Wheeled Robotic Mobility

Wheeled Robotic Mobility

Dimi Apostolopoulos

ROBOTIC MOBILITY – Dimi Apostolopoulos

Significance of Mobility

Move

Position

Transport

Employ instruments and tools

React to work loads

…in a controllable fashion


Classification by Locomotion Type

WheelsLegsTracksHybrids Special limbsSpecial joints

ESA ExoMars Rover

NASA JSC Chariot

NASA JPL ATHLETE

JAXA Rover


Selecting Locomotion Type

Wheels for

Faster movement

Generally fewer actuated DOFs

Better packaging & survivability

Hybrids for multi-mission tasks

Legged for very rough terrain

Reconfigurable, hopping systems for extreme terrain

Undulatory for confined spaces

Scaling considerations are critical


This Lecture – Wheeled Mobility

600 kg

1200 kg

6000 kg

400 kg20 kg

200 kg

CMU Systems


Elements of Robotic Mobility


Elements of Robotic Mobility

3-D Geometry

Sensor Placement

Optimized FOV

Wheel (number, geometry, disposition) Drive

(type, actuationRequirements)

C.G. & Ground

Clearance

Critical Dimensions

Steering(scheme, geometry,

kinematics)

Suspension

Actuation

Inherent features for controllability


Robotic Mobility

Locomotion elements (geometry, elastic vs. rigid)Wheel disposition and chassis geometryDrive scheme (independent vs. coordinated)Steering scheme (explicit vs. induced)Suspension (from passive to active, 2D vs. 3D)Articulation (passive vs. active, # & type of axis)Control (speed, traction, slip)Actuation (electric/hydraulic, etc.)Sensing (direct vs. inferred)Inherent features for higher terrainability and ease of control


Synthesizing Novel Robotic Mobility

RequirementsAnalysis

ConceptualDesign

Critical Design

Preliminary Design

Development

Configuration Design


Physics-based Analysis of Mobility

RequirementsAnalysis

ConceptualDesign

Critical Design

Preliminary Design

Development

Configuration Design

Quasi-static mechanics of robot-terrain interaction(force, torque, power, energy)

Kinematics & dynamics

Stability analysis

Controllability analysis

Physics of sensing


In-soil Performance – Terramechanics

Wheel-soil interaction models

Wheel sinkage

Motion resistance and traction

Force, torque, power, energy

Sizing wheels, drive actuation, drive electronics, drive mechanisms


Contact patch

This stress is called “ground pressure.”

WA

( , )A A b L

But ground pressure is not always uniform.Sometimes get more sinkage than expected.

p

p

Tracks -- rectangular patch.

Wheel-ground Contact


Basic Physics of Wheel-Soil Interaction

FpA

F

F

A Normal Stress (pressure)

Relates to traction, slip, and skid.

F

F

A

Shear StressFA

Relates to ground pressure and sinkage.


Traction and Force

What are drive forces to overcome soil resistances?

Will soil support the loads?

F1

F2

R1R2

F R

W

F: Traction, R: Resistance, F > soil’s capacity to react to loads


Motion Resistance

--Resistance by compacting soil (sinkage) under the wheel

Rc

W

F

σ

Tandem W1W2

F1F2

Rc2 Rc1

10

1

nc

ck zR b kb n

The wider the wheel and greater the sinkage, the greater the resistance.

Equal to work/length of pressing a block of width b to depth z .


Wheel Slip, Soil Thrust & Traction

or viv

Cannot be easily predicted, but can be measured and used for feedback control.

v

ω

Not all rotational velocity is translated into linear velocity.

Rate of slip:

tan 1 1oi

K

o

KH Ac W ei

Soil thrust actually takes slip into account:

Ideal Soil ThrustSlip Term

F

H


Physics-Based Modeling & Analysis

Rb

bw + sin

2 cossin--------------------------------- 2cKczw K zw

2+ l r

2 90 – 540

-------------------------------c lr

2

180----------- cl r

2 45 2---+

tan+ + +=

Kc N c tan– K 2N

tan----------- 1+ 2 1

2zw

dw---------–

l r zw 452---–

2tan=acos=cos=

2cos=

CMU’s LocSyn ToolExample:Required Drive Torque

Tdrws Rc Rb Rr+ + Rg+ dw

2------ – =

R cr w

3W w cos

dw

-------------------------

2 n 2+ 2 n 1+

------------------

3 n–

2 n 2+ 2 n 1+

----------------------n 1+ k c bw

k +

12n 1+

------------------------------------------------------------------------------------------------------------------------------ =

dwn 1+ k c bw

k + 3Ww cos

2n 2+

Rcrw2n 1+ 3 n– 2n 2+ n 1+ 2n 1+

------------------------------------------------------------------------------------------=

Number of wheels: 6Wheelbase: 2.5 m x 1.5 mRoll Radius: 0.25 mTire width: 0.20 m

Drive Torque vs. Wheel Loading

Drive Torquevs. Rolling Radius

Drive Torque vs. Slope

Drive Torque vs. Tire Width

Rb

bw + sin

2 cossin--------------------------------- 2cKczw K zw

2+ l r

2 90 – 540

-------------------------------c lr

2

180----------- cl r

2 45 2---+

tan+ + +=

Kc N c tan– K 2N

tan----------- 1+ 2 1

2zw

dw---------–

l r zw 452---–

2tan=acos=cos=

2cos=

CMU’s LocSyn ToolExample:Required Drive Torque

Tdrws Rc Rb Rr+ + Rg+ dw

2------ – =

R cr w

3W w cos

dw

-------------------------

2 n 2+ 2 n 1+

------------------

3 n–

2 n 2+ 2 n 1+

----------------------n 1+ k c bw

k +

12n 1+

------------------------------------------------------------------------------------------------------------------------------ =

dwn 1+ k c bw

k + 3Ww cos

2n 2+

Rcrw2n 1+ 3 n– 2n 2+ n 1+ 2n 1+

------------------------------------------------------------------------------------------=

Number of wheels: 6Wheelbase: 2.5 m x 1.5 mRoll Radius: 0.25 mTire width: 0.20 m

Drive Torque vs. Wheel Loading

Drive Torquevs. Rolling Radius

Drive Torque vs. Slope

Drive Torque vs. Tire Width

Parametric analysis: Select wheel & mobility chassis key dimensions, and size actuators

Compaction Resistance


Significance of All-Wheel Drive

W1W2

F1F2Rc2 Rc1

W1W2

F1F2Rc2 Rc1

W

N

DrawbarPull

θθ

Positive tractionGreater pullBetter slope climbingBetter obstacle climbingSmoother control


All-Wheel Drive for Obstacle Climbing

Wheel dimension

Chassis dimension


Wheel Size vs. Number of Wheels

Estimated ~2.2 W per wheel150 kg 3-wheeled rover / ~50 kg/wheel

0.75 m rolling radius SILVRCLAWMartian soil: c= 1 kPa, = 18 deg


Drawbar Pull (DP)

Direction of travel

Steel cable

Load cell

Wal

l

a. Robot driving normallyb. Cable tension rapidly increasesc. Wheels slippingd. Motion controller fault, at least one

wheel stops servoinge. Robot reverses, cable goes slack

c

a

b

d

e

Max DP: 550 NMax slope: 22 deg

c

a

b

d

e

Max DP: 550 NMax slope: 22 deg

Difference between soil thrust (max traction) and rolling resistance.

Key metric of mobility; “how much the vehicle can pull”

arctan(DP/W) is approximately equal to max gradeability as imposed by wheel-terrain interaction

Analytical estimates within 3% of actual measured DP


Inclined Terrain Mobility

Downhill gradeability

Cross-hill gradeability

Static stability vs. soil stability vs. actuator limitations


Static Stability Limits

*low*nominal

*high(values from tilt-table testing)


Gradeability – Static vs. Terrain Stability

Analysis to help optimize vehicle geometry (center of gravity C.G. location, wheel base, wheel size)

The robot static stability limits to be greater than the terrain stability limits

Tip-overRollover


Gradeability – Dynamic Limitations

Robot Braking

d2x/dt

Analysis to help optimize vehicle geometry (C.G. location) and dynamic characteristics (deceleration performance)

This analysis can be used to set max deceleration limits that the motion control imposes


Improving Gradeability through Active Posturing

Leaning posture at 20°


Improving Path Tracking with Active Posturing

Level posture Leaning posture


Maneuverability

Optimal steering geometry

Turning radius

Force, torque, power, energy

Sizing wheels, drive/steering actuation, drive/steering electronics, steering mechanisms


Steering Geometries

Knuckle steeringSingle-axis (Ackermann)Four-wheel steering (double Ackermann, independent)Crab steering

Articulated frame steering

Skid steering

Combined steering


Steering Quasi-static Mechanics

Overcome a moment resistance (MR) in addition to compaction and bulldozing resistance.

Moment resistance caused by lateral Coulomb friction.

To minimize moment resistance, widen the body (increase B) and shorten the wheel base (decrease L)

0

Ro

Ri

x

R i i

MF RB

MF RB

M pbxdx Q x


Skid Steering Power Draw

Operational Condition Power

Pivot turn about center axleHard SurfaceNo Obstruction = 0.7, Rr = 1.5%RR = 1.5%

3 x drive

Pivot turn about center axleSoft SurfaceNo Obstruction = 0.4, Rr= 25%fRR = 25%

3 x drive

Pivot turn around obstacleHard SurfaceFrt Wheel Obstructed = 0.7fRR = 1.5%

3.5 x drive

FY2

FY1 FY3

FY4

o

L

L/2

Pivot Turn Around Obstacle

Mr

o Fy1

Fy4

Fy3

Fy2

L/2 L/2

Pivot Turn About Center Axle

All Intermittent Torques


Evaluation of Steering Geometries

Ackerman (AS)

Articulated (RS)

Explicit (ES)


Significance of Explicit Wheel Steering

Better terrainabilityFiner maneuverabilityMore control flexibilityBetter tracking

Ackerman (AS)

Articulated (RS)

Explicit (ES)


Steering Limitations

mv2/r

Analysis to help optimize vehicle geometry (C.G. location, track width) and control parameters (max allowable steering speed)


Terrain Adaptation & Motion Smoothing

Optimal suspension geometry• Passive

Dynamic (spring/damper type)Geometric

• Passive with active adjustability

• Active

Elastic mobility elements


Geometric Suspensions

Averaging

Pivoted Arm

Body leveled

Rocker arms at opposite angles


Passive Geometric Suspensions - 6x6 Chasses

JPL Pathfinder

JPL MER

JPL Rocky Series

ESA ExoMars RoverEPFL SOLERO

EPFLCRAB


Passive Geometric Suspension – 4x4 ChassesCMU Hyperion

CMU Zoe

NASA Ames K10

ESA Lunar Robotic Mockup

Roll

Pitch


Semi-active Suspensions

NASA JSC Chariot

CMU Scarab Active DOF in series or parallel (e.g. Chariot) to passive suspension

Discrete or continuous use of active DOF (e.g. Scarab’s CG shifting)


Suspension Configuration – 6x6 w/ Pivoted Arms

All Leading Arm All Trailing Arm

Leading/Trailing/Trailing Leading/Leading/Trailing


Step Climbing (1)

How will this suspension layout perform during a step climb?Vehicle nose will rise firstHence Glacis plate will assist in step climb (Rem:- not all obstacles will be a step: Rugged boulders, tree stumps, etc.)


Step Climbing Performance (2)

Front Wheel Climbing

A

e

d FZ

FX

Direction of Travel

deFF XZ

Increased Reaction Force (Gives better

Traction)

Reaction Decreases


Step Climbing Performance (3)

Centre Wheel ClimbingCentre-axle trailing arm will easily lift over step corner


PHASE 1

Middle wheel loses contact

PHASE 2

PHASE 3

Both front and rear wheels lose contact during this phase

Analytical Configuration – Drive, Suspension, Chassis


12 3

11o

1 39.8o

11o2 39.8o

11o3 39.8o

i: angle between suspension arm and line hull-line: hull pitch angle

F1

N1

F2

N2

F3

N3

0.5WGR

N2 and N3 are computed from the spring curve

Combine Force Equilibrium with… (see next)


12 3

Hi

LA

L23

Rw

LALA

L12L12 0.375m=

L23 1.670m=

LA 0.780m=

Rw 0.5m=

0.5m Hi 1.0m

A B

LHi LA 1 – sin+ L12 sin LA 2 + sin Rw+ +=

LA 2 + sin LA 3 + sin L23 sin+=

…geometrically feasible configurations


Derivation of Torque & Power for Drive System


Tires/Wheels as Traction & Suspension Elements

LRV Wire-Mesh Wheel

Lunokhod Wire-Mesh Wheel

MER & MSL Wheels

Rc

W

F

σ

Mitigate sinkageIncrease contact areaMinimize motion resistanceMaximize traction


Transmissibility

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

Shock Duration / (s)

Tra

nsm

issi

bilit

yUnsprung MassSprung Mass

26 psi

20 psi

14 psi

Realistic shock duration

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.5

1

1.5

2

2.5

Shock Duration / (s)

Tra

nsm

issi

bilit

yUnsprung MassSprung Mass

26 psi

20 psi

14 psi

Realistic shock duration Realistic shock duration

Significant consideration in that it affects dynamic-induced motions to sensors, payloads, and computing


Posture Changing for Terrain Adaptation

JPL Gofor

JPL All-Terrain Explorer

Russian Wheel-Walking Rover


Posture Changing for Science and Work

JPL Nanorover

CMU Scarab


CMU Nomad

Dual-Use Locomotion Mechanisms

Suspension reconfiguration


Mobility for Teleoperation & Safeguarding

Significant inherent mobility features

All-wheel drive

In-plane, long-travel suspensions

Progressive-spring behavior passive suspensions

Geometric suspensions excellent too

Maximum wheel diameter (fewer could be better)

Skid-steered or explicitly steered

Velocity control adequate (for high-speed teleoperation)

Multiple wheels coupled to a single drivetrain (not always)

Sensing (absolute speed & vector, inclination, traction)


Closing Points

Well-designed mobility key to robotic performance

Use mechanics, geometry, analysis to design better robots

Rationalize subsystem selections

Blend methodological engineering and innovation to create high-performance systems

Test, test, test

Gladiator

Wheeled Robotic Mobility

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