regolith. For these reasons, excavation in Earth gravity (even with a robot of relevant scale in a

regolith simulant) overpredicts the performance of excavators in reduced gravity.

The ratioP20/W is an appropriate metric to use for excavation thrust coefficient, T , when

assuming thrust is generated through traction. When slip goes above 20%, the mobility of most

wheels can degrade rapidly; maintaining drawbar pull low enough to keep slip below 20% satis-

71

1 1.2 1.4 1.6 1.8 2 2.20

1

2

3

4

5

6

7

8

9

Length scale

F0

Figure 4.15: Scaling of flat-plate excavation resistance force intercept. Best fit power law expo-nent = 2.36

1 1.2 1.4 1.6 1.8 2 2.20

0.002

0.004

0.006

0.008

0.01

0.012

0.014

Length scale

dF/d

t

Figure 4.16: Scaling of the slope of flat-plate excavation resistance force. Best fit power lawexponent = 3.05

72

fies the assumption that an excavator maintains nominal capability during digging. T = P20/W

is approximately constant with changing load, for a given wheel with scale and gravity kept con-

stant. On the other hand,T is predicted to decrease for reduced gravity and for reducedmass &

scale. Kobayashi’s experiments support this prediction for reduced gravity [43].

The excavation thrust coefficient,F , is bounded in continuous excavation, and increases

approximately linearly with payload accumulation in discrete excavation.F anddF /dP for

cutting cohesive soil are predicted to increase for reducedgravity and for reduced mass & scale.

Boles’ experiments support this prediction forF in reduced gravity [13]. In cohesionless soil,F

anddF /dP are predicted to remain constant; this is supported by experimentation herein.

Further study of mobility and excavation in reduced gravityflights is recommended. Addi-

tional scaling experiments studying wheel traction as welland excavation in cohesive soils are

also suggested for future work.

73

74

5 The ‘lightweight threshold’

All excavators have a ‘lightweight threshold’ in the operating space, below which their produc-

tivity is limited by virtue of lacking the weight to produce enough thrust to overcome excavation

resistance. This threshold is crossed at lower weights for continuous excavators than discrete

excavators. The lightweight threshold is described by a non-dimensional quantity that relates

payload ratio, excavation resistance, and excavation thrust.

The lightweight threshold arises from the fact that mobility can quickly degrade if excavation

resistance surpasses excavation thrust, as shown in the previous chapter. An excavator that has

crossed this threshold is operating in the lightweight regime.

5.1 A non-dimensional ‘Lightweight number’

An excavator is operating in the lightweight regime if excavation thrust is less than excavation

resistance at any point during digging; i.e., an excavator that produces thrust through traction is

in the lightweight regime if at any point:

P20 < Fex (5.1)

Both thrust and resistance depend on the amount of payload collected. The ratioP20/W

can be assumed to be constant, as discussed in Section 4.2, and equates to the excavation thrust

coefficient,T , so:

75

P20 = TW

Note thatW is total weight:

W = Wrobot +Wpayload

Inequality (5.1) thus becomes:

T (Wrobot +Wpayload) < Fex

Normalizing both sides by empty robot weight,Wrobot, leads to:

T (1 + P ) < F

Defining a ‘lightweight number’,L, distinguishes the lightweight operating regime when:

L ≡ T (1 + P )

F< 1 (5.2)

The dependence ofF on P has been discussed in Chapters 2 and 4, and can be represented

by a linear approximation. Figure 5.1 shows the straight-line approximations ofF (P ) for both

continuous and discrete excavation. Agui et al. also found that, equivalently,Fex(x) can be

approximated by straight lines for discrete excavation [2]).

Denoting this linear approximation by:

F = F0 + F ′P

with F ′ shorthand fordF /dP . Factoring outF0 and substituting into (5.2) leads to:

76

Figure 5.1: F ′ ≈ 0.9 for discrete excavation, which is substantially higher than both F0,disc

and F0,cont; as a result, continuous excavators achieve higher lightweight numbers,L, and arethus more suitable for lightweight operation. Plot shows excavation resistance coefficient,F ,vs. payload ratio accumulated,P , for continuous (red) and discrete (blue) excavation at equalproduction rate. Raw data and linear regression shown.

L =T (1 + P )

F0(1 +F ′

F0

P )(5.3)

5.1.1 L for continuous and discrete excavation

The accumulation of payload has opposite effects onL for continuous and discrete excavators.

The most challenging operating point for continuous excavators is at the start of a cut, after which

digging gets easier. On the other hand, for discrete excavators digging becomes more difficult as

cutting proceeds.

For continuous excavation,F is bounded so a linear approximation yieldsF ′

cont = 0. Substi-

tuting into (5.3) gives:

Lcont =T (1 + P )

F0,cont

In this case, adding payload (i.e. increasingP ) increasesL. Additional payload pushes

continuous excavators away from the lightweight regime.

77

min(Lcont) =T

F0,cont

(5.4)

For discrete excavation,L decreases with increasingP as long asF ′/F0 > 1. In reality,

F ′

disc is greater thanF0,disc by between 1 and 2 orders of magnitude (again, see Figure 5.1 and

Agui [2]). This means that additional payload pushes excavators towards the lightweight thresh-

old. The theoretical lower bound (asP → ∞) for discreteL approaches:

min(Ldisc) =T

F ′

Even with an assumption ofP = 0.5 (which is more realistic, as discussed in Section 1.4.2):

min(Ldisc) <3T

F ′

(5.5)

Finally, another observation that can be drawn from Figure 5.1 is thatF ′

disc is orders of mag-

nitude greater thanF0,cont, at equivalent production ratios. Meanwhile, a factor of just 3 en-

sures a higher lightweight number,L, for the continuous configuration (for the practical case of

P = 0.5). This higher margin onL enables continuous excavator weight to be reduced further

than for discrete excavators, before crossing the lightweight threshold.

The lower lightweight threshold for continuous excavatorshinges onF ′

disc being larger than

F0,cont. In the experiments discussed in Section 4.4, as well as in those discussed below in

Section 5.2,F ′

disc is orders of magnitude larger thanF0,cont. Although these two distinct examples

do not prove the result generally, they strongly suggest that it likely holds in all but the most

degenerate of cases.

78

5.2 Gravity offloaded excavation experiments

Novel experimentats are described here that for the first time subject excavators to gravity of-

fload (a cable pulls up on the robot with 5/6 its weight, to simulate lunar gravity) while they

dig. Although not fully representative of excavation on planetary surfaces (where the regolith is

also subject to reduced gravity), these experiments are better tests of planetary excavation per-

formance than testing in Earth gravity. The experiments demonstrate the disproportionate effects

of reduced gravity on discrete excavation, compared to continuous excavation, predicted in the

preceding section.

Testing in Earth gravity is an inadequate evaluation of planetary excavators, as it overpredicts

excavation performance relative to reduced gravity. Operation in reduced gravity reduces exca-

vation thrust coefficient while also increasing excavationresistance coefficient in cohesive lunar

regolith. The most representative test environment is a reduced gravity flight, where excavator

and regolith are both subject to reducedg [13, 43]. Future research on lightweight excavation

would benefit from testing in reduced gravity flights. Opportunities for such tests are infrequent,

though, and their scale (both spatially and temporally) is severely constrained by the logistics of

the flights.

Another class of tests reduces the weight of the robot, but not the regolith. NASA JPL runs

mobility tests for the Curiosity rover using a full geometricscale3/8th mass ‘SCARECROW’

rover [71]. SCARECROW is comprised of the chassis and mobility subsystems and preserves

center of gravity location. SCARECROW’s3/8th mass loads the wheels with an equivalent

weight to the full mass Curiosity rover in Mars gravity. For equivalent testing for lunar condi-

tions, a full geometric scale1/6th mass rover would be required; this is very little mass even for

only the suspension and mobility subsystems. Another way toachieve equivalent results is to

use a full mass robot, but to offload gravity (see Section 2.2.2); this is the approach used in this

work.

Testing with reduced robot weight in Earth gravity may not exhibit the same mobility per-

79

formance as planetary driving, where the regolith is also subject to reduced gravity [79]. It

may in fact overpredict traction for scenarios governed by the ratioP20/W , such as pulling and

slope climbing. Terramechanics models and experiments both suggest thatP20/W is approx-

imately constant with changing load (i.e. changingW but keep scale and gravity constant, as

with SCARECROW or gravity offload). Meahwhile, they suggest that changingW by reducing

gravity reducesP20/W , as discussed in Section 4.2.

On the other hand, reducing robot weight but not regolith weight makes excavation more dif-

ficult than is to be expected in reduced gravity. Longitudinal soil-tool interactions are not directly

affected by reduced robot weight, soFex remains constant. Reducing weight to 1/6 thus directly

inceasesFex/W sixfold. For planetary excavation, this corresponds to theworst possible case

of purely cohesive regolith. As neither lunar nor Martian regolith is purely cohesive, excavation

resistance on these planetary surfaces in not expected to scale so poorly.

Excavating with gravity offload thus underestimates the detrimental effects of gravity on

traction, but overestimates the detrimental effects on excavation resistance. Though not ideal,

this is a more balanced test than excavating in Earth gravity, which underestimates detrimental

effects on both tractionand resistance.

5.2.1 Experimental setup

To explore the differences in lightweight thresholds for continuous and discrete excavation, grav-

ity offloaded excavation experiments were conducted at NASAGlenn Research Center’s (GRC)

Simulated Lunar OPErations (SLOPE) lab. The facility contains a large soil bin with GRC-

1 [56] lunar simulant. Continuous bucket-wheel and discretebucket excavation was performed

using the Scarab robot (for a detailed description of the robot, see [5, 70]). With Scarab’s shell

removed, excavation tools were mounted to the robot’s structural chassis.

For continuous excavation, a bucket-wheel was mounted withits axis of rotation aligned with

Scarab’s driving direction. The bucket wheel is 80 cm diameter with 12 buckets, and each bucket

80

Figure 5.2: Gravity offload testing with bucket-wheel (left) and front-loader bucket (right) on theScarab robot. A cable pulls up on the robot, tensioned by weights acting through a 2:1 lever arm.The weights and lever assembly hang from a hoist that is pulled along a passive rail by a separatewinch-driven cable.

has a width of 15 cm The bucket used for discrete excavation is66 cm wide, and was mounted

behind Scarab’s front wheels at a cutting angle,β, of 15 degrees from horizontal (see Fig. 3.3 for

a definition ofβ).

This research developed an experimental apparatus for achieving gravity offload in the SLOPE

lab. The main aspects of the apparatus are shown in Figure 5.2. A cable pulls up on the robot,

tensioned by weights acting through a 2:1 lever arm. The weights and lever assembly hang from

a hoist that is pulled along a passive rail by a separate winch-driven cable. All tests are conducted

in a straight line below the hoist rail. The winch speed is controlled so that the hoist is pulled

along at the same speed as the robot is driving, keeping the cable vertical. For tests where exca-

vator speed remains constant, winch speed is set open loop. For tests where the excavator enters

into high slip, winch speed has to be manually reduced to match the robot’s decreasing speed.

Scarab has a mass of 312 kg (weight of 3060 N in Earth gravity) in the configuration used for

these experiments. The connection point for the gravity offload cable was adjusted to preserve the

robot’s weight distribution (54% on the rear wheels). This was confirmed by weighing Scarab on

4 scales (one under each wheel) before and after being connected to the gravity offload apparatus.

81

The offloading cable was equipped with a 2-axis inclinometerand a single-axis load cell to

measure cable angle and tension, respectively.

Between each test run, soil conditions were reset using a technique developed at NASA

GRC. First, the GRC-1 simulant is fully loosened by plunging a shovel approximately 30 cm

deep and then levering the shovel to fluff the regolith to the surface; this is repeated every 15-

20 cm in overlapping rows. Next, the regolith is leveled witha sand rake (first with tines, then

the flat back edge). The regolith is then compacted by dropping a 10 kg tamper from a height of

approximately 15 cm; each spot of soil is tamped 3 times. Finally, the regolith is lightly leveled

again for a smooth flat finish. A cone penetrometer was used to verify that the soil preparation

consistently achieved bulk density between1700 kg/m3 and1740 kg/m3.

Continuous and discrete excavation experiments were conducted at equivalent nominal pro-

duction rates of approximatly 0.5 kg/s, and at equal speeds of 2.7 cm/s. To account for the

differing geometry of the excavation tools, the rectangular discrete bucket cut at a depth of 2 cm,

and the bucket-wheel cut at a depth of 5 cm. Depth was set usingScarab’s active suspension,

which raises and lowers the central chassis. Regolith pickedup by the bucket-wheel was col-

lected into 5-gallon buckets, as shown in Figure 5.3, and weighed. The discrete bucket collected

regolith directly, and after a test that regolith was transfered into 5-gallon buckets and weighed.

The lightweight threshold is characterized by a degradation of mobility. To capture mobility

information, the excavator’s position was tracked at a datarate of 1 Hz using a laser total station.

5.2.2 Predicted lightweight numbers

Estimates of lightweight numbers,L, for the various test conditions predict that Scarab will

not enter the lightweight regime for either mode of excavation at1 g, but that it will cross the

lightweight threshold when performing discrete excavation under gravity offload.

A maximum payload ratio ofP = 0.5 is assumed for the excavation configurations of in-

terest. In this case, Equation 5.5 is applicable for discrete excavation, and Equation 5.4 applies

82

Figure 5.3: Regolith collection during an offloaded bucket-wheel test

to continuous excavation (independent of the choice ofP ). Excavation thrust,T is the same for

both modes of excavation, as the excavator uses the same ‘spring tires’ for all the experiments.

For these tires,T ≈ 0.25, as seen in Figure 4.2. The value ofF ′

disc, between 0.2 and 0.3, is

estimated from experiments with a similar discrete bucket [2]. Force measurements from pre-

liminary tests with the bucket-wheel suggest aF0,cont between 0.002 and 0.004. These values

lead to estimates ofL between 60 and 130 for continuous excavation, and between 2 and 4 for

discrete excavation, in1 g.

Gravity offload reduces drawbar pull proportionally to the reduction in weight, without chang-

ing excavation resistance. This effectively reducesL in step with the weight reduction, leading

to L values between 10 and 20 for continuous excavation, and between 0.3 and 0.7 for discrete

excavation when operating with the excavator weight offloaded to 1/6. AnL below 1 for the dis-

crete excavation case represents crossing the lightweightthreshold and thus an inability to safely

collect a payload ratio of 0.5. Table 5.1 summarizes these predictions.

83

1g Offloaded to1/6 g

Continuous excavation60-130 10-20

Discrete excavation 2-4 0.3-0.7

Table 5.1: Predicted values forL for the relevant experimental conditions. The excavator ispredicted to cross the lightweight threshold (L < 1) when performing discrete excavation undergravity offload.

Excavation type ‘Gravity’ Averagev σv

Driving only 1g 2.6 cm/s 0.2 cm/s

Continuous 1g 2.6 cm/s 0.3 cm/s

Discrete 1g 2.6 cm/s 0.4 cm/s

Driving only 1/6g 2.7 cm/s 0.3 cm/s

Continuous 1/6g 2.7 cm/s 0.3 cm/s

Discrete 1/6g no S/S n/a

Table 5.2: Discrete excavation offloaded to1/6 g is the only test condition that does not maintainconstant steady state (S/S) velocity throughout. Note thatσv represents the mean of the 3 tests’σ values, not theσ of the 3 tests’ mean velocities (which showed negligible variation betweentests of any single set)

5.2.3 Experimental results

Experiments show that in1 g neither continuous nor discrete excavation crosses the lightweight

threshold. On the other hand, in gravity offloaded1/6 g, discrete excavation crosses the lightweight

threshold, while continuous excavation still does not.

Three or four runs were conducted at each of the test conditions, including baseline runs of

driving without digging. Total station data were analyzed to calculate excavator speed during

each test, as shown in Figure 5.4. The excavator maintains constant forward progress in all cases

except discrete excavation with gravity offload. Average speed (as well as standard deviation)

for the various test cases, is summarized in Table 5.2.

Tests in1 g exhibit a slightly slower speed, because the higher weight compresses the com-

pliant ‘spring tires’ and reduces their radius. Excavationand gravity offload both introduce a

small amount of additional variability in speed compared todriving without digging in1 g.

Continuous and discrete excavation in1 g, as well as continuous excavation in gravity of-

84

0 20 40 60 800

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Time (s)

Spe

ed (

m/s

)

0 20 40 60 800

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Time (s)

Spe

ed (

m/s

)

0 20 40 60 800

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Time (s)

Spe

ed (

m/s

)

0 20 40 60 800

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Time(s)

Spe

ed(m

/s)

Figure 5.4: Excavator forward driving speed during continuous excavation in1 g (top left),discrete excavation in1 g (top right), continuous excavation in gravity offloaded1/6 g (bottomleft), and discrete excavation in gravity offloaded1/6 g (bottom right; time axes aligned at stallpoint). The excavator maintains constant forward progressin all cases except discrete excavationwith gravity offload.

85

Figure 5.5: Discrete bucket at end of excavation tests without gravity offload (left; full withapprox. 45 kg of GRC-1) and with gravity offload (right; only 15-20 kg of GRC-1 collected)

floaded1/6 g, all collected approximately 45 kg during each 2.5 m test run. Discrete excavation

in gravity offloaded1/6 g collected only 15-20 kg, in contrast. Figure 5.5 shows the state of fill

of the discrete bucket after1 g and1/6 g experiments.

Gravity offload was controlled with sufficient precision to avoid pulling the excavator for-

ward or backward. Figure 5.6 shows longitudinal cable angleand cable tension for a continuous

excavation test. Cable angle was unbiased about vertical, with a mean value of just 0.1 degrees.

Transient motions of the cable did not exceed 0.8 degrees from vertical for more than a fraction

of a second; with a cable tension of 2600 N, this corresponds to brief transients of 35 N, or 7%

of offloaded excavator weight. Cable tension varies just±1% which, amplified by the offloading

ratio, corresponds to 5% variation in the offloaded excavator weight. Figure 5.7 shows longitu-

dinal cable angle and cable tension for a discrete excavation test. Variability in angle and tension

were again small.

5.3 Conclusions regarding the lightweight threshold

All excavators have a ‘lightweight threshold’ in the operating space, below which their pro-

ductivity is limited. This threshold is crossed at lower weights for continuous excavators than

discrete excavators. The lightweight threshold is described by a non-dimensional quantity, the

86

0 20 40 60 80 100−1.5

−1

−0.5

0

0.5

1

1.5

Time (s)

Cab

le a

ngle

(de

gree

s)

0 20 40 60 80 1002600

2620

2640

2660

2680

2700

Time (s)

Cab

le te

nsio

n (N

)

Figure 5.6: Longitudinal angle (left) and tension (right) of the gravity offloading cable during acontinuous excavation experiment, showing minimal variation.

0 20 40 60 80 100−1.5

−1

−0.5

0

0.5

1

1.5

Time (s)

Cab

le a

ngle

(de

gree

s)

0 20 40 60 80 1002440

2460

2480

2500

2520

2540

2560

2580

Time (s)

Cab

le te

nsio

n (N

)

Figure 5.7: Longitudinal angle (left) and tension (right) of the gravity offloading cable during adiscrete excavation experiment, showing minimal variation.

87

‘lightweight number’L, that relates payload ratio, excavation resistance, and excavation thrust.

For continuous excavation,L depends on the initial excavation resistance coefficient,F0,cont.

For discrete excavation it depends on the rate of increasingresistance with respect to increasing

payload,F ′

disc. The lower lightweight threshold for continuous excavators hinges onF ′

disc being

larger thanF0,cont; two distinct experiments show thatF ′

disc is orders of magnitude larger than

F0,cont. Although this does not prove the result generally, it strongly suggests that it likely holds

in all but the most degenerate of cases.

An excavator’s lightweight threshold can be estimated using laboratory experiments. Draw-

bar pull tests with a full-scale wheel and soil bin excavation tests with a full-scale tool predict

T and F , respectively, for terrestrial gravity. The dependence ofL on reduced gravity is not

fully characterized, but assuming direct scaling ofL with g provides a balanced estimate. Future

research involving reduced gravity flights to directly investigate the effects ofg on drawbar pull

coefficient and excavation resistance would provide more refined estimates forL(g).

Testing in Earth gravity is an inadequate evaluation of planetary excavators, as it underesti-

mates detrimental effects of reduced gravity on both traction and excavation resistance. Gravity

offloaded testing effectively makes the assumption of direct scaling ofL with g in an experi-

mental context. This research developed a novel experimental apparatus for achieving gravity

offload, and was the first to subject excavators to offload while they dig.

88

6 Lightweight excavator development

This research developed a novel robotic bucket-wheel excavator prototype, based upon the prin-

ciples identified in prior chapters of this thesis. It is distinguished by high payload ratio and

high driving speed, features shown to govern lightweight excavator productivity in Chapter 3.

It is a continuous excavator, the preferable tooling configuration according to the theory and

experiments presented in Chapter 5. Its wheels were developed for high drawbar pull, another

important characteristic discussed in Chapters 4 and 5. The excavator prototype is shown in

Figure 6.1.

Lightweight excavator productivity is governed by productivity during the haul stage of the

load-haul-dump cycle, as discussed in Section 3.4. This depends directly on payload ratio and

driving speed, treated here, but also on operational efficiency (percentage of time spent actu-

ally performing work, as opposed to waiting for commands or performing computations). High

operational efficiency relies upon high performance autonomy or teleoperation algorithms, rec-

ommended as a direction for related future work. Combining high payload ratio and high speed

driving is an important improvment upon the state of the art.Past lightweight excavator proto-

types were too slow or carried too little regolith payload, as summarized in Table 6.1.

6.1 Excavation tooling configuration

Bucket-wheel excavators have been shown to produce low resistance forces suitable for lightweight

operation [36]. Bucket-wheels, and any other continuous excavators such as bucket-ladders, also

89

Robot MassPayloadRatio

DrivingSpeed

Image Ref.

Bucket wheelexcavator

< 100 kg n/a 0 [52]

Bucket drumexcavator

< 100 kg Mod. < 5 cm/s [17]

Bucket ladderexcavators

< 100 kg High Various [NASA]

NASA Cratosscraper

< 100 kg High 5 cm/s [16]

Juno load-haul-dump

> 300 kg Low > 1 m/s [67]

NASA Chariotw/ LANCEblade

> 1000 kg Low > 1 m/s [39]

NASA Cen-taur II w/bucket

> 500 kg Low > 1 m/s [NASA]

Table 6.1: Lunar and planetary excavation robot prototypes

90

Figure 6.1: Lightweight robotic excavator prototype featuring central bucket-wheel, high pay-load dump-bed, high traction wheels, and high-speed wheel actuation

do not suffer from increasing resistance from soil accumulation described in the previous chap-

ters. Prototype bucket-wheel excavators have had difficulty transferring regolith from bucket-

wheel to collection bin in the past, and as a result bucket-ladders have gained favor [37].

Bucket-ladders use chains to move buckets along easily shapeable paths, making transfer to a

collection bin easy. Winners of the NASA Regolith ExcavationChallenge and subsequent Lun-

abotics mining competitions (which require digging in lunar regolith simulant for 30 minutes)

all employed bucket-ladders driven by exposed chains [49].However, bucket-ladder chains are

exposed directly to the soil surface and these would degradevery quickly in harsh lunar regolith

and vacuum. Exposed bucket-ladder chains are thus not relevant to operation in lunar conditions.

A novel excavator configuration, with bucket-wheel mountedcentrally and transverse to driv-

ing direction, achieves direct regolith transfer into a dump-bed. The bucket-wheel is a single

moving part, with no need for chains or conveyors. This reduces complexity and risk from re-

golith and dust. Once regolith has been carried to the top of the wheel in an individual bucket, it

91

Figure 6.2: Robotic excavator configuration with transversebucket-wheel and large dump-bed(left). Close-up of unique direct regolith transfer into dump-bed enabled by transverse orientation(right)

drops down out the back of the bucket and into a dump-bed. Thisconfiguration offers a simple

solution to the transfer problem for bucket-wheels identified in past literature. The dump-bed

transfer concept is shown in Figure 6.2, and implemented in practice in Figure 6.3.

The large dump-bed achieves a high payload ratio, enabling productive execution of excava-

tion tasks.

6.1.1 Testing transverse bucket-wheels

The novel bucket-wheel excavator configuration simplifies regolith transfer into a dump-bed, but

it is important to establish if that does not come at a cost, such as higher excavation resistance. A

transverse bucket-wheel configuration must not lose the lowresistance that makes bucket-wheels

desirable in the first place.

Excavation forces and production rates of bucket-wheels digging in lunar simulant are mea-

sured experimentally. Experiments compare resistance forces encountered by bucket wheels

92

Figure 6.3: Sand in dump-bed, having been transfered directly by gravity from bucket-wheel

advancing through GRC-1 lunar simulant in a transverse configuration (axis of rotation along

direction of travel) and in a forward configuration (axis of rotation lateral to direction of travel).

An experimental apparatus pushes a bucket-wheel along a direction of travel while rotating

it; the bucket-wheel orientation can be set either transverse or forward. A load cell measures the

horizontal force opposing travel.

Excavation resistance for a transverse bucket-wheel is shown to depend on rotation speed (as

a ratio to forward advance rate). Once a sufficiently high rotation speed is achieved, there is little

difference in excavation resistance between transverse and forward bucket-wheel configurations.

To further reduce excavation resistance for the excavator prototype’s transverse bucket-wheel,

cutting faces are angled outward (see Figure 6.6). This prevents bulldozing by the cutting face.

During gravity offloaded bucket-wheel excavation tests, excavation resistance forces were

low enough that mobility was unaffected. Force data were collected using a 6-axis force/torque

sensor mounted between the bucket-wheel actuator and the robot chassis. Lateral and longitudi-

nal forces acting on the bucket-wheel were on the order of 10-20 N, and 5-10 N, respectively (as

shown in Figure 6.7). Lateral forces of this magnitude are less than 5% of the vehicle’s offloaded

weight, and did not induce discernable slew or yaw in the robot’s trajectory.

93

Figure 6.4: Experimental apparatus for bucket-wheel orientation testing

Figure 6.5: Transverse bucket-wheels do not exhibit significantly higher excavation resistanceonce bucket rotation speed is sufficient

94

Figure 6.6: Side view of bucket-wheel, noting the cutting face angle. The angle is 14 degrees onboth faces of the transverse bucket-wheel to enable excavation during both forward and backwarddriving.

0 20 40 60 80 100 120

0

5

10

15

20

25

30

Time (s)

Late

ral f

orce

(N

)

0 20 40 60 80 100 120

0

5

10

15

20

25

30

Time (s)

Long

itudi

nal f

orce

(N

)

Figure 6.7: Lateral (lower left) and longitudinal (lower right) excavation resistance forces arelow enough that excavator mobility is unaffected, even withgravity offload. Lateral forces, dueto the transverse bucket-wheel orientation, do not cause the excavator to slew or yaw. Lateral(blue) and longitudinal (red) directions relative to bucket-wheel are indicated in the upper image.

95

6.2 Excavator mobility system

High driving speed, while shuttling between dig and dump sites, governs lightweight excavator

productivity, as shown in Chapter 3. The maximum driving speed of the excavator developed in

this work is 0.41 m/s, as measured during field testing. For comparison, the Lunakhod rovers

(the fastest planetary mobile robots deployed to date) typically operated at 0.26 m/s. They had a

top speed approaching 0.56 m/s, although this speed was usedquite infrequently [38].

The excavator’s wheels are made of lightweight composite materials, and are rigid. To

achieve high drawbar pull with rigid wheels, grousers are employed. Grouser spacing and height

are selected to mitigate resistive forward soil flow, in compliance with the grouser spacing equa-

tion derived in Appendix B. Nominal operating conditions of 20% slip and 10% sinkage (mea-

sured as a percentage of wheel radius) are assumed. The selection of a 60 cm diameter wheel

with 36 grousers fixes the appropriate grouser height at 2 cm.The excavator’s wheels can be

seen prominently in Figure 6.10.

Soil flow imaging tests confirm that the selected grouser geometry appropriately mitigates

resistive forward flow. Figure 6.8 shows experimental data of soil flowing beneath the wheel.

Forward flow induced by a wheel with insufficient grousers is shown in Figure 6.9 for compari-

son.

6.3 Conclusions regarding lightweight robotic excavator de-

velopment

Continuous excavator configurations, such as bucket-wheelsand bucket-ladders, are preferable

to discrete wide bucket excavators, such as scrapers and front-loaders, for lightweight lunar

and planetary excavation. Bucket-wheel excavators producelow resistance forces that enable

lightweight operation, but in the past have had difficulty transferring regolith from bucket-wheel

to collection bin or dump-bed (necessitating impractical conveyor systems). As a result, bucket-

96

Figure 6.8: Grouser spacing tests for excavator wheel. Processed imagery of soil motion inducedby driving at 20% slip, shown by pairs of processed images at 6instances. The top image of eachpair shows soil velocity magnitude (colors range from blue for stationary soil to red for maximumobserved speed); the bottom image shows soil velocity direction (colors correspond to directionsindicated by the color wheel in the bottom right). Red dots areadded to aid in following theprogress of three individual grousers (each dot indicates the base of a grouser). Periodic effectsof grouser interactions are observed, with little to no resistive forward flow (which would appearas large yellow areas in direction plots) seen. Compare to Figure 6.9

Figure 6.9: Processed imagery of soil motion with a wheel with insufficient grousers. The (lower)direction plot shows a large region of resistive forward flow, indicated by yellow and orange.

97

Figure 6.10: Excavator wheels with proper grouser spacing ensure high traction performance

ladders have gained favor, but their exposed chains would fare poorly in harsh lunar regolith and

vacuum.

A centrally mounted and transverse bucket-wheel configuration, developed in this work,

achieves simplified transfer of regolith into a dump-bed with no significant increase in exca-

vation resistance. The dump-bed is designed to collect substantial payload ratio. The excavator

also has a high driving speed, as payload ratio and driving speed govern lightweight excava-

tor productivity. The design and testing of the excavator’srigid wheels demonstrate successful

application of a grouser spacing equation derived as part ofthis work.

98

7 Conclusions and future work

7.1 Conclusions

This thesis shows that there is a quantifiable, non-dimensional threshold that distinguishes lightweight

from heavy excavation. This threshold is crossed at lower weights for continuous excavators than

discrete excavators. The lightweight threshold relates payload ratio (weight of regolith payload

collected to empty robot weight), excavation resistance (force imparted on an excavator by cut-

ting and collecting soil), and excavation thrust (force supplied by an excavator that is available

for cutting soil).

Payload ratio governs lightweight excavator productivity

Payload ratio, driving speed, and operational efficiency govern productivity of excavation

tasks by small robots. This has been shown using simulation and sensitivity analysis. Experi-

ments using Lysander validate these sensitivity analysis results quantitatively, by varying driving

speed, payload ratio, and number of wheels and measuring output productivity. The task had

a relatively short travel distance (3 m) between dig and dump. Longer distances would be ex-

pected to only further increase the importance of payload ratio and driving speed, as an even

higher percentage of the task would be devoted to hauling regolith, as opposed to digging or

dumping.

Experiments lend credence to simulated results and highlight the reality of some potentially

counter-intuitive findings. It may not be surprising that payload ratio and driving speed should

govern productivity, as making each load-haul-dump cycle faster and carrying more load each

99

time directly speed up the task. The relatively negligible effect of changing the number of wheels

is not necessarily obvious though; one might have thought that added traction could significantly

speed up the digging process and thus overall task productivity. Both experiment and simulation

suggest that optimizing a traction system is not the best place to expend resources that should

rather be used maximizing speed and payload ratio.

The prominence of the three hauling productivity parameters shows that hauling is the impor-

tant part of load-haul-dump excavation tasks, in terms of productivity. An important underlying

assumption in this result is that the excavators in questioncan achieve a basic level of excavation

capability. If an excavator gets stuck while digging, or must regularly correct and adjust its cuts,

the time spent digging would grow relative to time spent hauling.

Continuous excavation resistance remains constant as payload accumu-

lates, while discrete excavation resistance increases without bound

The excavation thrust coefficient,F , is bounded in continuous excavation, and increases

approximately linearly with payload accumulation in discrete excavation.F anddF /dP for

cutting cohesive soil are predicted to increase for reducedgravity and for reduced mass & scale.

Boles’ experiments support this prediction forF in reduced gravity [13]. In cohesionless soil,F

anddF /dP are predicted to remain constant; this is supported by experimentation herein.

The ratioP20/W is an appropriate metric to use for excavation thrust coefficient, T , when

assuming thrust is generated through traction. When slip goes above 20%, the mobility of most

wheels can degrade rapidly; maintaining drawbar pull low enough to keep slip below 20% satis-

fies the assumption that an excavator maintains nominal capability during digging. T = P20/W

is approximately constant with changing load, for a given wheel with scale and gravity kept con-

stant. On the other hand,T is predicted to decrease for reduced gravity and for reducedmass &

scale. Kobayashi’s experiments support this prediction for reduced gravity [43].

Excavation is thus more difficult on planetary surfaces, especially on the Moon, than it is

on Earth. Lightweight operation with small robots and/or inreduced gravity disproportionately

100

reduces excavation thrust while also increasing excavation resistance disproportionately in cohe-

sive lunar regolith. For these reasons, excavation in Earthgravity (even with a robot of relevant

scale in a regolith simulant) overpredicts the performanceof excavators in reduced gravity.

Continuous excavators can operate productively at lower weights than

discrete excavators

All excavators have a ‘lightweight threshold’ in the operating space, below which their pro-

ductivity is limited. This threshold is crossed at lower weights for continuous excavators than

discrete excavators. The lightweight threshold is described by a non-dimensional quantity, the

‘lightweight number’L, that relates payload ratio, excavation resistance, and excavation thrust.

For continuous excavation,L depends on the initial excavation resistance coefficient,F0,cont.

For discrete excavation it depends on the rate of increasingresistance with respect to increasing

payload,F ′

disc. The lower lightweight threshold for continuous excavators hinges onF ′

disc being

larger thanF0,cont; two distinct experiments show thatF ′

disc is orders of magnitude larger than

F0,cont. Although this does not prove the result generally, it strongly suggests that it likely holds

in all but the most degenerate of cases.

An excavator’s lightweight threshold can be estimated using laboratory experiments. Draw-

bar pull tests with a full-scale wheel and soil bin excavation tests with a full-scale tool predict

T and F , respectively, for terrestrial gravity. The dependence ofL on reduced gravity is not

fully characterized, but assuming direct scaling ofL with g provides a balanced estimate. Future

research involving reduced gravity flights to directly investigate the effects ofg on drawbar pull

coefficient and excavation resistance would provide more refined estimates forL(g).

Excavating in Earth gravity does not adequately test planetary excava-

tors

Testing in Earth gravity is an inadequate evaluation of planetary excavators, as it underesti-

mates detrimental effects of reduced gravity on both traction and excavation resistance. Gravity

offloaded testing effectively makes the assumption of direct scaling ofL with g in an experimen-

101

tal context. This research develops a novel experimental apparatus for achieving gravity offload,

and was the first to subject excavators to offload while they dig. A 300 kg excavator offloaded to

1/6 g successfully collects 0.5 kg/s using a bucket-wheel, with no discernable effect on mobility.

For a discrete excavator of the same weight, production rapidly declines as rising excavation

resistance stalls the robot; in total the discrete bucket collects less than 20 kg of regolith.

Prior study of lightweight excavation had not identified the core princi-

ples

There is no consensus on appropriate excavation force modeling for lunar excavation. How-

ever, it is instructive to rise above the fray of contrastingmodels and focus on their commonly

shared features. Any estimate of excavation resistance must take into account soil weight (and

thus friction) and cohesion. Surcharge is also very important, particularly for discrete excava-

tion; the weight, and perhaps cohesion, of the accumulatingsoil comprise this surcharge. These

common features provide a theoretical framework for broadly predicting dependence on key

variables such as soil density and cohesion as well as gravity and cut depth.

Past experiments have studied the effects of many excavation parameters, and have shown

that bucket-wheel excavators produce low resistance forces suitable for lightweight operation.

Only preliminary efforts had been made to study excavation forces in reduced gravity. Exper-

iments with excavator prototypes simulating low gravity constitute a novel contribution to the

field of study.

The wide variability in configurations resulting from lunarexcavation trade studies and proto-

type developments highlight the lack of consensus on appropriate configurations for lightweight

excavators. The result that most closely resembles consensus is the fact that bucket-ladder

trenchers have won the Regolith Excavation Challenge and Lunabotics mining competitions each

of the 4 times such competitions were held.

A transverse bucket-wheel excavator offers a unique solution for lightweight

excavation

102

Continuous excavator configurations, such as bucket-wheelsand bucket-ladders, are prefer-

able to discrete wide bucket excavators, such as scrapers and front-loaders, for lightweight lunar

and planetary excavation. Bucket-wheel excavators producelow resistance forces that enable

lightweight operation, but in the past have had difficulty transferring regolith from bucket-wheel

to collection bin or dump-bed (necessitating impractical conveyor systems). As a result, bucket-

ladders have gained favor, but their exposed chains would fare poorly in harsh lunar regolith and

vacuum.

A centrally mounted and transverse bucket-wheel configuration, developed in this work,

achieves simplified transfer of regolith into a dump-bed with no significant increase in exca-

vation resistance. The dump-bed is designed to collect substantial payload ratio. The excavator

also has a high driving speed, as payload ratio and driving speed govern lightweight excava-

tor productivity. The design and testing of the excavator’srigid wheels demonstrate successful

application of a grouser spacing equation derived as part ofthis work.

7.2 Contributions

The major contribution of this thesis is the reduction of risk related to future planetary excavation

missions. It also establishes directions and resources to continue refining the results.

7.2.1 Bringing planetary excavation missions forward

Identifying the core principles of lightweight excavationincreases the probability of successful

excavation operations. At the same time, distinguishing features that enable lower mass exca-

vators reduces mission cost. Taken together, these factorsincrease the feasibility of near-term

planetary excavation missions. Successful small scale missions could then be scaled up, follow-

ing the approach used for the Mars rovers.

The key developments that lead to this contribution are a quantifiable lightweight thresh-

103

old and a methodology for estimating it for planetary conditions. An excavator’slightweight

number, L, relates to its operational risk. Determining that a proposed excavator’s predictedL

(in planetary conditions) is near or below 1, for example, could prevent haphazardly sending a

discrete excavator into dangerous operating conditions. On the other hand, a very highL means

that a lower mass machines could just as well meet excavationrequirements.

The insight thatcontinuous excavationhas inherently higherL, and thus is more applica-

ble to lightweight excavation, reveals excavator designs that increase mission confidence while

lowering cost. This brings in-situ resource utilization (ISRU) missions forward, by enabling the

production of consumables from native regolith and the building of earthwork infrastructure, at

lower risk and cost.

7.2.2 Establishing resources and direction for future work

This work developed a novelbucket-wheel excavator. This robotic platform is a resource that

enables further research into planetary excavation tasks.For example, it can be used to study op-

erational issues of deep digging. For safe excavation to depth, the sides of a pit must be terraced

or gently sloping; this prevents collapse and cave in of the pit walls. The bucket-wheel excavator

enables testing of operation plans for excavating such a pit. Another example application is using

the robot’s sensing and actuation to test control strategies for dealing with buried rocks.

This research also developed a load-haul-dump model, Regolith Excavation, MObility &

Tooling Environment (REMOTE ). The model could be a useful tool for mission planners and

excavator designers alike.

7.3 Future work

Future research on lightweight excavation would benefit from testing in reduced gravity flights.

These provide the most representative test environment short of actually operating on a planetary

104

Figure 7.1: Rocks produce large spikes in excavation resistance, posing a challenge forlightweight continuous and discrete excavators alike.

surface, as excavator and regolith are both subject to reduced gravity. The dependence of the

lightweight number,L, on reduced gravity is not yet fully characterized. Reduced gravity flights

to directly investigate the effects ofg on drawbar pull coefficient and excavation resistance would

provide more refined estimates forL(g).

Another important direction for future study is deep excavation in the presence of submerged

rocks, which pose challenges for lighweight continuous anddiscrete excavators alike. Initial tests

show that rocks produce large spikes in excavation resistance, as shown in Figure 7.1. Rocks are

especially important to consider during deep excavation. For safe excavation to depth, the sides

of a pit must be terraced or gently sloping; this prevents collapse and cave in of the pit walls.

Shallow slopes translate into large excavated volumes, though, and thus higher probability of

encountering rocks of any given size.

Continuous excavators have a lower lightweight threshold than discrete excavators; this re-

sult hinges onF ′

disc being at least 3 times larger thanF0,cont. Two distinct experiments herein

show thatF ′

disc is orders of magnitude larger thanF0,cont. This strongly suggests that continuous

excavators will have a lower lightweight threshold in all but the most degenerate of cases, though

105

Figure 7.2: Bucket soil flow imaged and processed. The top image shows soil velocity magnitude(colors range from blue for stationary soil to red for maximum observed speed); the bottom imageshows soil velocity direction (colors correspond to directions indicated by the color wheel in thebottom right)

it does not directly prove the result generally. Experiments to confirm the generality of these

results could explore a wide assortment of continuous and discrete excavation tools.

Additional experiments to study the effects of scaling on traction and excavation resistance

would provide further insight into the dependence of excavation on changes in weight. Such

experiments include (continuous) bucket-wheel and (discrete) flat-plate tests in cohesive soil, as

well as rigid and compliant wheel scaling in relevant soils.

Excavation modeling is fruitful ground for future research. Some aspects of excavation tasks

are ignored within REMOTE, including wheel slip sinkage and soil accumulation at the bucket

cutting edge. Soil accumulation and slip sinkage are appropriate directions for future modeling

development. Excavation resistance varies significantly during a cut as soil accumulates in the

bucket, and classical models only approximate this effect.They fail to capture excavation soil

flows. Novel soil flow imaging techniques developed as part ofthis work (see Appendix B) shed

light on soil flow during excavation, as shown in Figures 7.2 and 7.3. Discrete Element Modeling

(DEM) shows promise in modeling such excavation soil flows.

106

Figure 7.3: Bucket-wheel soil flow imaged and processed.

107

108

8 Bibliography

[1] Nader Abu El Samid. Infrastructure robotics: A trade-off study examining both au-

tonomously and manually controlled approaches to lunar excavation and construction. Mas-

ter’s thesis, University of Toronto, 2008. 2.4

[2] Juan H. Agui and Allen Wilkinson. Granular flow and dynamics of lunar simulants in

excavating implements. InASCE Earth & Space 2010 Proceeding, Honolulu, HI, March

2010. 2.2, 2.2.1, 4.3.1, 5.1, 5.1.1, 5.2.2

[3] Maximilian Apfelbeck, Sebastian Kuß, Bernhard Rebele, and Bernd Schafer. A systematic

approach to reliably characterize soils based on bevametertesting. Journal of Terrame-

chanics, 48(5):360–371, 2011. 4.4.2

[4] Vladilen Ivanovich Balovnev.New methods for calculating resistance to cutting of soil.

Amerind Publishing Company, 1983. 3.1.2, 3.1.2

[5] Paul Bartlett, David Wettergreen, and William Whittaker.Design of the scarab rover for

mobility and drilling in the lunar cold traps. InInternational Symposium on Artificial Intel-

ligence, Robotics and Automation in Space, pages 3–6. Citeseer, 2008. 5.2.1

[6] Mieczyslaw Gregory Bekker. Photographic method of determining the soil action beneath

footings. InProc. 2nd Int. Conf. on Soil Mechanics and Foundation Engineering, pages

193–194, 1948. B

[7] Mieczyslaw Gregory Bekker.Introduction to terrain-vehicle systems. University of Michi-

gan Press Ann Arbor, MI, 1969. 3.1.1

109

[8] Leonhard E. Bernold. Experimental studies on mechanics of lunar excavation.Journal of

Aerospace Engineering, 4(1):9–22, January 1991. 2.6

[9] Jeffrey K. Berry. System model for lunar regolith excavation machine optimization. Me-

chanical engineering, Bradley University, Peoria, Illinois, 2006. 2.1.4

[10] Michael J Black and Paul Anandan. The robust estimation of multiple motions: Parametric

and piecewise-smooth flow fields.Computer vision and image understanding, 63(1):75–

104, 1996. B

[11] Stephane Blouin, Ahmad Hemami, and Mike Lipsett. Review of resistive force models

for earthmoving processes.Journal of Aerospace Engineering, 14(3):102–111, July 2001.

1.4.4

[12] Walter W Boles, David B Ashley, and Richard L Tucker. Lunar-base construction equip-

ment and methods evaluation.Journal of Aerospace Engineering, 6(3):217–235, 1993. 1.3,

2.4

[13] Walter W Boles, Wesley D Scott, and John F Connolly. Excavation forces in reduced

gravity environment.Journal of Aerospace Engineering, 10(2):99–103, 1997. 2.2.2, 4.3,

4.4, 4.5, 5.2, 7.1

[14] Ha H Bui, Taizo Kobayashi, Ryoichi Fukagawa, and John C Wells. Numerical and ex-

perimental studies of gravity effect on the mechanism of lunar excavations.Journal of

Terramechanics, 46(3):115–124, 2009. 2.1.4

[15] D Carrier.The four things you need to know about the geotechnical properties of lunar soil.

Lunar Geotechnical Institute, P.O. Box 5056, Lakeland, FL 33807, September 2005. 4.4.2

[16] John J Caruso, Dan C Spina, Lawrence C Greer, Wentworth T John, Clem Michele, Mike J

Krasowski, and Norman F Prokop. Excavation on the moon: Regolith collection for oxygen

production and outpost site preparation. Technical Report 20080012503, NASA Glenn

Research Center, Cleveland, Ohio 44135, 2008. 2.5, 6

110

[17] D Larry Clark, R Patterson, and D Wurts. A novel approach to planetary regolith collection:

the bucket drum soil excavator. InAIAA Space 2009 Conference & Exposition, September

2009. 2.5, 6

[18] J. Craft, J. Wilson, P. Chu, K. Zacny, and K. Davis. Percussive digging systems for robotic

exploration and excavation of planetary and lunar regolith. In Aerospace conference, 2009

IEEE, Big Sky, MT, March 2009. 2.2.2, 2.6

[19] GF Diaz Lankenau, K Skonieczny, WL Whittaker, and DS Wettergreen. Effect of bucket-

wheel scale on excavation forces and soil motion.Journal of Terramechanics, 49(6):341–

348, 2012. 4.4.1

[20] L. Ding, H. Gao, Z. Deng, and J. Tao. Wheel slip-sinkage and its prediction model of lunar

rover. Journal of Central South University of Technology, 17(1):129–135, 2010. 3.1.1

[21] Liang Ding, Haibo Gao, Zongquan Deng, Keiji Nagatani, and Kazuya Yoshida. Experi-

mental study and analysis on driving wheels performance forplanetary exploration rovers

moving in deformable soil.Journal of Terramechanics, 48(1):27–45, 2011. 4.2

[22] Matthew Dunbabin, Peter Corke, Graeme Winstanley, and Jonathan Roberts. Off-world

robotic excavation for large-scale habitat construction and resource extraction. InTo Boldly

Go Where No Human-Robot Team Has Gone Before: Papers from the 2006 AAAI Spring

Symposium, Technical Report SS-06-07, pages 95–103. AAAI, March 2006. 2.7

[23] R. C. Elphic, D. A. Paige, M. A. Siegler, A. R. Vasavada, V. R. Eke, L. F. A. Teodoro, and

D. J. Lawrence. South pole hydrogen distribution for present lunar conditions: Implications

for past impacts. In41st Lunar and Planetary Science Conference, page 2732, Woodlands,

TX, March 2010. 1.1, 1.1

[24] D.R. Freitag, A.J. Green, and K.J. Melzer. Performance evaluation of wheels for lunar

vehicles. Technical report, DTIC Document, 1970. 1.4.3, 4.2

[25] Philippe Gachet, Georg Klubertanz, Laurent Vulliet, and Lyesse Laloui. Interfacial behav-

111

ior of unsaturated soil with small-scale models and use of image processing techniques.

Geotechnical Testing Journal, 26:12–21, 2003. B

[26] C. A. Gallo, R. A. Wilkinson, R. P. Mueller, J. M. Schuler, and A. J. Nick. Comparison of

isru excavation system model blade force methodology and experimental results. Technical

Report TM2010-215591, NASA, 2010. 2.1

[27] Leslie Gertsch, Robert Gustafson, and Richard Gertsch. Effect of water ice content on

excavatability of lunar regolith. InAIP Conference Proceedings, volume 813, page 1093,

2006. 2.6

[28] Alex Green, Kris Zacny, Juan Pestana, Dennis Lieu, and Robert Mueller. Investigating

the effects of percussion on excavation forces.Journal of Aerospace Engineering, 26(1):

87–96, 2013. 2.6

[29] Robert Gustafson and Leslie Gertsch. Cutterhead development for the low-energy planetary

excavator. InSpace Technology and Applications International Forum, Albuquerque, NM,

February 2008. American Institute of Physics. 2.6

[30] Grant H Heiken, David T Vaniman, and Bevan M French, editors. The Lunar sourcebook:

A user’s guide to the Moon. Cambridge University Press, 1991. 2.6, 3.1.1, 3.2.1

[31] DRP Hettiaratchi and AR Reece. The calculation of passivesoil resistance.Geotechnique,

24(3):289–310, 1974. 4.4.2

[32] DRP Hettiaratchi, BD Witney, and AR Reece. The calculationof passive pressure in two-

dimensional soil failure. Journal of Agricultural Engineering Research, 11(2):89–107,

1966. 2.1, 2.1, 2.1.2

[33] Karl Iagnemma and Steven Dubowsky. Traction control ofwheeled robotic vehicles in

rough terrain with application to planetary rovers.The International Journal of Robotics

Research, 23(10-11):1029–1040, 2004. 3.2.2

[34] M Iai. Scaled experimental study on excavation of lunar regolith with rakes/rippers and

112

flat blade. PhD thesis, Missouri University of Science and Technology, 2010. 2.6

[35] Caterpillar Inc., editor.Caterpillar performance handbook. Caterpillar Inc., Peoria, IL, 33

edition, 2002. 1.4.2, 4.1

[36] LL Johnson and RH King. Measurement of force to excavate extraterrestrial regolith with

a small bucket-wheel device.Journal of Terramechanics, 47(2):87–95, 2010. ISSN 0022-

4898. 2.2, 2.5, 6.1

[37] LL Johnson and PJ Van Susante. Excavation system comparison: Bucket wheel vs. bucket

ladder. InSpace Resources Roundtable VIII, Golden, CO, November 2006. 2.5, 2.5, 6.1

[38] Simon Kassel. Lunokhod-1 soviet lunar surface vehicle. Technical Report R-802-ARPA,

RAND Corporation, 1971. 2.7, 6.2

[39] R.H. King, P.J. van Susante, and R.P. Mueller. Comparison of lance blade force measure-

ments with analytical model results. InSpace Resources Roundtable XI / Planetary &

Terrestrial Mining Sciences Symposium Proceedings, 2010. 2.1, 2.2.1, 2.3, 6

[40] J Ledlie Klosky, Stein Sture, Hon-Yim Ko, and Frank Barnes. Vibratory excavation and

anchoring tools for the lunar surface. InEngineering, Construction, and Operations in

Space V. ASCE, 1996. 2.6

[41] J Ledlie Klosky, Stein Sture, Hon-Yim Ko, and Frank Barnes. Geotechnical behavior of

jsc-1 lunar soil simulant.Journal of Aerospace Engineering, 13(4):133–138, 2000. 4.3

[42] T Kobayashi, H Ochiai, R Fukagawa, S Aoki, and K Tamoi. A proposal for estimating

strength parameters of lunar surface from soil cutting resistances. InEarth & Space, 2006.

2.1.3

[43] Taizo Kobayashi, Yoichiro Fujiwara, Junya Yamakawa, Noriyuki Yasufuku, and Kiyoshi

Omine. Mobility performance of a rigid wheel in low gravity environments. Journal of

Terramechanics, 47(4):261–274, 2010. 4.2, 4.5, 5.2, 7.1

[44] Takashi Kubota, Kenji Nagaoka, Satoru Tanaka, and TaroNakamura. Earth-worm typed

113

drilling robot for subsurface planetary exploration. InRobotics and Biomimetics, 2007.

ROBIO 2007. IEEE International Conference on, pages 1394–1399. IEEE, 2007. 2.5

[45] O Luengo, Sanjiv Singh, and Howard Cannon. Modeling and identification of soil-tool

interaction in automated excavation. InIntelligent Robots and Systems, 1998. Proceedings.,

1998 IEEE/RSJ International Conference on, volume 3, pages 1900–1906. IEEE, October

1998. 2.7

[46] H.J. Luth and R.D. Wismer. Performance of plane soil cutting blades in sand.Transactions

of the ASAE, 14(2):255–262, Mar-Apr 1971. 3.1.2

[47] Scott Moreland, Krzysztof Skonieczny, David Wettergreen, Colin Creager, and Vivake As-

nani. Soil motion analysis system for examining wheel-soilshearing. In17th International

Conference for the Society of Terrain-Vehicle Systems, 2011. B

[48] Scott Moreland, Krzysztof Skonieczny, Hiroaki Inotsume, and David Wettergreen. Soil

behavior of wheels with grousers for planetary rovers. InAerospace Conference, 2012

IEEE, pages 1–8. IEEE, 2012. B

[49] Robert P Mueller and Paul J Van Susante. A review of lunar regolith excavation robotic

device prototypes. InAIAA Space, 2011. 2.8, 6.1

[50] Robert P Mueller, Jonathan D Smith, Rachel E Cox, Jason M Schuler, Tom Ebert, and

Andrew J Nick. Regolith advanced surface systems operationsrobot (rassor). InIEEE

Aerospace, 2013. 2.5

[51] R.P. Mueller and R.H. King. Trade study of excavation tools and equipment for lunar

outpost development and isru. InAIP Conference Proceedings, volume 969, pages 237–

244, January 2008. 2.4

[52] T Muff, L Johnson, R King, and MB Duke. A prototype bucketwheel excavator for the

moon, mars and phobos. InAIP Conference Proceedings, volume 699, page 967, 2004.

2.5, 6

114

[53] Tim Muff, RH King, and MB Duke. Analysis of a small robot for martian regolith exca-

vation. InAIAA Space 2001 Conference & Exposition, Albequerque, NM, August 2001.

AIAA. 2.3, 3.1.2

[54] Tejas G Murthy, Ebenezer P Gnanamanickam, Christopher Saldana, and Srinivasan Chan-

drasekar. Deformation field in indentation of granular materials. In AIP Conference Pro-

ceedings, volume 1145, page 263, 2009. B

[55] H. Nayar, A. Jain, J. Balaram, J. Cameron, C. Lim, R. Mukherjee, M. Pomerantz, L. Reder,

S. Myint, N. Serrano, and S. Wall. Recent developments on a simulator for lunar surface

operations. InAIAA SPACE 2009 Conference & Exposition, 2009. 3.1.4

[56] H.A. Oravec, X. Zeng, and V.M. Asnani. Design and characterization of grc-1: A soil for

lunar terramechanics testing in earth-ambient conditions. Journal of Terramechanics, 47

(6):361–377, 2010. 2.2.2, 4.4.1, 4.4.2, 5.2.1

[57] Yang Qinsen and Sun Shuren. A soil-tool interaction model for bulldozer blades.Journal

of terramechanics, 31(2):55–65, 1994. 2.1.3, 4.3.1

[58] G. Sanders and W. Larson. Progress made in lunar in situ resource utilization under nasas

exploration technology and development program.Journal of Aerospace Engineering, 26

(1):5–17, 2013. 1.1, 1.2

[59] A Sanin, I Mitrofanov, W Boynton, G Chin, N Demidov, J Garvin, D Golovin, L Evans,

K Harshman, A Kozyrev, et al. Mapping of lunar hydrogen according to the lend neutron

measurements onboard the nasa lro. InLunar and Planetary Institute Science Conference

Abstracts, volume 41, page 2437, 2010. 1.1

[60] Thomas B. Sheridan. Space teleoperation through time delay: Review and prognosis.IEEE

Transactions on Robotics and Automation, 9(5):592–606, October 1993. 2.7

[61] I Shmulevich, Z Asaf, and D Rubinstein. Interaction between soil and a wide cutting blade

using the discrete element method.Soil and Tillage Research, 97(1):37–50, 2007. 2.1.3,

115

4.3.1, 4.3.1, 4.6

[62] Sanjiv Singh. The state of the art in automation of earthmoving. Journal of Aerospace

Engineering, 10(4):179–188, October 1997. 2.7

[63] Krzysztof Skonieczny, David S. Wettergreen, and W. L. ”Red” Whittaker. Parameters gov-

erning regolith site work by small robots. InASCE Earth & Space 2010 Proceedings,

Honolulu, HI, March 2010. 3.1.5, 3.3

[64] Krzysztof Skonieczny, Scott J Moreland, and David S Wettergreen. A grouser spacing

equation for determining appropriate geometry of planetary rover wheels. InIntelligent

Robots and Systems (IROS), 2012 IEEE/RSJ International Conference on, pages 5065–

5070. IEEE, 2012. B

[65] Krzysztof Skonieczny, Matthew Delaney, David S Wettergreen, and William LRed Whit-

taker. Productive lightweight robotic excavation for the moon and mars. Journal of

Aerospace Engineering, in press, 2013. 3.1, 3.10, 3.12

[66] B. Szabo, F. Barnes, S. Sture, and H-Y. Ko. Effectiveness of vibrating bulldozer and plow

blades on draft force reduction.Transactions of the ASAE, 41(2):283–290, 1998. 2.6

[67] Ronny Theiss, Dale Boucher, Marcel Viel, Dave Roberts, andJames Kutchaw. Interchange-

able payloads for isru mobility chassis. InSpace Resources Roundtable XI / Planetary &

Terrestrial Mining Sciences Symposium Proceedings, 2010. 2.5, 6

[68] G.W. Turnage and D.C. Banks. Lunar surface mobility studies past and future. Technical

report, DTIC Document, 1989. 1.4.3, 4.2

[69] Otis R. Walton and Scott M. Johnson. Dem simulations of the effects of particle shape,

interparticle cohesion and gravity on rotating drum flows oflunar regolith. InASCE Earth

& Space 2010 Proceedings, Honolulu, HI, March 2010. 2.1.4

[70] D. Wettergreen, S. Moreland, K. Skonieczny, D. Jonak, D. Kohanbash, and J. Teza. Design

and field experimentation of a prototype lunar prospector.The International Journal of

116

Robotics Research, 29(12):1550–1564, 2010. 1.4.3, 4.2, 5.2.1

[71] Christopher V White, John K Frankovich, Philip Yates, George Wells Jr, and Losey Robert.

A capable and temporary test facility on a shoestring budget: the msl touchdown test fa-

cility. In 24th Aerospace Testing Seminar, April 8, 2008, Manhattan Beach, California.

Pasadena, CA: Jet Propulsion Laboratory, National Aeronautics and Space Administration,

2008., 2008. 5.2

[72] DJ White, WA Take, and MD Bolton. Soil deformation measurement using particle image

velocimetry (piv) and photogrammetry.Geotechnique, 53(7):619–631, 2003. B

[73] A. Wilkinson and A. DeGennaro. Digging and pushing lunar regolith: Classical soil me-

chanics and the forces needed for excavation and traction.Journal of Terramechanics, 44:

133–152, 2007. 2.1, 2.1.1, 2.3, 3.1

[74] Brian M. Willman. Modeling Soil-Tool Interaction in a Lunar Soil Simulant. PhD thesis,

Texas A&M University, 1994. 2.1, 2.2.2, 2.3

[75] R.D. Wismer and H.J. Luth. Performance of plane soil cutting blades in clay.Transactions

of the ASAE, 15:211–216, 1972. 3.1.2

[76] J. Y. Wong.Theory of Ground Vehicles. John Wiley & Sons, Inc., 3rd edition, 2001. 3.1.1,

3.2.2

[77] Jo-Yung Wong. Behaviour of soil beneath rigid wheels.Journal of Agricultural Engineer-

ing Research, 12(4):257–269, 1967. B

[78] Jo-Yung Wong and AR Reece. Soil failure beneath rigid wheels. In Proceedings of the

Second International Conference of the International Society for Terrain-Vehicle Systems,

JN Siddall, and PH Southwell, pages 425–445, 1966. B

[79] JY Wong. Predicting the performances of rigid rover wheels on extraterrestrial surfaces

based on test results obtained on earth.Journal of Terramechanics, 49(1):49–61, 2012. 5.2

[80] JY Wong and VM Asnani. Study of the correlation between the performances of lunar

117

vehicle wheels predicted by the nepean wheeled vehicle performance model and test data.

Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile

Engineering, 222(11):1939–1954, 2008. 1.4.3, 4.2

[81] Kris Zacny, Robert P. Mueller, Jack Craft, Jack Wilson, Magnus Hedlund, and Joanna

Cohen. Five-step parametric prediction and optimization tool for lunar surface systems

excavation tasks. InASCE Earth & Space 2010 Proceedings, Honolulu, HI, March 2010.

4.3

[82] A Nikolaevich Zelenin, Vladilen Ivanovich Balovnev, Igor Petrovich Kerov, et al.Machines

for moving the earth.AA Balkema, 1986. 4.4.2

[83] Xiangwu Zeng, Chunmei He, Heather Oravec, Allen Wilkinson, Juan Agui, and Vivake

Asnani. Geotechnical properties of jsc-1a lunar soil simulant. Jou, 23(2):111–116, April

2010. 2.2.2

118

A Extensions

This appendix discusses closely related topics that lie outside the scope of this thesis.

A.1 Regolith shaping

This thesis focuses on the load-haul-dump cycle that is central to all relevant planetary excavation

tasks. However, as described in Section 1.2, there is a classof tasks that also requires the regolith

to be shaped, molded, and perhaps compacted after being dumped. This class of tasks includes

building berms and covering habitats.

Bucket-wheels are not conducive to regolith shaping the way that wide flat (discrete) buckets

are. Discrete buckets, such as front-end loaders, can be used to flatten, smooth, and compress

regolith. This versatility is an important feature to tradeoff against continuous excavators’ pro-

ductivity and mobility advantages. Another advantage of discrete buckets is the lower chance of

clogging, due to their inherently open geometry. For these reasons, it may sometimes be desir-

able to use a discrete excavator even in conditions where it technically falls below the lightweight

threshold.

If a discrete excavator is operating below the lightweight threshold, it will not be able to

safely collect its desired payload ratio in a single cut. However, for operations with a lightweight

number,L, just below 1, the desired payload ratio can be achieved with2 cuts as long as regolith

from the first cut is cleared from the cutting edge of the bucket. In practice this clearing can

be performed by overshot dumping into a secondary dump-bed,or perhaps by tilting the bucket

119

back until soil shifts to the back of the bucket (as was done inthe Lysander experiments described

in Section 3.2). An even smallerL may require 3 cuts, and so on. At some point the operation

begins to resemble continuous excavation, except for the fact that cutting and clearing are per-

formed serially by a single bucket rather than in parallel byseveral; which is less productive and

less efficient. There will be a point in the trade space whereL is so low as to make multi-cut

discrete excavation impractical.

The additional sensing and control complexity must also be taken into account when con-

sidering multi-cut operations with a discrete excavator. To ensure slip does not exceed some

safety threshold (of 20%, for example), slip or drawbar loadneeds to be estimated. Setting an

appropriate cut depth (for a subsequent cut) is also not trivial in soil disturbed by the pushing and

breakout of the previous cut.

A.2 Non-tractive excavation thrust

This thesis assumes that excavation thrust is provided by traction, as excavator configurations

typically considered for space application cut by driving forward. However, configurations exist

that do no rely on traction for cutting. RASSOR (Figure 2.3) has counter-rotating bucket-drums

that can theoretically achieve zero net horizontal excavation resistance. Clamshell excavators are

another example of machines that can achieve zero net horizontal excavation resistance. In these

cases, vertical excavation resistance dominates.

The concepts presented in this thesis can be extended to these non-tractive excavation modes,

with a few minor adjustments. Vertical forces replace longitudinal forces when considering

excavation resistance coefficient,F . Excavation thrust is provided directly by the robot weight,

so T = 1. For discrete vertical excavation (e.g. clamshell), depthincreases with cut progress.

Equation 2.1 suggests that excavation resistance increases with the square of depth. Compared

to the linear increase in resistance with cut length observed for horizontal cutting, the advantages

of continuous excavation may thus be even more pronounced inthis mode of operation. Further

120

study of this hypothesis is recommended if considering vertical thrust for lightweight excavation.

121

122

B Soil flow imaging and grouser spacing

A novel analysis technique has been developed to enable detailed investigation of robot interac-

tions with granular regolith. This technique provides visualization and analysis capability of soil

shearing and flow as it is influenced by a wheel or excavation tool. During controlled motion a

test implement up against a glass sidewall, images are takenof the sub-surface soil, and are pro-

cessed with optical flow software. Analysis of the resultingdisplacement field identifies clusters

of soil motion and shear interfaces. This enables analysis of robot-soil interactions in richer de-

tail than possible before. Prior art relied on long-exposure images that provided only qualitative

insight, while the new processing technique identifies sub-millimeter gradations in motion and

can do so even for high frequency changes in motion (several Hz).

Direct observation of soil motion through glass sidewalls has been utilized in soil mechanics

and terramechanics research for over half a century [6]. Wong concluded experimentally that

as long as shear stress between glass and soil is negligible,the glass surface acts as a plane of

symmetry and the soil behaves as it would directly below an implement twice as wide [77, 78].

One archetypical photographic method for observing soil motion uses long-exposure photos

and distinguishes sharp and streaking soil grains as stationary and moving, respectively. Streaks

in the photos also provide information about the directionsof soil motion. With advances in

digital camera technology and computer vision processing techniques, new methods providing

much richer data have become possible [25, 72]. The image processing technique discussed

in this work is similar in its implementation to Murthy’s, who performed a preliminary study

of sand displacement under a footing-like indenter [54]. This work applies these newest soil

123

observation techniques to wheel and tool interactions pertinent for planetary robots.

A description of experimental apparatus hardware is found in [47]. A digital SLR camera

with a 50mm macro lens is used to image the soil where it interfaces with the test implement,

logging frames simultaneously with the rest of the telemetry. A frame rate of 8 frames-per-

second is used and is sufficiently fast for the slow implementspeeds. The camera is mounted

perpendicular to the soil bin glass wall and travels with theimplement in the horizontal direction

as the carriage moves. External halogen flood lights at a highangle (from the normal) to the

glass illuminate the soil particles.

Image processing comprises of optical flow and clustering techniques. An overview of the

process described herein is presented in Figure B.1. The optical flow algorithm [10] tracks dis-

placement of soil regions relative to a prior frame and calculates a motion vector at each pixel.

Initial clustering separates each image into ‘soil’ and ‘not soil’ regions. Additional processing

and output is continued only for ”soil” regions. The magnitude of flow at each pixel of the soil

regions is calculated from the optical flow vector fields. Soil flow is clustered into ”significant”

and ”insignificant” magnitudes of motion. No explicit threshold is used to demarcate these clus-

ters, but rather automatically adaptive k-means clustering is used. The shear interface is derived

from the boundary between significant and insignificant motions. Soil flow direction is calcu-

lated from the optical flow vector fields, for soil regions exhibiting significant soil flow. Soil flow

in any direction (360 degrees) is visualized, and an additional boundary is identified at points

where the soil transitions between forward and rear flow. Figure B.2 is a sample output of the

process, showing soil flow magnitude, shear interface between significant and insignificant flow,

soil flow direction (within region of significant flow), and boundary between forward and rear

flow.

This soil imaging technique was used to derive a quantitative expression for determining

appropriate grouser spacing for rigid wheels. The intuition guiding the search for a grouser

spacing equation is an endeavor to ensure grousers encounter soil ahead of a wheel before the

124

Figure B.1: Overview of image processing and output

wheel rim does. When a wheel rim encounters soil it bulldozes it forward and compacts it,

producing resistance, in addition to shearing it to producethrust [48]. Grousers, on the other

hand, have a net rearward motion near the bottom of a rotatingwheel, and thus pull soil back and

constrain it from undergoing resistive forward flow. The grouser spacing equation is discussed

in detail in [64], and the derivation is provided here for reference.

125

Figure B.2: Sample processed output for driven wheel. Soil flow speed (upper) is denoted fromblue (static) to red (max. speed). Soil flow direction (lower) within the shear interface is denotedaccording to the color wheel is the bottom right.

126

127

128

129