Behavioral Strategies for Stable Maneuvers during Locomotion

by

Mu Qiao

A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree

Doctor of Philosophy

Approved August 2012 by the Graduate Supervisory Committee:

Devin Jindrich, Chair

Natalia Dounskaia James Abbas

Richard Hinrichs Marco Santello

ARIZONA STATE UNIVERSITY

December 2012

i

ABSTRACT

Humans moving in the environment must frequently change

walking speed and direction to negotiate obstacles and maintain balance.

Maneuverability and stability requirements account for a significant part of

daily life. While constant-average-velocity (CAV) human locomotion in

walking and running has been studied extensively unsteady locomotion

has received far less attention. Although some studies have described the

biomechanics and neurophysiology of maneuvers, the underlying

mechanisms that humans employ to control unsteady running are still not

clear. My dissertation research investigated some of the biomechanical

and behavioral strategies used for stable unsteady locomotion. First, I

studied the behavioral level control of human sagittal plane running. I

tested whether humans could control running using strategies consistent

with simple and independent control laws that have been successfully

used to control monopod robots. I found that humans use strategies that

are consistent with the distributed feedback control strategies used by

bouncing robots. Humans changed leg force rather than stance duration to

control center of mass (COM) height. Humans adjusted foot placement

relative to a “neutral point” to change running speed increment between

consecutive flight phases, i.e. a “pogo-stick” rather than a “unicycle”

strategy was adopted to change running speed. Body pitch angle was

correlated by hip moments if a proportional-derivative relationship with

ii

time lags corresponding to pre-programmed reaction (87 ± 19 ms) was

assumed. To better understand the mechanisms of performing successful

maneuvers, I studied the functions of joints in the lower extremities to

control COM speed and height. I found that during stance, the hip

functioned as a power generator to change speed. The ankle switched

between roles as a damper and torsional spring to contributing both to

speed and elevation changes. The knee facilitated both speed and

elevation control by absorbing mechanical energy, although its

contribution was less than hip or ankle. Finally, I studied human turning in

the horizontal plane. I used a morphological perturbation (increased body

rotational inertia) to elicit compensational strategies used to control

sidestep cutting turns. Humans use changes to initial body angular speed

and body pre-rotation to prevent changes in braking forces.

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DEDICATION

To my mum, Ping Zhang, and dad, Xianbo Qiao. I love you!

To my friends whose encouragement and pray helped me to walk

through my hard time!

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ACKNOWLEDGMENTS

I am grateful to my supervisor Prof. Devin L. Jindrich for his

invaluable help during my PhD studies. Talks and meetings across years

cultivated me the way to do scientific reasoning by asking appropriate and

important questions rather than merely focusing on methods to solve

them. Careful comments in those manuscripts shaped me the do scientific

writing. Those unselfish and cogent comments will be infinite help in my

career.

My special thanks also go to my dissertation committees, Prof.

Marco Santello, Prof. Richard Hinrichs, Prof. James Abbas, and Prof.

Natalia Dounskaia, whose advice through many semester meetings and

help out of class benefit me from different research areas.

Department staffs, Penny Pandelisev, provided me many useful

suggestions during my study in kinesiology program. Technician, Jamie

Stovall, helped me to arrange the schedule of gait lab facilities in Center of

Adaptive Neural Systems. Computer technician, Guy Anderson, spent his

time to fix my computer failures and internet problems. Prof. Shannon

Ringenbach also gave me a lot of support at ASU.

Besides, I would like to thank my friends while I was in the LIMB

lab. They were undergraduates, Alex Wilson, David Morrison, Marc

Surdyka, graduates, Kari Rich, Mark Hughes, Chih-Chia Chen, Xianglong

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Meng, and postdocs Wei Zhang, Cecil Lozano, Mark Jesunathadas. I

enjoyed the time with them.

I was also awarded twice (2008 and 2010) the Douglas L. Conley

Memorial scholarships from the former kinesiology department which

funded some of the locomotion experiments.

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"Just go on… and faith will soon return."

[To a friend hesitant with respect to infinitesimals.]

D’Alembert, Jean le Rond (1717-1783)

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TABLE OF CONTENTS

Page

LIST OF TABLES ......................................................................................... ix

LIST OF FIGURES ........................................................................................ x

LIST OF SYMBOLS / NOMENCLATURE ................................................... xiii

CHAPTER

1 INTRODUCTION ....................................................................... 1

2 TASK-LEVEL STRATEGIES OF HUMAN SAGITTAL-PLANE

RUNNING MANEUVERS ..................................................... 5

Abstract .................................................................................... 5

Introduction .............................................................................. 7

Materials and methods .......................................................... 11

Results ................................................................................... 16

Discussion ............................................................................. 21

3 JOINTS IN LOWER EXTREMITIES SHOW FUNCTIONAL

PREFERENCE IN RUNNING MANEUVERBILITY ............ 40

Abstract .................................................................................. 40

Introduction ............................................................................ 42

Materials and methods .......................................................... 46

Results ................................................................................... 50

Discussion ............................................................................. 54

viii

CHAPTER Page

4 BEHAVIORAL COMPENSATIONS FOR INCREASED

ROTATIONAL INERTIA DURING HUMAN CUTTING

TURNS ................................................................................ 68

Abstract .................................................................................. 68

Introduction ............................................................................ 69

Materials and methods .......................................................... 73

Results ................................................................................... 79

Discussion ............................................................................. 82

Turning model ........................................................................ 87

5 SUMMARY ............................................................................... 99

References ............................................................................................... 103

Appendix

A INSTITUTIONAL REVIWE BOARD/HUMAN SUBJECT

APPROVAL FORMS ON DATA COLLECTION IN

CHAPTER 2, 3, and 4 ....................................................... 118

B STATEMENT ON AUTHORS' PERMISSION .................... 122

Biographical Sketch ................................................................................... 124

ix

LIST OF TABLES

Table Page

2.1 Parameters in PD controller with/without lag ........................ 30

4.1 Variables measured in different rotational inertias in TURN

tasks ....................................................................................... 90

x

LIST OF FIGURES

Figure Page

2.1 Variable definitions and experiment setup ............................. 31

2.2 Definitions on leg force, virtual leg force, and leg spring ....... 32

2.3 Work look, leg force, stiffness, and increment of COM apex in

constant speed running, stepping up and down tasks ......... 34

2.4 Relationship between foot placement and speed increment .. 35

2.5 Relationship between hip joint moment, leg force, and speed

increment (dependent variable) ............................................. 36

2.6 Body pitch angle and angular speed, coefficient of

determination as a function of lag, and hip moment generated

by using the parameters from optimal lag ........................... 37

2.7 Simulated body pitch angle and angular speed using the

parameters determined from optimal lag ............................. 39

3.1 Experiment setup in dual-goal task, definitions on dependent

variables, definition on joint moment in the lower extremities,

and the moment arm of ground reaction force relative hip, knee

and ankle ................................................................................ 59

3.2 Hip work, moment, excursion, and moment arm relative to

ground reaction force in all dual-goal conditions .................... 61

xi

Figure Page

3.3. The times series of hip moment, angle, power, and work loop

during stance phase in all speed increment and COM elevation

conditions ............................................................................... 62

3.4 Ankle work, moment, excursion, and moment arm relative to

ground reaction force in all dual-goal conditions .................... 63

3.5 The times series of ankle moment, angle, power, and work loop

during stance phase in all speed increment and COM elevation

conditions ............................................................................... 64

3.6 Knee work, moment, excursion, and moment arm relative to

ground reaction force in all dual-goal conditions .................... 65

3.7 The times series of knee moment, angle, power, and work loop

during stance phase in all speed increment and COM elevation

conditions ............................................................................... 66

3.8 The relationship between hip work, ankle work with kinetic and

potential energy increment ..................................................... 67

4.1 Horizontal plane turning model and harness used to change

body rotational inertia ............................................................. 91

4.2 Anterior-posterior and medio-lateral forces under different

rotational inertias .................................................................... 92

xii

Figure Page

4.3 Recorded braking force with predicted braking forces by taking

more parameters into the turning model ................................ 93

4.4 The components within body deflection angle (θd), rotational

angle (θr), and its components ............................................... 94

4.5 Recorded braking force with braking force predicted from

refined turning model .............................................................. 95

4.6 The contribution of different parameters within the turning more

to predicting braking force ...................................................... 96

4.7 Initial body rotational angular speed and body pre-rotation in

both sidestep cutting turns and straight running .................... 97

4.8 A comprehensive turning model in the horizontal plane ........ 98

xiii

LIST OF SYMBOLS / NOMENCLATURE

rANOVA repeated measure Analysis of Variance

ACC Acceleration running

AP Anterior-Posterior

bh Body height

bm, M Body mass

bw Body weight

CAV Constant average velocity

CNS Central Nervous System

COM Center of mass

COP Center of Pressure

CSR Constant speed running

DEC Deceleration running

Fr Froude number, √ ⁄

FP Force platform

g Acceleration due to gravity, 9.81m/s2

GRF Ground Reaction Force

hk COM apex in flight phase of step k

J The moment of inertia of upper extremities relative to hip in the

sagittal plane

ki The integrative parameter in the PID controller

xiv

kp The proportional parameter in the PD controller, Eq. 2

kx The gain between COP-to-NP distance and speed increment,

Eq. 1

l Leg length from foot to the greater trochanter

Macc the moment relative to hip caused by the acceleration of upper

body’s COM in the sagittal plane

Mg the moment relative to hip in sagittal plane caused by the

upper body’s COM

NP Neutral Point

PD Proportional-derivative

s.e.m standard error of the mean

std. Standard Deviation

SU Stepping Up

SD Stepping Down

t time

TD Touch Down

TO Take Off

Ts Stance duration, Eq. 2.1

vk COM horizontal speed at during the kth flight phase, Eq. 2.1

xf The horizontal plane displacement between foot and COM at

TD, Eq. 2.1

xv

Body pitch angle, Eq. 2.2

The desired pitch angle, Eq. 2.2

The time derivative of body pitch angle, Eq. 2.2

The sum of both hips’ extensional moment, Eq. 2.2

d substratum height

dhip Moment arm of GRF relative to hip

dknee Moment arm of GRF relative to knee

dankle Moment arm of GRF relative to ankle

MTP Metatarsophalangeal

Whip Hip work

Wknee Knee work

Wankle Ankle work

ΔEk COM kinetic energy increment between flight phase in step k

and k+1

ΔEp COM potential energy increment between apex in step k and

k+1

ΔSPEED the name of the factor on running speed increment

ACL Anterior Cruciate Ligament

AEP Anterior extreme position

imd initial original movement direction

Fhmax Predicted braking force

xvi

Fimd(t) AP direction GRF during turning task

Fp(t) ML direction GRF during turning task

Fpmax Peak ML GRF

F1 Predicted peak braking force, Eq. 4.3

F'1 Predicted peak braking force, Eq. 4.4

F1(+θi) Predicted peak braking force with pre-rotation correction

F'1(+θTz) Predicted peak braking force from Eq. 4.4 with free moment

correction

Izz Body rotational inertia

LGT Left Greater Trochanter

ML Medio-Lateral

PAMP,imd AP foot placement at TD

Pp ML foot placement relative to COM at TD

R Correction items in braking force prediction equation, Eq. 4.5

RGT Right Greater Trochanter

Tmax The amplitude of sine wave in free moment

Tz Free moment

VAEP,imd COM approaching speed at TD

ω0 Initial body rotational angular speed

β Measured peak braking force

α Alpha component in Fimd(t)

xvii

θα Body rotational angle caused by alpha component

θαFp Body rotational angle caused by the interaction between alpha

component and ML GRF

θr Body rotation angle

θd COM velocity deflection angle

θi Initial angular difference between COM velocity and body

orientation

θFp Rotational angle caused by ML GRF

θβ Rotational angle balanced by braking force

θTz Rotational angle caused by free moment

τ Stance duration

ε Leg effectiveness number

1

Chapter 1

INTRODUCTION

Humans use both walking and running to perform terrestrial

locomotion. At lower speeds walking is employed in which the body center

of mass (COM) vaults over a rigid stance leg (Alexander, 1996; Kuo,

2007). This can be modeled as an inverted pendulum in which potential

and kinetic energy are out of phase (Heglund, Willems, Penta, & Cavagna,

1995; Maloiy, Heglund, Prager, Cavagna, & Taylor, 1986). An optimal

walking speed exists when the exchange between potential and kinetic

energy are maximally out of phase (Cavagna, Thys, & Zamboni, 1976). At

higher speeds, running is employed where in the first half of the stance

phase both COM kinetic and potential energy are converted to elastic

energy which is later released back during the second half of stance

(Blickhan, 1989). A spring-mass template, Spring Loaded Inverted

Pendulum (SLIP), can represent the COM trajectory in running. Moreover,

walking and running can be unified by SLIP and the amount of the total

mechanical energy of the system determines the gait (Geyer, Seyfarth, &

Blickhan, 2006). Despite the simplicity of these template models, they

represent the COM trajectory and ground reaction force (GRF) for a

variety of terrestrial locomotors (Blickhan & Full, 1993).

However, SLIP is a conservative system whose mechanical energy

is maintained constant. Changes to locomotion, such as maneuvers,

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require adjustments to convert between potential and kinetic energy

and/or power absorption or generation (McGowan, Baudinette,

Usherwood, & Biewener, 2005). In daily life humans have to frequently

change their movement state by changing running speed, direction, and

compensate for perturbations (Glaister, Bernatz, Klute, & Orendurff, 2007;

Hof, Vermerris, & Gjaltema, 2010; McAndrew, Dingwell, & Wilken, 2010;

Peterson, Kautz, & Neptune, 2011). How humans change running state to

maneuver and maintain stability is not clear. However, relatively simple

control strategies of monopod robots regulate sagittal plane maneuvers

(Raibert, 1986). In Chapter 2 of this dissertation I tested whether humans

control running maneuvers using behavioral mechanisms consistent with

the control algorithms used by monopod robots. I hypothesized that

humans 1) changed leg force to control COM apex in aerial phase, 2)

adjusted foot placement to change running speed, and 3) the relationship

between hip moments and body pitch angle followed a proportional-

derivative control rule.

The segmental structure of human legs has several advantages

over simple spring-mass systems because joint properties can enlarge the

range of parameters for achieving stable locomotion (Rummel & Seyfarth,

2008). However, the presence of several joints increases the number of

strategies available to manage energy during locomotion. The principles

that determine joint function during unsteady locomotion remain unclear.

3

For example, during uphill running the hip is the primary power source

(Roberts & Belliveau, 2005), while ankle joint can also shift its function to

add energy as well (McGowan, Baudinette, & Biewener, 2005; Roberts,

Marsh, Weyand, & Taylor, 1997). Moreover, the ankle can contribute to

COM elevation because peak ankle power is associated to vertical COM

acceleration in stair climbing (Wilken, Sinitski, & Bagg, 2011), and ankle

work increases with substratum elevation (Rietdyk, 2006). For the knee, a

linear relationship between moment and ankle has been observed

indicating its behavior as a torsional spring with little net work production

or absorption (Günther & Blickhan, 2002). Do all joints or some of the

joints in the lower extremities contribute to the change of running speed or

COM elevation? In Chapter 3 of this dissertation I tested whether where

was a preference for using individual leg joints to change either COM

speed or elevation. I hypothesized that during sagittal plane

maneuverability tasks 1) hip contributed to COM speed increment, 2)

ankle favored COM elevation control, and 3) knee functioned as a

torsional spring.

Besides changing speed magnitude in sagittal plane, humans also

have to change speed direction in the horizontal plane by making turns.

Turning involves matching COM speed deflection with body rotation.

Previous studies have hypothesized that braking forces (deceleratory

forces in the initial fore-aft movement direction) could be used to control

4

body rotation during cutting turns (Jindrich, Besier, & Lloyd, 2006).

However, several alternative strategies are available, such as changing

foot placement, stance period, or initial conditions. In Chapter 4 of this

dissertation I tested whether braking forces were used to control body

rotation during turning. In order to elicit those strategies, I used a

morphological perturbation, increasing body rotational inertia up to 4 times

the normal, to test the strategies used by humans to perform sidestep

cutting turns. Based on a previously-developed model of turning, I

hypothesized that increased body rotational inertia would decrease

braking force.

5

Chapter 2

TASK-LEVEL STRATEGIES OF HUMAN SAGITTAL-PLANE RUNNING

MANEUVERS

ABSTRACT

The strategies that humans use to control locomotion are not well

understood. A “spring-mass” template with body mass bouncing over

ground by a sprung leg can account for both the trajectory of center of

mass and ground reaction forces. Legged robots that operate as “spring-

mass” systems can maintain stable motion using relatively simple,

distributed feedback rules. I tested whether the changes to sagittal-plane

movement parameters on leg force, foot placements, and hip moments

during five running tasks involving active changes to running height in

aerial phase, speed, and orientation were consistent with the rules used

by bouncing monopod robots to achieve maneuverability. Changes to

running height were associated with changes to leg force but not stance

duration. To change speed, humans primarily used a “pogo stick” strategy

similar to “spring-mass”, where speed changes were associated with

adjustments to fore-aft foot placement, and not a “unicycle” strategy

involving systematic changes to stance leg hip moment. However, hip

moments were related to changes to body orientation and angular speed.

Hip moments could be described with first order proportional-derivative

relationship to trunk pitch if a time lag of 87±19ms was included. Overall,

6

the task-level strategies used for body control in humans were consistent

with the strategies employed by bouncing robots.

7

INTRODUCTION

How do humans control walking and running? Although locomotion

is an important motor behavior, the strategies used for body control are

not well understood. Legs can act like springs to store and release

mechanical energy and reduce metabolic cost (Alexander, 1991). Spring-

like properties can describe leg mechanics, and may potentially be control

targets (Farley, Glasheen, & McMahon, 1993). For example, humans

adjust leg spring stiffness to maintain a relatively constant center of mass

(COM) displacement (Ferris, Louie, & Farley, 1998). Although legs may

often resemble symmetrical, Hookean springs, asymmetries between

compression and thrust mechanics may also be functional (Cavagna &

Legramandi, 2009).

In addition to force, energy and power requirements, constant-

speed locomotion also requires stability. Stability can be defined as

maintaining non-divergent patterns of cyclic movement over time (Full,

Kubow, Schmitt, Holmes, & Koditschek, 2002). Challenges to stability, as

posed by age or disease, are associated with shorter strides and wider

stance (Jindrich & Qiao, 2009; Kuo & Donelan, 2010). However, the rules

governing how leg spring stiffness, foot placement, ground reaction forces

(GRFs), muscle activity and other variables are adjusted to stabilize

locomotion and maneuver remain largely uncharacterized (Biewener &

Daley, 2007).

8

A spring-mass model, where the body is approximated as a point

mass and the leg approximated by a linear spring, can successfully

capture many aspects of locomotion mechanics (Full & Koditschek, 1999;

Geyer et al., 2006). Spring-mass systems like runners can benefit from

passive mechanical stability, augmented by relatively simple adjustments

like leg retraction and changes to end-of-swing leg stiffness (Grimmer,

Ernst, Günther, & Blickhan, 2008; Seyfarth, Geyer, & Heff, 2003).

However, passive dynamic stability may be limited to specific ranges of

parameters, and only able to reject small perturbations to movement

(Abdallah & Waldron, 2009; Cham & Cutkosky, 2007; Ringrose, 1997;

Rummel & Seyfarth, 2008). Consequently, anticipation and feedback are

also necessary for robust bipedalism in a variable environment (Müller &

Blickhan, 2010).

Although anticipation is often used for maneuvers, robotics

research has shown that independent, distributed feedback rules can

stabilize bipedal locomotion. For example, Raibert and colleagues built

stable monopods by independently controlling hopping height with leg

thrust force, forward speed with foot placement, and body attitude with hip

moments (Raibert, 1986). Analogous principles can be used for bipedal

robot walking that foot placement within the capture region can prevent

from falling under push (Pratt, 2006). Humans in walking also adjust foot

placement relative to the foot placement estimator , which is used to

9

restore stability from falling, to maintain balance in sagittal plane (Millard,

Wight, McPhee, Kubica, & Wang, 2009). That feedback strategies can

stabilize both walking and running robots presents the question of whether

humans could employ similar mechanisms.

This study sought to describe the strategies used by humans for

body control during locomotion. Specifically, I tested the hypothesis that

humans actively change running height (COM apex in flight phase),

forward speed, and body attitude during sagittal plane running using

strategies consistent with those used by Raibert’s robots. I chose these

specific control laws because they are simple enough to serve as

experimentally testable hypotheses, have rules to account for both

translational and rotational stability, and, importantly, have been

demonstrated to work together to stabilize running robots over level

ground. They therefore represent strategies that, together, are sufficient to

provide a basis of stability for spring-mass systems. In addition, they are

relationships that could potentially be available to organize more complex

maneuvers. I therefore investigated whether (1) running height is related

to leg thrust, and not the alternative strategy of increasing stance duration

(Cham & Cutkosky, 2007); (2) speed changes are linearly correlated to

foot placement, i.e. the distance from the center of pressure (COP) to a

“Neutral Point” (NP); and (3) a proportional-derivative (PD) function can

describe the relationship between hip moments and trunk pitch, during

10

running tasks involving changes to running height, speed, and pitch. In

addition, I also sought to determine whether legs act as symmetrical

springs during maneuvers, or whether leg properties differ during the

compression and thrust phases of stance.

11

MATERIALS AND METHODS

Tasks and participants. I recruited 16 males (age 27±4years;

body mass 70±8kg; height 177±7cm, mean±std) during five tasks requiring

changes to COM height and running speed, while maintaining body

orientation: constant-average-speed running (CSR), stepping up (SU),

stepping down (SD), acceleration (ACC), and deceleration (DEC).

Participants selected a comfortable speed during approximately 10 warm-

ups. For the SU and SD tasks, a wooden runway (20cm high) was placed

either 94cm behind the 2nd platform (SU) or in front of the 1st platform

(SD). For SU only the step before takeoff (i.e. before the change in ground

level, and for SD only the step after landing was analyzed. For ACC, CSR,

and DEC both steps were used for analysis. For ACC and DEC,

participants accelerated (decelerated) to their comfortable speed between

two ground markers 5 meters apart. The task order was randomized, and

a short (5 min) rest was provided if requested. Because participants could

not see the locations of force platforms under the rubber mat, I was able to

select starting positions that maximized the probability of successive steps

on both platforms without informing the participants about the locations of

the platforms or the purpose of the adjustments to starting position. Each

participant performed approximately 50 trials to result in 25 successful

trials: 5 replicates for each task. All procedures were approved by the

Arizona State University Institutional Review Board.

12

Data collection. I collected whole-body 3-D kinematics by tracking

39 markers (Plug-In-Gait marker set) from 10-camera motion tracking

system at 120Hz (VICON® 612, Oxford Metrics Ltd., Oxford, UK). For all

tasks, participants ran from a starting position, over two 0.6×0.4m force

platforms (FPs) sampling at 3000Hz (FP4060-NC, Bertec Corporation,

Columbus, OH, USA) covered by 120×160cm, 2mm-thick rubber mat

(Ironcompany, Lafayette, CA, USA), to a stopping position approximately

10m away (Fig. 2.1B). Dynamic tests using forces approximating human

peak forces (1900N) showed that the mats caused negligible force

attenuation (<0.5%) and cross-talk (<0.6%). Body mass, height, and leg

length (from the sole to the greater trochanter) were also measured.

Data analysis. The COM was calculated by segmental average

after inverse kinematics. Its trajectory was then refined by accounting for

GRF to yield accurate initial velocity at TD and TO(McGowan, Baudinette,

Usherwood, et al., 2005). Kinetic and kinematic data were filtered using a

4th-order, low-pass zero-lag Butterworth digital filter at 60Hz and 33Hz.

Inverse dynamics was used to calculate net joint moments (Huston, 1982).

Positive hip, knee, and ankle moments indicated extension, flexion, and

plantar flexion, respectively.

Data analysis was performed in MATLAB (R2011b, Mathworks,

Natick, MA, USA). Statistical power (0.93 across all participants by

13

assuming a low effect size of 0.15) for the regression analysis was

calculated by G*Power (3.0.10, Franz Faul, University Kiel, Germany).

To evaluate the running height hypothesis (1), I used repeated-

measures ANOVA to compare leg force, stiffness and stance duration

during CSR, SU, and SD (Keppel & Wickens, 2004). Post-hoc

comparisons were based on a Bonferroni procedure with Šidák correction

(p<(1–(1–α)1/c), c=(a–1)*a/2, a is the number of levels). Running height

was calculated by fitting a 2nd order polynomial to flight-phase vertical

COM position and selecting the maximum. Leg force was calculated as

the projection of the GRF onto a “virtual leg” vector connecting COP to

COM. The beginning of stance was identified as when the vertical GRF

increased for 60ms, and mid-stance as the instant of minimum “virtual leg”

length. The period from stance onset to mid-stance when the leg length

was minimum was defined as “compression;” the period from mid-stance

to take off as “thrust” (Fig. 2.2A). The average leg force in compression

and thrust phases were defined as compression and thrust forces,

respectively (Fig. 2.2B). I calculated leg stiffness by linear regression of

leg force relative to virtual leg length during thrust and compression (Fig.

2.2C).

To evaluate the running speed hypothesis (2), I calculated forward

speed and foot placement during CSR, ACC and DEC. Raibert’s control of

speed takes the form

14

( ) (1)

where xf is average COP position over the stance phase relative to the

COM, kx is a gain, vk and vk+1 are COM horizontal speeds in flight in two

consecutive steps. The NP relative to COM was calculated as half the

product of vk and subsequent stance duration (Ts; Fig. 2.1A). When COP

and NP coincide, there is zero net acceleration. I used linear regression to

test the relationship between xf –Ts·vk/2 and vk+1–vk.

To evaluate the body orientation hypothesis (3), body pitch angle ϕ

was estimated with a vector between the midpoints of the four pelvic

markers and the midpoint of the 7th cervical vertebra and clavicular

markers. Raibert’s control of body orientation takes the PD form

( ) (2)

where τ is the reaction moment of hip moment relative to upper

extremities. τ has the save positive direction as ϕ and is equal to the

algebra sum of both leg extension hip moments. ϕ is the trunk pitch

angle (Fig. 2.1A), ϕd is the desired pitch angle, and kp and kv are

gains (Fig. 2.1A).

Based on action and reaction law positive τ was the same as

the positive direction of . Negative kp and kv therefore suggests error

attenuation, such as due to negative feedback. I tested the

relationship between τ, , and its time derivative, , for Eq. 2 by using

linear regressions for each trial. However, given that time lags that

15

can be associated with neural control, I also determined whether

adding time delays resulted in substantial improvements to the fits.

For each 8.3ms increment, lag from 8.3 to 160ms (1 to 20 multiples of

each sampling period, 1/120Hz), Eq. (2) was evaluated using and

values from the given lag before τ, ( ) ( ( ) )

( ). The best fit lag maximized R2. I also used t-test to examine

whether the kp and kp were significantly different from zero.

To account for size differences, I normalized force by body weight

(bw), apex height by body height (bh), and expressed speed as a Froude

number (Fr), calculated as

√ , where l is leg length(Bullimore & Donelan,

2008). All values are mean±std except where indicated.

16

RESULTS

Changes to COM running height were associated with changes to

leg force and not the alternative of changing stance period. Stance periods

during SU (250±41ms) were not significantly different from CSR

(260±28ms, paired t-test, p=0.06). Stance periods during SD dropped by

7% to 243±34ms with respect to CSR (p<0.01). On average, mid-stance

instant was significantly later than the instant of peak leg force (5±4%

stance duration, paired t-test, p<0.001). For individual tasks, mid-stance

preceded peak force by 8±6% (ACC), 0±3% (CSR), -12±12% (DEC),

3±8% (SU), -23±9% (SD) stance duration. The hip height at TO in SU

(0.59±0.01bh) was significantly greater than CSR (0.56±0.01bh) (paired t-

test, p<0.001) indicating the adjustment of taking off according to the task

goal. Overall, these data support Hypothesis 1 that force magnitude, not

duration, is used to regulate running height.

Humans did not alter leg force uniformly over stance, but appeared

to independently change leg behavior during compression and thrust

phases. Under most conditions, a linear relationship between leg force

and length in loading and unloading that could be effectively described as

a “stiffness” (Fig. 2.3A-C). However, different tasks involved alterations to

leg stiffness during separate phases of stance. SU involved significant

changes to leg stiffness relative to CSR during thrust (17±8% decrease,

p<0.001), without significant changes during compression (p=0.25, Fig.

17

2.3E). This resulted in increases in average thrust forces that were 5-fold

larger (39±13%) than increases in compression (7±8%; Fig. 2.3D;

p<0.001). In SD, compression leg stiffness showed an abrupt decrease in

stiffness near mid-stance, causing overall leg stiffness during compression

to decrease significantly (41±8%, p<0.001), and average compression

force to increase 39±13% relative to CSR (p<0.001), In contrast, changes

to leg stiffness during thrust were small (6±6% increase, p<0.05). SU and

SD maneuvers both involved decreases in leg stiffness and increases in

leg force, but during different phases of stance. Moreover, SU and SD

incurred significant change of COM height change in two consecutive

flight phases (hk+1-hk) (p< 0.001, Fig. 2.3F).

Foot placement used for ACC, CSR, and DEC was consistent with

a NP strategy (supporting Hypothesis 2). Linear regressions performed

within individuals on COP-to-NP distance and speed increment were all

significant (slope of -2.1±0.25Fr/bh, R2=0.81±0.16, p<0.001), as was a

linear regression using pooled data (Fig. 2.4). Moreover, regressions

within tasks yielded significant correlations between speed increment and

COP-to-NP distance (slope of CSR -1.63Fr/bh, R2=0.42; ACC -1.4Fr/bh,

R2=0.67; DEC -1.36Fr/bh, R2=0.36, p<0.001).

Maintenance of body pitch was consistent with a PD feedback rule

to determine hip moments. Figure 6 AC indicated the history of ϕ(t) and

( ) during stance phase. During stance, increased, indicating that the

18

upper torso changed from leaning forward to back from ACC to DEC

(Table 1, Fig. 2.6A). Without time lags, gains in Eq. 2 fit to each trial in

stance were negative (kp=-16.4±14.4N·m/deg, t-test, p<0.001, kv=-

1.2±0.33N·m·s/deg, p<0.001, across all tasks, Table 1 for individual task).

Both negatives indicated that hip moments attenuated body posture from

reference. Moreover, the PD model could not describe hip moments well

(R2=0.51±0.14 across all tasks).

Inclusion of appropriate time lags, ( ) ( ( ) )

( ), substantially improved the linear fits (Table 1). Over all tasks,

adding a lag changed gains to kp=24±10N·m/deg, t-test, p<0.001, kv=-

0.65±0.37N·m·s/deg, p<0.001, R2=0.87±0.05. Positive proportional gains

indicated that hip moments deviates body posture away from . For each

trial I observed that at a certain lag R2 peaked. The average optimal lag

from all task trials was 87±19ms (Fig. 2.6B). The coefficient of

determination, R2, dropped off rapidly to either side of the 87ms. Including

the optimal task-specific lags for each trial in Eq. (2) and predicting hip

moments resulted in close matches to measured moments across all

trials, tasks and participants (Fig. 2.6D). Moreover, moment due to

proportional component contributed more than derivative components in τ.

The hypothesis that the relationship between hip moments and

trunk movement is consistent with a PD rule was supported by the failure

of other relationships to yield better fits. Both P-only (kp=-

19

14.1±12.4N·m/deg, p<0.001, R2=0.15±0.14) or D-only (kv=-

1.14±0.4N·m·s/deg, p<0.001, R2=0.28±0.09) controllers resulted in

significantly poorer fits compared to PD control. Moreover, a PID (I,

integrative) controller did not improve fits, but actually showed decreased

R2 (R2=0.64±0.13; kp=-30±15N·m/deg, p<0.001, kv=-1.0±0.5N·m·s/deg,

p<0.001, ki=-1.9±3.1N·m/(deg·s), p<0.05, t-test).

Anticipated maneuvers involved simultaneous changes to more

than one parameter. For example, stance leg hip moment, which was the

time average of hip moment during stance phase, that could contribute to

acceleration were significantly correlated to speed increment (Fig. 2.5A)

(p<0.001). However, regressions within tasks showed significant but weak

relationships (R2=0.01, p<0.001 in ACC, R2=0.1, p<0.001 in CSR,

R2=0.18, p<0.001 in DEC), suggesting that between-task differences

reflected task-, not speed-, dependent changes to hip moment. When

correlating ankle moment, time average during stance phase, with speed

increment, the same pattern as hip moment was observed: the pooled

regression had a slope of 2.9Fr/(bw·bh), R2=0.36, but within-task fits were

poor (1.1Fr/(bw·bh), R2=0.13 ACC; 0.46Fr/(bw·bh), R2=0.02 CSR;

1.5Fr/(bw·bh), R2=0.09 DEC). Similarly, although ACC and DEC involved

changes to leg force relative to CSR (16±13% increase in thrust, p<0.001,

and 13±12% decrease, p<0.001, in compression during ACC, 16±7%

decrease in thrust, p<0.001, and 4±8% increase in compression, p=0.06,

20

during DEC), leg forces were only weakly correlated to speed increment

within each condition (R2 of 0.06, 0.19, 0.16 for thrust and 0.29, 0.12, 0.14

for compression for ACC, CSR, and DEC, respectively; Fig. 2.5B,C).

SU and SD tasks were also associated with foot placement

changes (0.02±0.016bh anterior and 0.014±0.017bh posterior to NP for

SU and SD, respectively). However, these shifts did not substantially alter

the relationship between speed increment and COP-to-NP distance from

CSR, ACC, and DEC, apart from a steeper slope for SU (compare Fig.

2.5D to Fig. 2.4).

21

DISCUSSION

Although anticipated maneuvers involved task-dependent changes

to multiple parameters, the underlying relationships among parameters

remained consistent with the control strategies used by Raibert’s robots.

Changes to COM height require changes to vertical force impulses (Müller

& Blickhan, 2010). For both SU and SD tasks, humans changed leg force

magnitude, not duration or peak phase, to change running height. Speed

changes were correlated with foot placement but not strongly with stance

leg hip moment or leg force. Hip moments were consistent with a PD

relationship to body pitch with a 87ms lag.

Increases in thrust force during SU and compression during SD

were both associated with decreased leg stiffness that facilitated energy

release or absorption. For example, increasing thrust force in SU resulted

from more leg compliance and greater excursion during thrust than during

compression, forming a clockwise work loop between leg force and virtual

leg length and net work production (Fig. 2.3B). For SD, the behavior of the

leg during compression showed a shift near mid-stance to a period of high

compliance and negative work. Negative work during compression was

similar to birds stepping down, where the energy was absorbed in the

hip(Daley, Felix, & Biewener, 2007).

Although the stance leg is often described with a single stiffness

(Ferris et al., 1998), these patterns during maneuvers appear to represent

22

functionally relevant asymmetries between compression and thrust

(Cavagna & Legramandi, 2009). During SU overall stance stiffness was

not different from CSR, consistent with the unchanged stiffness found for

smaller (10cm) steps (Müller & Blickhan, 2010). However, apparently

independent changes to stiffness during thrust and compression for SU

and SD, respectively, suggest that overall stiffness may not sufficiently

characterize leg mechanics during maneuvers.

Humans changed speed during ACC or DEC by adjusting foot

placement consistent with a “Neutral Point” strategy. Primarily using foot

placement to change speed could allow human legs to function like the

telescoping legs of Raibert’s robots. For example, during long jumps a

lower angle of attack (AOA; i.e. positive “COP-to-NP distance”) results in

lower horizontal velocity and decreased jumping distance (Seyfarth,

Friedrichs, Wank, & Blickhan, 1999). Foot placement can be used to

determine the conversion between potential and kinetic energy (Daley &

Biewener, 2006; McGowan, Baudinette, Usherwood, et al., 2005).

However, other mechanisms, such as increasing leg length in thrust, are

also available for controlling energy (Abdallah & Waldron, 2009). I

observed strategies consistent with a linear control rule and the legs

acting as telescoping springs. The observed changes in foot placement

are consistent with those found during walking, where the COM

acceleration is proportional to the horizontal distance between COP and

23

COM (Winter, 1995). The way controlling foot placement for maneuver is

similar in stability tasks as birds adjust the initial foot position from limb

retraction determining the joint mechanics during stance phase (Daley,

Usherwood, Felix, & Biewener, 2006). Foot placement during walking is

also used to maintain lateral stability, potentially reflecting relatively simple

predictive rules (Hof, 2008). Moreover, such a maneuver may also be

applicable in horizontal turning where COM decelerates in AP and

accelerates in ML direction. Expanding the foot placement control law to

2D in the horizontal plane would also provide understanding of human

turning maneuvers (Jindrich et al., 2006). This presents the possibility that

shared strategies are used for both walking and running.

A telescoping or “pogo stick” strategy decouples torso translation

from rotation and could facilitate the use of independent strategies to

control translation and rotation. The alternative, a “unicycle” strategy,

where fore-aft forces are generated by increased stance leg hip moment

without alterations to contact placement, was not observed (Fig. 2.5A).

This does not, however, diminish the role of joint moments for powering

running because in the “unicycle” hip is the only power source(Roberts &

Belliveau, 2005). Aligning GRF along the leg orientation has the

advantage that it increases the effective muscular advantage which then

reduces the efforts in muscular force of hip flexors/extensors in providing

hip moment. Hip flexors contribute to braking in early stance phase and

24

plantar flexors to COM propulsion in the 2nd half of stance (Hamner, Seth,

& Delp, 2010). For the distal joints, in the ACC task, ankle moments

accounted for 36% of the speed increment, potentially preventing running

height decreases.

The behavioral of proximal joints may be reflected from more

centralized control than the distal joint. The proximal muscles in the lower

extremities are under feed forward control while the distal muscles are

load sensitive indicating feedback control (Biewener & Daley, 2007; Daley

et al., 2007). For humans maneuvers mainly require anticipation in a feed

forward control initiated from hip to foot placement based on the transient

temporal requirement, and long-time neural communication to cortical

level may be too late (Blickhan et al., 2007). Without centralized feedback

the ability to adjust movement is limited as it relies on the ballistics of

mechanics and uses the preflex within the muscles to absorb the

perturbation (Biewener & Daley, 2007; Jindrich & Full, 2002). Hence, feed

forward control on foot placement, such as in turning, speed increment,

and obstacle clearance, are important in injury prevention for the distal

joints because it is too late to apply active muscular force to prevent tissue

from over loading in fast movements (Williams, Chmielewski, Rudoph,

Buchanan, & Snyder-Mackler, 2001). Although anticipated maneuvers

were associated with task-related changes to leg force and hip moment,

these changes did not appear to affect the relationship of speed increment

25

to foot placement. Task-specific offsets to locomotion parameters may

therefore be superimposed onto body control strategies, potentially

representing a de-coupling of task-specific changes from underlying

locomotory patterns (Khatib et al., 2009).

The relationship between body pitch and hip moments were

consistent with a PD strategy common to many robotic applications.

Behavior consistent with PD control can also be found in biology. Flies use

behavior consistent with PD control with delays of several wing beats to

overcome yaw perturbations and maintain their original movement

direction and orientation (Ristroph et al., 2010). Cockroaches also exhibit

behavior consistent with PD control during wall following (Cowan, Lee, &

Full, 2006; J. Lee et al., 2008).

Mechanical factors such as segmental inertias and intrinsic

musculoskeletal properties can contribute to stability at very rapid

timescales (Hasan, 2005). However, I found evidence for the presence of

time delays associated with maintaining body attitude. The average

optimum time delays of 87ms are closest to those associated with rapid,

pre-programmed reactions (Dietz, Quintern, & Sillem, 1987; Latash,

1998). Because the tasks involve maneuvers with which participants had

extensive experience, the use of programmed motor strategies that could

enhance stability and reduce injury risk is reasonable (Williams et al.,

2001).

26

For stable systems using PD control, gains must be appropriate to

resist perturbations and return the system to a desired state. Body attitude

control was simplified in Raibert’s hoppers by locating the COM very near

the hip, reducing hip moments due to body inertia and gravity(Raibert,

1986). The positive P gains, kp, found from the best fit with lag suggested

positive feedback and a source of instability. However, together with lag,

its dynamics response needs more examination. Further, even an

unstable controller in τ(t) does not exclude the stability of ϕ(t) because it

may experience complex long cyclical pattern of stability when extending

to local and orbital stability realms(Dingwell & Kang, 2007). Finally, to test

the stability of the controller in regulating body pitch angle, I simulated the

trunk motion starting at its angle and angular velocity at the optimal lag

after the beginning of stance, and integrated forward by using τ

determined from ( ) ( ( ) ) ( ). It demonstrated

that the pattern of motion was reasonable and the action of the PD

controller with delay could lead to a re-entrant pattern of trunk rotational

position/velocity (Fig. 2.7A,B).

Our experiments studied body control during anticipated changes to

running height or speed. However, I observed that humans changed

parameters that were consistent with those used by the distributed,

independent feedback rules used by Raibert’s robots to maintain stability.

This presents the possibility that locomotion in humans involves task-level

27

feedback rules that relate movement parameters to behavioral

adjustments. The ability of task-level rules to control locomotion, a

mechanically complex behavior involving many muscles, could be

facilitated by physiological organization at several levels. Muscle and

reflex properties can contribute to mechanical stability of the limbs (Rack

& Westbury, 1974). Muscle groups may be activated to achieve specific

movement objectives (Tresch & Jarc, 2009). Synergistic activity at the

spinal or brainstem level could also contribute to the sensing and control

of higher-order parameters such as leg orientation and endpoint (Bizzi,

Mussaivaldi, & Giszter, 1991). Consequently, task-level policies could be

separated from the complexity of neuromuscular structure and dynamics.

This correlational study of sagittal-plane maneuvering behavior was

not designed to provide a test of the underlying control mechanisms used

by humans to maintain stability or execute maneuvers. Although these

results are consistent with distributed feedback rules, they do not exclude

other motor control structures, such as central, model-based control, could

also result in the observed correlations. Moreover, these results also do

not exclude the possibility that locomotion control is task-specific, phase-

dependent, or involves several mechanisms operating hierarchically or in

parallel. These experiments on anticipated maneuvers also do not

establish that simple control rules are sufficient for, or employed by,

humans to maintain stability. Perturbation and neurophysiological studies

28

will be necessary address these limitations and distinguish among the

many potential mechanisms that could underlie unsteady locomotion

performance.

The design of monopod robot decouples the control laws from three

different aspects of locomotion (Raibert, 1986). Controlling leg force to

increase COM aerial height can still possibly cause additional forward

momentum to increase running speed. Hence, it depends on the task in

which humans 1) switch to different controls, 2) couples them, or 3)

employ them all. Locomotors use the conversion mechanism between

kinetic and potential energy to increase running height while decelerating

(Abdallah & Waldron, 2009; McGowan, Baudinette, Usherwood, et al.,

2005). Substratum height drop also incurs compensation strategies by

switching to speed increment which is not perturbed (Daley et al., 2006).

Factorial design experiment with independent control of COM aerial height

and speed increment will further elicit the relationships among control laws

humans adopt in maneuver.

Moreover, the possibility of task-level rules does not diminish the

importance of anticipation for stability and maneuverability. For example,

maintaining speed through foot placement relative to NP requires

estimation of NP. In complex natural environments, locomotion must be

continuously adjusted to account for changes due to substratum

compliance and incline (Ferris et al., 1998; Roberts & Belliveau, 2005).

29

Anticipatory adjustments and learning provide continuous modulation of

motor output (Reisman, Bastian, & Morton, 2010). Finally, whether running

humans use reactive strategies in response to external perturbations

similar to the proactive strategies I studied remains to be determined.

30

Table 2.1

Parameters in Eq. 2 for different tasks with/without best lag added

tasks kp (N·m/deg) kv (N·m·s/deg) ϕd (deg) lag (ms) R2

ACC -25±17 -1.3±0.73 74±6.7 0.67±0.17 ACClag 20±20 -1.3±0.63 70±7.3 50±26 0.87±0.13

CSR -20±17 -1.3±0.45 85±4.6 0.57±0.19 CSRlag 40±23 -0.39±0.67 83±4.4 110±20 0.92±0.057

DEC -9.6±18 -0.82±0.38 94±7 0.42±0.16 DEClag 21±23 -0.43±0.67 92±7.2 90±25 0.85±0.15

SU -21±18 -1.3±0.35 83±5.1 0.65±0.21

SUlag 26±15 -0.55±0.52 80±4 98±26 0.93±0.057

SD -14±15 -1.2±0.84 84±5.3 0.4±0.18 SDlag 17±8.1 -0.51±0.31 81±4.8 90±22 0.84±0.098

31

Figure 2.1 Methods used to evaluate body control strategies for running.

(A) Definition of parameters: running height (hk+1), leg force (projection of

GRF on vector COP-COM), components of the NP strategy for

maintaining forward running speed, and definition of body orientation ( ).

(B) Experimental coordinates and force platform setup. Dashed line box

indicates dimensions of rubber mat used to obscure the force platforms.

32

Figure 2.2 (A) Virtual leg length during stance phase. Middle stance was

defined as the instant of minimum leg length. (B) Leg force during stance

phase. (C) The relationship between leg length and force was plotted as a

work loop. In the compression (loading) phase leg length decreased and

leg force increased (red dashed and dot line). In the thrust (unloading)

phase leg length increased and leg force decreased (blue dashed and dot

line). A linear fit was used to account for the relationship between leg

length and force in each phase (red in loading, blue in unloading). The

slope of that linear fit was defined by the leg spring stiffness. According to

the definitions on leg force and length, clockwise work loop indicated

additional energy was added to the system. All trials within each condition

33

were averaged first, then averaged across all conditions and participants.

Shade areas are mean±s.e.m.

34

Figure 2.3 The relationship between leg force (bw) and length (bh) during stance phase in CSR (A), SU (B), and SD (C).

Changes to (D) leg force (bw) and (E) stiffness (bw/leg length) during the compression and thrust phases of stance for

CSR, SU and SD. Interaction effect pAB was obtained by factorial repeated ANOVA (task and phase). (F) The COM height

change in two consecutive flight phases (hk+1 – hk) (Fig. 2.1A). * means p<0.05, ** means p<0.01, and *** means p<0.001.

35

Figure 2.4 Parameters contributing to speed change. Relationship

between COP-to-NP distance (bh) and speed increment (vk+1 – vk) (Froude

#) for ACC, DEC and CSR. For scatter plots, each participant is

represented by a different symbol and tasks by colors (Black: ACC; red:

CSR; blue: DEC).

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-0.3

-0.2

-0.1

0

0.1

0.2 Pooled slope = -2 intercept = 0

R2 = 0.79slope = -1.41

R2 = 0.67

slope = -1.63

R2 = 0.42

slope = -1.36

R2 = 0.36

COP-to-NP distance (bh)

Spe

ed

incre

me

nt

v k+

1-v

k (

Fro

ud

e #

)

36

Figure 2.5 Relationships between speed increment (vk+1 – vk) (Froude #) and independent variables (A) stance leg hip

moment (bw*bh), the time average of hip flexion (+)/extension (–) moment during stance phase, (B) compression (bw), (C)

thrust force (bw) for ACC, DEC and CSR. (D) Relationship between COP-to-NP distance (bh) and vk+1 – vk for SU

(magenta) and SD (green).

-0.05 0 0.05 0.1 0.15

-0.2

0

0.2

Pooled slope = 2.6

R2 = 0.4

ACC slope = -0.22

R2 = 0.01

CSR slope = 0.84

R2 = 0.1DEC

slope = 1.38

R2 = 0.18

Stance leg hip moment (bw*bh)

Spe

ed

incre

me

nt

(Fro

ud

e #

)

0.5 1 1.5 2

-0.2

0

0.2

Pooled slope = -0.3

R2 = 0.36

ACC slope = -0.13

R2 = 0.29CSR slope = -0.08

R2 = 0.12

DEC slope = -0.12

R2 = 0.14

Compression (bw)

Spe

ed

incre

me

nt

(Fro

ud

e #

)

0.5 1 1.5 2

-0.2

0

0.2Pooled slope = 0.3

R2 = 0.52 ACC

slope = 0.07

R2 = 0.06CSR

slope = 0.11

R2 = 0.19

DEC slope = 0.16

R2 = 0.23

Thrust (bw)

Spe

ed

incre

me

nt

(Fro

ud

e #

)

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

-0.2

0

0.2 SU slope = -2.85

R2 = 0.71

SD slope = -1.99

R2 = 0.63

COP-to-NP distance (bh)

Spe

ed

incre

me

nt

(Fro

ud

e #

)

BA

C D

37

Figure 2.6 Relationship of hip moments to body orientation. (A) ϕ(t) (C)

( ) during stance phase. Line colors corresponded to the tasks. (Black:

ACC; red: CSR; blue: DEC; magenta: SU; green SD). For ϕ(t) the

reference angles ϕd from each task were also indicated by the dashed

lines. (B) R2 in Eq. (2) as a function of lag. Shaded area indicates mean

standard errors. (D) Compare between real hip moment and predicted hip

moments. Raw hip moment was the sum of both legs' hip

flexion/extension moments (blue solid). The replicated trials for each

participant in each task were averaged first, and then were averaged

across all participants and tasks. Shaded area are mean±std. τ (PD, dash

and dotted) was predicted by (Eq. 2) using the lag associated with the

maximum R2. P (dashed) is the proportional portion of τ, while D (dotted)

38

is the derivative component of τ. τ, P, and D were first averaged from all

trials within each task then averaged across all participants for each task.

39

Figure 2.7 Feasibility of PD control for body pitch. Pitch angle ϕ(t) (A) and

angular speed ( ) (B) predicted by Eq. 2 in stance phase. Each trial was

simulated from the initial conditions ϕ(lag) and ( ) at optimal lag with

respect to TD. For each participant the simulation was implemented under

dde23 function of MATLAB ( ) [ ( ( ) ) ( )] .

J was the pitch direction moment of inertia of upper extremities relative to

the hip in sagittal plane. Due to the delay the beginning part of response

was shown by dotted line because they are generated by the time before

TD. For each participant all trials within each task were averaged then

averaged across all participants within a task.

0 20 40 60 80 100

70

80

90

100

110

stance phase (%)

(t

) (d

eg

)

A

0 20 40 60 80 100-100

-50

0

50

stance phase (%)

d(t

)/d

t (d

eg

/s) B

40

Chapter 3

JOINTS IN LOWER EXTREMITIES SHOW FUNCTIONAL

DIFFERENCES DURING RUNNING MANEUVERS

ABSTRACT

Studies of human locomotion have primarily focused on constant

average velocity (CAV) walking and running. However, the need to

change running speed is also important, and the mechanism used for

running maneuvers is still not clear. For example, how multi-joint legged

systems are coordinated to achieve the mechanical and behavioral goals

of maneuvers remains unclear. I studied the function of individual joints

from the lower extremities in running tasks where both center of mass

speed and elevation were required to change independently. I

hypothesized that the proximal joint, the hip, was the primary power

source for changing speed while the distal joint functioned as a torsional

spring and contributed to changing COM height. I found that the

hypothesis was supported. The hip contributed most to changing speed by

generating power while the ankle contributed most to COM elevation by

switching between a torsional spring and a damper. The knee absorbed

small amounts of energy, contributing to both speed and elevation control.

Musculoskeletal factors such as the role of bi-articular muscles and

muscle architecture were related to the division of labor among joints.

These results may provide insight on the design for humanoid legged

41

robots and movement assistance devices in lower extremities to improve

maneuvering performance.

Key words. Maneuverability, dual goal, stability, joint function,

running speed, running height, functional shift, power generator, spring,

damper, hip, ankle

42

INTRODUCTION

Research on constant average velocity (CAV) locomotion has

revealed important functional principles of behavior, biomechanics, and

the motor control of multiple muscle systems that underlie effective

performance (Novacheck, 1998). Movement in the environment also

requires unsteady locomotion: maneuvers and the maintenance of stability

(i.e. returning to a steady periodic trajectory following a perturbation).

Necessary maneuvers include acceleration/deceleration, negotiating

steps, and turning (Peterson et al., 2011). For older adults, maneuvers

such as gait initiation and obstacle clearance can be limits to mobility and

increase fall risks (Patla & Rietdyk, 1993; Winter, 1995). However,

comparatively little is known about the behavioral or physiological

principles that underlie unsteady locomotion (Jindrich and Qiao, 2009).

Several factors could contribute to effective performance of unsteady

locomotion. The body and limbs of terrestrial animals show mechanical

behavior similar to spring-mass systems, which could confer some

passive-dynamic stability (Biewener & Daley, 2007; Blickhan et al., 2007;

Ferris, Liang, & Farley, 1999). For example, recovery from sudden drops

in substratum or impulse perturbations may involve inherent limb passive

properties (Daley, Voloshina, & Biewener, 2009; Jindrich & Full, 2002).

Spring-mass systems can make adjustments by interconverting kinetic

and potential energy (Daley et al., 2007; McGowan, Baudinette,

43

Usherwood, et al., 2005). Control of foot placement can be used to govern

energy exchange (Daley & Biewener, 2006).

However, passive mechanisms alone are insufficient for locomotion in

a complex environment. Maintaining stability and executing maneuvers

requires the integration of body, limb and muscle dynamics with reflex

feedback and feed-forward neural control (van Emmerik, Hamill, &

McDermott, 2005). Compensatory forces and moments necessary to

return the center of mass (COM) to a desired trajectory are often

generated by changes to joint moments. For example, recovery from

stumbles involves increased leg moments (Pijnappels, Reeves,

Maganaris, & van Dieën, 2008). However, the task of controlling COM

movement by organizing changes to joint moments is indeterminate: many

combinations of moments at different joints could result in appropriate

responses. Consequently, how joint dynamics are organized to achieve

task-level goals has emerged as an important question (Chang, Roiz, &

Auyang, 2008).

Changes to joint moments could primarily be centered at a single

joint, or could involve synergistic changes at several joints. Muscle

properties may facilitate division of mechanical behavior among joints. For

example, the relatively short tendons typical of proximal-joint muscles may

favor power generation whereas distal joint muscles with longer tendons

may facilitate conservative energy storage and return (Biewener, 1998).

44

Consistent with this possibility, changes to hip moments are primarily

responsible for increased vertical work during incline running in humans

(Roberts & Belliveau, 2005). Power generation at the hip in dogs may also

be distinguishable from weight support at distal joints during maneuvers

(Usherwood & Wilson, 2005).

However, functional differences among joints may be task-specific.

Simulation studies have argued that knee moment determines the GRF

profiles in the stance phase of both high and long jumps (Alexander,

1990). A torsional spring can describe the relationship between knee

moment and angle (Günther & Blickhan, 2002), and knee can also

stabilize running because the segmental advantage to resist perturbation

(Rummel & Seyfarth, 2008). Distal joints can show shifts from

conservative behavior to power generation (Daley & Biewener, 2003;

Roberts et al., 1997). During acceleration, the ankle contributes to speed

increases (Roberts & Scales, 2002), while during deceleration, kinetic

energy is absorbed by the ankle, potentially reflecting transfer to proximal

joints via bi-articular muscles (McGowan, Baudinette, & Biewener, 2005).

Ankle is also used to raise the COM in elevated walking (Rietdyk, 2006),

and peak ankle power is correlated with peak COM vertical acceleration in

stair climbing (Wilken et al., 2011). Consequently, several strategies

involving functional alterations to both proximal and distal joints may be

available for performing unsteady locomotion. However, determined by

45

their muscular-tendon architecture, it may not be possible for all joints to

shift their function to different modalities, power producing motor/torsional

spring/damper, according to the task demand.

The factors that determine the joints employed, and the contributions

of energy exchange versus power generation and absorption during

unsteady locomotion have not been determined. I therefore sought to

investigate joint function during permutations of two tasks with potentially

divergent requirements: acceleration/deceleration and

ascending/descending steps. Those two tasks are the most frequent

maneuverability tasks in the sagittal plane. Compared with previous

studies on each task individually, this dual-goal paradigm 1) identified the

shift of the function of joints in the lower extremities, and 2) the preference

of an individual joints in contributing COM speed or elevation. Specifically,

I sought to address two general questions: 1) whether there is a

preference for individual joints to control COM speed or elevation, and 2)

whether maneuvering involves a reorganization of the work among joints

in the lower extremities in maneuverability tasks. I hypothesized that the 1)

proximal joint, the hip, favored COM speed control and functioned as a

power generator by delivering mechanical energy to COM, 2) the ankle,

favored COM elevation control and functioned as a torsional spring, and 3)

and knee also behaved as torsional spring in maneuverability tasks.

46

MATERIALS AND METHODS

Participants. Nine male college students (body mass (m) = 74.0 ± 8.2

kg, height (bh) = 1.78 ± 0.06 m, age = 27.1 ± 5.7 yrs., leg length = 0.984 ±

0.022 m, mean ± std) participated in the data collection. They were all free

of any movement related diseases or disorders. All the procedures were

approved by the Institutional Review Board of Arizona State University.

Each participant finished data collection within 2.5 hours at the gait lab in

the Center for Adaptive Neural Systems.

Data Capture. Whole body kinematics was recorded by using 10-

camera motion capture system at 120 Hz (VICON®, version 612, Oxford

Metrics, Oxford, UK). Reflective markers (14 mm in diameter) placement

was according to the Plug-In-Gait marker set. Two force platforms (400 ×

600 mm, FP4060-NC, Bertec Corporation, Columbus, OH, USA) were

used to record ground reaction force (GRF) at 3000Hz. The touch down

(TD) and take off (TO) of foot contact with force platform were determined

by 60ms continuous ascending and descending of vertical GRF. The first

force platform (FP1) was embedded within the cement ground while the

2nd (FP2) was accommodated by the substratum elevation (Fig. 3.1).

Experiment. I designed a dual-goal task with Factor A, ΔSPEED (3

levels: acceleration, ACC, constant speed running, CSR, and

deceleration, DEC) and Factor B, the substratum height (5 levels, -30cm, -

20cm, 0, 20cm, 30cm relative to the ground, height d in Fig. 3.1). By such

47

a setup COM speed and apex in two consecutive flight phases were

forces to change independently. In each condition 5 successful trials

determined by both feet placed completely on the force platforms were

recorded. FP1 recorded the taking off GRF of the right foot and FP2

recorded the landing GRF of the left foot (Fig. 3.1A). Although participants

could see the location of force platforms, before data collection an

appropriate starting position was chosen to maximize the likelihood of

stepping on the force platforms to reduce the effect of targeting.

Calculations. Kinematic data were upgraded to the same sampling

frequency of kinetic data by a spline fit. First, the Cartesian coordinates of

the markers were converted by inverse kinematics to the inter-joint-

anatomical angles of a 15 segment and 34-DOF multiple-rigid-body

human model (Fig. 3.1A) (Huston, 1982). The COM was determined by

segmental average. The joint angle histories were filtered by a 4th-order-

zero-lag low-pass Butterworth filter at 11Hz before differentiation obtaining

angular velocities. Angular velocities were filtered and differentiated again

to obtain the angular accelerations for inverse dynamics (Kuo, 1998).

Kinetic data were filtered at 60Hz. For the lower extremities, hip was

defined as a ball-and-socket joint while both knee and ankle were hinges

(Fig. 3.1B). The right hip angles, the orientation of thigh relative to the

lower torso, were defined by Cardan angles in the order of roll (adduction

(+)/abduction (-)), pitch (flexion (+)/extension (-)), and yaw (internal

48

(+)/external (-) rotation). Positive knee and ankle angles indicated knee

flexion and ankle dorsiflexion. The joint moments at hip, knee, and ankle

were relative the distal limb (Fig. 3.1B), which reflected the inherent

muscular effort in generating active force and passive property. Hip power

was determined by the instantaneous dot product of hip moment and thigh

angular speed vector. The work loop formed by joint moment and angle

caused non-zero net area where mechanical energy was

generated/dissipated.

All the calculations were performed by MATLAB code (2012a, Math

Works, Inc., Natick, MA, USA).

Statistics. I designed experiment to independently change the

increment of COM kinetic (ΔEk = ½·m·(vk+12-vk

2)) and potential energy

(ΔEp = mg·(hk+1-hk)) in two consecutive flight phases (step k and k+1 in

Fig. 3.1A). They then elicited the change of the work from all joints (Whip,

Wknee, and Wankle) on FP1. I used a two-way factorial repeated ANOVA to

determine the influence of the main factors (A: ΔSPEED with 3 levels,

ACC, CSR, and DEC; B: substratum height with5 levels, -30cm, -20cm,

0cm, 20cm, 30cm) (Keppel & Wickens, 2004). For post-hoc comparisons

Bonferroni procedure with Šidák correction was adopted (p < (1–(1–α)1/c),

c = (a–1)·a/2, a is the number of levels). Multiple linear regression was

also used to determine the relationship between the joint work and energy

49

increment. All values within the texts are mean ± standard deviation

unless indication.

50

RESULTS

Hip functions as a power generator and contributes to COM

speed increment. Under each condition hip generated positive work

indicating its power generator property (Fig. 3.2A, Fig 3.3EFGH). Hip

increased positive work in acceleration than deceleration under each

substratum elevation (p < 0.001, Fig. 3.2A, Fig. 3.8A). Hip work did not

contribute to COM elevation because hip work decreased as elevation

was required (p < 0.01 in ACC, p < 0.01 in CSR, p < 0.01 in DEC, Fig.

3.8D). These findings supported the 1st hypothesis that hip functioned as a

power producing motor in maneuverability tasks and had its preference in

speed control.

The contribution of hip work to COM speed increment was caused by

both greater hip extension moment and hip excursion (Fig. 3.2BC).

However, greater hip extension moment was not associated with greater

moment arm of GRF relative to hip (Fig. 3.2D), and greater hip excursion

was caused by more protraction of hip at stance beginning (Fig. 3.3C).

However, hip work contributed negatively to COM elevation that stepping

down incurred greater positive work (Fig. 3.2A). This was caused by the

increase of hip extension moment in stepping down rather than hip

excursion (Fig. 3.2BC, Fig. 3.3BD). The increase of hip extension moment

in stepping down was also not associated with the increase of moment

arm of GRF relative to hip (Fig. 3.2D).

51

Ankle behaves between a torsional spring and damper, and

contributes both to COM speed and elevation. Ankle moment

contributed to both COM speed and elevation control (pA < 0.01, pB <

0.05, Fig. 3.4B). Ankle work contributed to COM elevation greater than

speed control (Fig. 3.8BE). Ankle behaved differently from hip because

the sign of work changed between accelerations and deceleration,

stepping up and down (Fig. 3.4A). During deceleration or substratum

height drop, ankle switched its function from a torsional spring to a damper

(Fig. 3.5EFGH). Hence, the 2nd hypothesis that ankle contributed to

elevation was supported. Besides, I found that ankle adjusted its function

between a torsional spring and a damper to facilitate task goals.

In acceleration, more dorsiflexion at TD and greater plantar flexion at

TO resulted in more angle excursion and positive work (Fig. 3.4AC, Fig.

3.5CG). For stepping up, maintaining the same plantar flexion at TD ankle

increased plantar flexion at TO to increase work (Fig. 3.5DH). In stepping

up the moment arm of GRF relative to ankle did not change (Fig. 3.4D),

however, together with greater GRF, ankle moment was still greater under

plantar flexion (Fig. 3.4B). In deceleration greater plantar-flexion and more

dorsiflexion resulted in work dissipation (Fig. 5CG), while in stepping down

human only increase dorsiflexion at TO to absorb mechanical energy (Fig.

3.5D).

52

Knee contributes minimal work to maneuverability tasks and

does not behave as a spring. Knee contributed to COM elevation (pB <

0.01, Fig. 3.6A). However, the amount of knee work was close to zero and

less than hip and ankle indicating its contribution to COM mechanical

energy was minimal (Fig. 3.6A, Fig. 3.8CF). This was caused by the close-

to-zero knee moment associated with shorter moment arm relative to hip

and ankle (Fig. 3.6BD). Different from the ankle, knee did not conserve

work as a torsional spring and only absorbed work (Fig. 3.6A). Power

profiles showed fluctuation indicating offset between the positive and

negative work (Fig. 3.7EF). There was no linear relationship between

angle and moment in the work loop of knee (Fig. 3.7GH). This rejects the

3rd hypothesis that knee functioned as a torsional spring during human

sagittal plane maneuverability tasks.

The negative knee work was determined by opposite knee moment

and angle excursion. For speed control, in acceleration humans started

with more flexion and ended with less flexion resulting in more knee

excursion in extension (Fig. 3.7C), and this net extension excursion was

with flexion moment (In deceleration net flexion excursion was with

extension moment) (Fig. 3.6BC). Under each substratum height knee work

was determined by the magnitude and sign of both knee excursion and

moment (Fig. 3.6BC). Under each speed increment condition knee flexed

more under unchanged knee moment as substratum height increased,

53

and resulted in more work toward positive (Fig. 6ABC). Speed increment

or substratum height had no effect of GRF moment arm relative to knee

(Fig. 3.6D). Hence, the increase of knee moment in acceleration was

caused by the increase of GRF (Fig. 3.6B).

54

DISCUSSION

The aims of this study were to 1) determine the contribution of

individual joints from the lower extremities to change COM speed and

elevation, and 2) identify whether there is a functional preference of

individual joints specializing speed or elevation control. I found that in

sagittal plane maneuverability tasks where COM speed and elevation

changed independently: 1) hip functioned as power generator and favored

in speed control, 2) ankle favored both COM speed and elevation control

by switching its function between a torsional spring and damper, and 3)

knee functioned as damper and adjusted its work to fulfill the task goals.

Hip contributes to speed control by providing power. Hip favored

COM speed control over elevation control (Fig. 3.2A, Fig. 3.8AB). In

acceleration hip generated greater extension moment associated with the

decrease of effective muscular advantage as uphill running (Roberts &

Belliveau, 2005). In this study hip angle was defined relative to the upper

torso which was the inter-joint angle as extension/flexion. When converted

to the vertical axis, it resulted in less protraction at TD associated with

acceleration (Roberts & Scales, 2002). Together with more hip excursion

greater hip work was generated. Positive hip work increased from

deceleration to acceleration conforming to the fact that proximal joint

powering uphill running (Ferris, Sawicki, & Daley, 2007; Roberts &

Belliveau, 2005). However, hip's contribution to forward propulsion resides

55

at late swing and early stance (Riley, Croce, & Kerrigan, 2001). Hip

contributes to COM elevation negatively because stepping up in walking

also resulted in negative hip work (Rietdyk, 2006).

The analysis from the joint level, the relationship between joint

moment and angle, reflected the underlying muscular coordination.

Studies from unsteady bipedal locomotion revealed that there is a

functional difference, labor division, among the joints of lower extremities

(McGowan, Baudinette, & Biewener, 2005; Roberts, 2002). Hip primarily

functions as a power generator because the proximal joint muscles are

spanned with longer muscle fibers than tendon and favors power

generation (Biewener & Daley, 2007). Proximal limb muscle in the lower

extremities dominates power generation over distal muscles in incline

climbing (Biewener, McGowan, Card, & Baudinette, 2004).

Ankle favors both COM elevation and speed and behaves

between a torsional spring and a damper. Ankle provides support to

COM with assistance from knee extension moment (Kepple, Siegel, &

Stanhope, 1997). Elevating COM in walking requires greater ankle work

due to the up straight shank (Rietdyk, 2006; Wilken et al., 2011). Also,

ankle increases its stiffness to increase whole leg stiffness and increase

hopping height (Farley & Morgenroth, 1999). Further, induced acceleration

indicates that ankle only contributes to propulsion at low speeds (Riley et

al., 2001).

56

Ankle does not generate much positive work as hip because the

elastic behavior of the distal limb muscle limits its capability to generate

work (Biewener, McGowan, et al., 2004; Ker, Bennett, Bibby, Kester, &

Alexander, 1987). Generally, a linear spring existed between ankle

moment and angle in stepping up or acceleration tasks (Fig. 3.5GH). The

spring behavior can be compensated for by the bi-articular isometric

gastrocnemius and caused ankle to shift from a spring to generate limited

positive work by transferring energy flow from the proximal muscles

(McGowan, Baudinette, & Biewener, 2005). Stepping down resulted in the

power transferring from distal to proximal joints, and the negative ankle

work was performed by the bi-articular gastrocnemius and uni-articular

soleus with the former removing energy to proximal (Prilutsky &

Zatsiorsky, 1994). Although ankle power is negative, segmental power

analysis revealed that ankle contributed to trunk energy increment in

walking (Siegel, Kepple, & Stanhope, 2004).

Finally, it is possible that division of support and propulsion between

ankle and hip are inherently determined by the structure of the lower

extremities. For example, in standing ankle moment is used to balance

vertical GRF while hip only swings body forward and backward.

The switch of functional role of ankle between spring and damper was

similar to terrain perturbations on bipedal runners where the distal joints

behaves as a spring or damper depending on the leg orientation (Daley et

57

al., 2007). It also posted challenge to prosthetics design of distal limb

because the requirements from both adaption of stiffness and damping for

maneuverability (South, Fey, Bosker, & Neptune, 2010).

Knee contributed to both COM speed and elevation but its

amount is limited (Fig. 3.8CF). Knee contributed to 1) COM speed by

assisting ankle plantar flexion moment, and 2) COM support (Kepple et

al., 1997). Switching from walking to running increases the moment arm of

GRF relative to knee and requires more knee moment (Biewener, Farley,

Roberts, & Temaner, 2004). Knee moment changed its direction

frequently due to the smaller moment arm relative to GRF (Fig. 3.1C, Fig.

3.6D). From the muscular-tendon level due to the bi-articular muscles

(rectus femurs, gastrocnemius, and hamstring) transferring energy in and

out of it (Prilutsky & Zatsiorsky, 1994), knee balances the energy flow

among the segments in the stance leg (Siegel et al., 2004). Hence, the net

knee work was less than ankle or hip. Moreover, the muscles spanning

knee primarily functions to stabilize it rather than provide power (Williams

et al., 2001).

Unexplained and limitations. The foot was modeled as a single rigid

body without the Metatarsophalangeal (MTP) joint. However, this did not

alter the moment calculation of the joints in the lower extremities (Farris &

Sawicki, 2011). I also could not fully exclude the possibility that

participants identify on the location of force platform by using visual cue.

58

Anticipation of the upcoming substratum height in this study enabled

locomotors to adopt appropriate leg orientation at TD to reduce the load in

joints (Houck, Duncan, & de Haven, 2006). However, this targeting effect

was reduced by initial trial and error in determining the start position

(Grabiner, Feuerbach, Lundin, & Davis, 1995), and did not alter the joint

moments (de Vita, Torry, Glover, & Speroni, 1996; Farris & Sawicki,

2011).

During different percentages of gait cycle, joints in the lower

extremities propel or support torso (Sadeghi et al., 2001). In this study I

focused on the whole progress during stance phase which indicated the

integrated effect of induced acceleration of each instant in stance phase

(Kepple et al., 1997). This represented the average effect of individual

joints during whole gait cycles in running maneuvers.

Conclusions. In sagittal plane running maneuvers the joints in the

lower extremities showed functional preference in contributing to COM

speed and elevation control. Hip functioned as a power generator and

preferred in speed control, ankle switched between a torsional spring and

a damper and contributed to both COM speed and elevation control, and

knee mainly absorbs energy and adjusts its work according to the task

goals.

59

Figure 3.1 The setup of experiment for maneuverability. (A) Body postures

were at the instants of TD and TO on force platform 1 (FP1). COM

trajectory was indicated by dash and dotted line. The COM apex (hk) in

60

flight phase and associated horizontal speed (vk) in two consecutive steps

(k, k+1) were forced to change independently. The current figure is a

condition of deceleration (DEC) while stepping up 30cm. (B) The

definitions of joint angle and moment in the lower extremities. Hip was

defined as a ball-and-socket joint while both knee and ankle were hinges.

For hip moment three components were defined (adduction (+)/abduction

(-)), pitch (flexion (+)/extension (-)), and yaw (internal (+)/external (-)

rotation). Positive knee and ankle angles indicated knee flexion and ankle

plantar flexion, respectively. (C) Calculation of GRF moment arm with

respect to each joint in the lower extremities of stance leg.

61

Figure 3.2 The joint work (A), moment (flexion/extension) averaged during stance (B), excursion angle (joint angle

displacement) (C), and moment arm of GRF averaged during stance (D) for hip as influenced by the speed increment

(ΔSPEED, Factor A) and COM elevation (substratum height, d, Factor B). mean ± std.

-30cm -20cm 0cm 20cm 30cm-100

0

100

200

300

pA < 0.001

pB < 0.001

Hip

wo

rk (

J)

A ACC

CSR

DEC

-30cm -20cm 0cm 20cm 30cm50

100

150

200

250

pA < 0.05

pB < 0.05 H

ip m

om

en

t (N

m)

B

-30cm -20cm 0cm 20cm 30cm0

20

40

60

80

pAB

< 0.001

Hip

excu

rsio

n (

deg

)

C

-30cm -20cm 0cm 20cm 30cm0

5

10

Hip

arm

(cm

)

D

62

Figure 3.3 The hip moment in ΔSPEED (A) and substratum height (B), joint angles in ΔSPEED (C) and substratum height

(D), joint power in ΔSPEED (E) and substratum height (F), and work loop in ΔSPEED (G) and substratum height (H). For

work loop, according to the definition of joint angle and moment clockwise indicated positive work. Cycle started from TD

and terminated at TO (x). Under each ΔSPEED condition, trials were averaged within the replicates of each participant,

and then averaged across all participants and all substratum height (ACC black, CSR red, DEC blue solid). Under each

substratum height condition, trials were averaged within the replicates of each participant, and then averaged across all

participants and all ΔSPEED (-30cm solid, -20cm dash, 0cm dash and dotted, 20cm dotted, 30cm solid and cross).

63

Figure 3.4 The joint work (A), moment (flexion/extension) averaged during stance (B), excursion angle (joint angle

displacement) (C), and moment arm of GRF averaged during stance (D) for ankle as influenced by the speed increment

(ΔSPEED, Factor A) and COM elevation (substratum height, d, Factor B). mean ± std.

-30cm -20cm 0cm 20cm 30cm-100

-50

0

50

pAB

< 0.001

Ankle

wo

rk (

J)

A

ACC

CSR

DEC

-30cm -20cm 0cm 20cm 30cm0

50

100

150

200p

A < 0.01

pB < 0.001

Ankle

mo

men

t (N

m)

B

-30cm -20cm 0cm 20cm 30cm-20

-10

0

10

20

30

pAB

< 0.05

Ankle

excurs

ion

(de

g)

C

-30cm -20cm 0cm 20cm 30cm-1

0

1

2

3

Ankle

arm

(cm

)

D

64

Figure 3.5 The ankle moment in ΔSPEED (A) and substratum height (B), joint angles in ΔSPEED (C) and substratum

height (D), joint power in ΔSPEED (E) and substratum height (F), and work loop in ΔSPEED (G) and substratum height

(H). The definition of symbols and lines follows Fig. 3.3.

65

Figure 3.6 The joint work (A), moment (flexion/extension) averaged during stance (B), excursion angle (joint angle

displacement) (C), and moment arm of GRF averaged during stance (D) for knee as influenced by the speed increment

(ΔSPEED, Factor A) and COM elevation (substratum height, d, Factor B). mean ± std.

-30cm -20cm 0cm 20cm 30cm-40

-30

-20

-10

0

10

pB < 0.01

Kne

e w

ork

(J)

A

ACC

CSR

DEC

-30cm -20cm 0cm 20cm 30cm-40

-20

0

20

40

60

pA < 0.01

Kne

e m

om

ent

(Nm

)

B

-30cm -20cm 0cm 20cm 30cm-50

0

50

100

pAB

< 0.05

Kne

e e

xcurs

ion

(de

g)

C

-30cm -20cm 0cm 20cm 30cm0

1

2

3

4

5

Kne

e a

rm (

cm

)

D

66

Figure 3.7 The knee moment in ΔSPEED (A) and substratum height (B), joint angles in ΔSPEED (C) and substratum

height (D), joint power in ΔSPEED (E) and substratum height (F), and work loop in ΔSPEED (G) and substratum height

(H). The definition of symbols and lines follows Fig. 3.3.

67

Figure 3.8 Relationships between joint work and energy increment in all conditions. Hip (A), knee (B), and ankle (C) work

vs. kinetic energy increment, hip (D), knee (E), and ankle (F) work vs. potential energy increment. Each symbol

represents individual participant. (A)(B)(C) were from 0cm substratum height, ACC, black, CSR, red, DEC, blue. (D)(E)(F)

were from all CSR condition, and substratum heights were not distinguished.

-100 0 100-400

-200

0

200y = 2.5*x- 89.3

R2 = 0.78

p < 0.001

Whip

(J)

E

k =

1/2

*m*(

v k+

1

2-v

k2)(

J)

A

-100 0 100-400

-200

0

200

y = -1.9*x+ 110.9

R2 = 0.23

p < 0.001

Whip

(J)

E

p =

m*g

*(h

k+

1-h

k)(

J)

D

-100 -50 0 50

-400

-200

0

200

y = 2.6*x+ 64.7

R2 = 0.51

p < 0.001

Wankle

(J)

E

k =

1/2

*m*(

v k+

1

2-v

k2)(

J)

B

-100 -50 0 50

-400

-200

0

200

y = 6.5*x- 33.2

R2 = 0.69

p < 0.001

Wankle

(J)

E

p =

m*g

*(h

k+

1-h

k)(

J)

E

-60 -40 -20 0 20

-400

-200

0

200

y = 3.5*x+ 62.2

R2 = 0.13

p < 0.001

Wknee

(J)

E

k =

1/2

*m*(

v k+

1

2-v

k2)(

J)

C

-60 -40 -20 0 20

-400

-200

0

200

y = 5.6*x+ 64.4

R2 = 0.24

p < 0.001

Wknee

(J)

E

p =

m*g

*(h

k+

1-h

k)(

J)

F

68

Chapter 4

BEHAVIORAL COMPENSATIONS FOR INCREASED ROTATIONAL

INERTIA DURING HUMAN CUTTING TURNS

ABSTRACT

Locomotion in a complex environment is seldom steady-state, but

the mechanisms used by animals for unsteady locomotion (stability and

maneuverability) are not well understood. I used a morphological

perturbation (increased rotational inertia) to determine the compensations

used to perform sidestep cutting turns during running. I tested the

hypotheses that increase body rotational inertia would decrease braking

force during stance. I recorded ground reaction force and body kinematics

from seven participants performing 45° sidestep cutting turns and straight

running at 5 levels of body rotational inertia. Braking forces remained

consistent at different rotational inertias, facilitated by anticipatory changes

to horizontal plane body rotational angular speed and body pre-rotation.

These results suggest that in submaximal effort turning humans employ

anticipatory strategies and changes to between stride variables to result in

constant state within stance phase.

Key Words. Locomotion, stability, maneuverability, braking force,

sidestep cuttings, rotational inertia, turning model

69

INTRODUCTION

Maneuverability is necessary for locomotion in natural environments

(Jindrich & Qiao, 2009). Maneuvers involve behaviorally-generated

changes to speed, direction, and/or body orientation. Animals must

maneuver to forage, negotiate uneven terrain, or escape predation, with

direct impacts on fitness (Demes, Fleagle, & Jungers, 1999; Dunbar,

1988; Howland, 1974; Losos & Irschick, 1996). Performance depends on

morphology, behavior and motor control (Aerts, van Damme, d'Aout, &

van Hooydonck, 2003; Alexander, 2002; Carrier, Walter, & Lee, 2001;

Dial, Greene, & Irschick, 2008; Eilam, 1994; Jindrich et al., 2006; Jindrich

& Full, 1999; Jindrich, Smith, Jespers, & Wilson, 2007; van Damme & van

Dooren, 1999). For humans, turns alone comprise up to 50% of walking

steps during daily living (Glaister et al., 2007), and can cause injuries

directly by increasing the forces and moments experienced by the legs

(Besier, Lloyd, Ackland, & Cochrane, 2001; Colby et al., 2000; Cross,

Gibbs, & Bryant, 1989; Kawamoto, Ishige, Watarai, & Fukashiro, 2002;

McLean, Huang, Su, & van den Bogert, 2004; Stacoff, Steger, Stussi, &

Reinschmidt, 1996), and indirectly by decreasing stability and causing

falls. Maneuvering performance reflects dynamic interactions among

mechanics, musculoskeletal physiology, and motor control (Biewener &

Daley, 2007; Dickinson et al., 2000; Full et al., 2002; Jindrich & Qiao,

2009). Determining the principles governing unsteady locomotion

70

therefore requires assessing both the mechanical and behavioral

compensations associated with maneuvers.

Previous studies have hypothesized that braking forces, i.e.

deceleratory forces in the initial velocity direction, are used to control body

rotation during running turns (Jindrich et al., 2006). The hypothesis was

supported by finding that a simple model based on the assumption that

body rotation should align with the change in velocity direction at the end

of a turning step can predict braking forces used during turns in a range of

animals (Jindrich et al., 2006). The model relates several morphological

(i.e. body mass, M, yaw moment of inertia, Izz), task (i.e. turn magnitude,

θd, speed, V) and behavioral (i.e. fore-aft foot placement, PAEP,imd, lateral

foot placement, Pp, and stance duration, τ) variables.

Running robot controls foot placement to change braking or propelling

force (Raibert, 1986). Hence, braking forces reflects the strategies to

control anticipated maneuvers. For example, humans may adopt different

initial landing patterns from body level to control braking force (Jindrich et

al., 2006).

Different initial strategies at the beginning of turning, together with

braking force, will also fulfill the turning demand by matching body rotation

with center of mass (COM) deflection. However, it is not clear whether

braking force can reflect all the motor control strategies used in turning as

1) co-variation on gait variables cancels out the effect on braking force, or

71

2) strategies which cannot be reflected by braking force. Humans adjust

foot placement in anterior-posterior or medio-lateral directions relative to

COM in different turning directions (Jindrich et al., 2006). However,

changes to other variables, such as stance duration, in the turning model

can also affect the ability to control body rotation. Moreover, human may

use pre-rotate of body resulting in an initial body rotational angular speed

at the beginning of turn. However, the extent to which those strategies in

step transitions are used in anticipatory turning to control or maintain

braking force are not known. I wondered whether increased rotational

inertia can provide greater flexibility for body orientation control by

observing the co-variations among gait variables, or can elicit other

potential strategies not covered in the original turning model. Further, the

function of those variables, each of which representing a strategy in

turning, can be understood by its contribution to braking force.

The aims of this study were to explore human submaximal effort

turning strategies in terms of the motor control strategies reflected from

braking force and those independent of braking force. In order to elicit the

potential turning strategies I built a harness that independently increased

body mass and rotational inertia up to 117% and 4 times of normal.

Participants performed both straight running and 45° sidestep cutting

turns. I hypothesized that humans maintained the same kinematics before

landing, so that braking force in stance phase will decrease with the

72

increase of rotational inertia. The alternative hypothesis was that there

was no influence of body rotational inertia on braking force as humans

chose different landing patterns at the beginning of turning.

73

MATERIALS AND METHODS

Turning model. The model (Fig. 4.1A) assumes that an individual

approaches touch down (TD) at a horizontal speed of VAEP,imd and makes

a turn that changes COM velocity direction by θd within a stance duration

of τ. Relative to COM the foot is placed a distance of 1) Pp in the medio-

lateral (ML) direction generating a half-sine shaped ML force Fp(t) with

peak of Fpmax and 2) PAEP,imd in the anterior-posterior (AP) direction

generating a full sine wave (with a peak of α) and half-sine (peak β)

shaped braking force Fimd(t) (Turning model Fig. 4.8) (Jindrich et al.,

2006). Fp(t) causes a moment relative to COM favoring rotation and Fimd(t)

causes a moment opposing rotation, and this is the effect of braking force

on rotation. The “leg effectiveness number” (ε) is defined as the body

rotation angle cause by Fp(t) (θFp) relative to COM deflection angle (θd)

(Eq. 1). Peak braking force, Fhmax, supposed to be equal to β, can be

predicted by Eq. 2. The primary assumptions are that 1) body rotation (θr)

matches θd during turning; and 2) initial body pre-rotation angle (θi) and

angular speed (ω0) are zero. θFp, is part of θr. The other part of θr, θβ, is

caused by braking part in Fimd(t). Positive braking force is deceleratory and

negative is acceleratory. Substituting Eq. 2 into Eq. 1 indicated that when

Izz increases braking force first reduces it magnitude against initial running

direction, and then reverses its direction when 1 – ε switches its sign, the

74

further increases its magnitude by accelerating in the original running

direction.

(

) (1)

( )

(2)

Experiment. A customized harness (8.3kg) built by galvanized steel

bars and hard plastic frame was used to change body rotational inertia

(Izz) by adding equal balanced weights (tiny lead balls contained in bag)

both anterior and posterior to its COM (Fig. 4.1B). The dimension of the

harness was 0.7 (ML) × 1.5 (AP) × 0.8 (z) m. Treated as a rigid body its

principal moments and products of inertia (1.35 (ML), 0.100 (ML, AP),

0.463 (ML, z), 0.601 (AP), 0.0972 (AP, z), and 1.38 (z) kg·m2) were

determined by pendulum swing.

Human rotational inertia (Izz) as a function of body mass and

height. Anthropometric data for individual participants were obtained by

scaling assuming that the reference human model and participants shared

identical density and segment mass percentage (Herr & Popovic, 2008;

Huston, 1982). The principal moments of inertia of each individual

segment in yaw, roll and pitch directions were then scaled accordingly.

Whole body moment of inertia tensor relative to COM in stance posture as

a function of body mass (M) and height (bh) was calculated by using the

parallel axis theorem. This resulted in that Izz had a power exponent of 5/3

75

to body mass (Carrier et al., 2001). Participant’s body inertia about the

vertical axis were again validated by having participants make stationary

turns on a force platform, and calculating Izz using a least-squares fit

between free moment and rotation angular acceleration (R2 = 0.72)

(Jindrich et al., 2007).

Participants. Seven participants (age = 22.5±1.5yrs; body mass (M) =

68.2±4.0kg; body height (bh) = 174.9±4.2cm, leg length = 96.1±4.6cm, 5

males, mean±std) ran at 2.79±0.26 m s-1 and performed both straight

running (RUN) and left 45° sidestep cutting turns (TURN) by placing right

foot within the force platform. Turning direction was indicated by the tape

on the floor. In each task 5 different harness mass and Izz increment

combinations (M0%I1 (control, no harness), M15%I3 (mass increased by

15% and body inertia to 3-fold), M15%I3.5, M17%I3.5, and M17%I4) were

applied. M0%I1 served as the no harness level while the other levels were

harnessed. The added even mass was attached to the horizontal bars with

equal distance both anterior and posterior to the harness COM to change

Izz systematically according to levels. Added weight together with harness

equaled to a percentage (15% or 17%) of participant’s M. This inevitably

incurred a concomitant change of body pitch moment of inertia. However,

to change moment of inertia in only one direction without changing other

direction is not physically possible. On the other hand, the difference

between condition M15%I3.5 and M17% I3.5 was the AP direction mass

76

distribution of the harness. In M15%I3.5 condition, less weight was placed

further from the COM of harness while in M17%I3.5 more weight was

closer. This resulted in same Izz but different in pitch moment of inertia and

mass. Similarly, the difference between M15%I3 and M15% I3.5, or

M17%I3.5 and M17% I4 was not only Izz but also pitch moment of inertia.

The selection of these M and Izz levels was determined by 1) independent

manipulation of M and Izz, 2) avoiding too much mass added influencing

locomotion, and 3) comparing the effect of Izz under the same M is

possible (or comparing the effect of M under the same Izz).

In each condition 5 trials were collected. All procedures within the

experiment were approved by the Institutional Review Board of Arizona

State University.

Data Capture. I used a 3-D motion tracking system (VICON®, model

612, Oxford Metrics, Oxford, UK) to record the kinematics of 37 reflective

markers at 120 Hz. I replaced the markers LASI, RASI, LPSI and RPSI in

Plug-In-Gait marker set by left and right greater trochanter markers (LGT

and RGT). Two force platforms (400 × 600 mm, model FP4060-NC,

Bertec Corporation, Columbus, OH, USA) embedded in the ground were

used to record GRF at 3000 Hz. The inertia coordinates system was

defined by Fig. 4.1A. AP (AEP,imd original running direction) and ML

directions were relative to the horizontal projection of COM velocity at TD.

The COM was calculated by segmental average and its velocity was tuned

77

by GRF following a path finding algorithm by minimizing the different

between COM acceleration and GRF profile (McGowan, Baudinette,

Usherwood, et al., 2005). Body rotation was defined as the vector

connecting hip markers (LGT, RGT) (Fig. 4.1A). I also tuned rotational

angle with resultant vertical moment, similar as COM and GRF, to

determine the initial rotational angular speed (ω0) at the beginning of

turning. The correlation between tuned and un-tuned rotational angle

history was 0.86±0.12. Due to the harness was at the height of pelvis,

LGT and RGT markers were not visible in some of the trials. Those trials

were excluded from analysis, but at least one trial for each participant at

each condition was available. Kinematic data were scaled to have the

same frames as GRF using a spline fit. The instants of TD or TO were

determined as when vertical GRF continuously increased or decreased for

15 consecutive frames, respectively. They were also referred to as the

beginning and end of turning. To determine the average foot placement in

stance phase in calculating PAEP,imd and Pp, first all COP trajectories in

stance relative to toe markers at TD from the same participant were

pooled in, scaled by 100%, and averaged. Then for each trial the foot

placement was calculated by toe marker at TD plus the 80% percentage

of COP trajectory. Kinetic/kinematics was filtered by 4th-order-zero-lag

low-pass Butterworth digital filter at 60/30 Hz.

78

To compare the effect of rotational inertia (different M and Izz

combinations) on turning performance I used repeated measure of

Analysis of Variance (rANOVA) with participants as the repeated factor

(Keppel & Wickens, 2004). To compare the effects of gait and rotational

inertia on the variables, a factorial rANOVA were employed with factor A

the gait (TURN vs. RUN) and factor B the levels of different rotational

inertia conditions. Post-hoc analysis was based on Bonferroni procedure

with Šidák correction (p<(1–(1–α)1/c), c = (a–1)·a/2, a is the number of

levels).

All calculations were performed by MATLAB (R2012a, Math Works,

Inc., Natick, MA, USA). All values with the text and tables are mean ±

standard deviation except indication.

79

RESULTS

In sidestep cutting turnings rotational inertia had no change on GRF

(ML Fp(t) and AP Fimd(t), Fig. 4.2). Increasing rotational inertia had no

significant influence on most of the performance variables in the turning

model (Initial COM approaching speed, VAEP,imd, p = 0.32; COM deflection

angle, θd, p = 0.49; body rotational angle, θr, p = 0.97, Table 1).

As predicted leg effectiveness number (ε) decreased significantly as

rotational inertia increased (p < 0.001, Table 1) causing the predicted

braking force, Fhmax, to decrease significantly and become acceleratory at

M15%I3 and M17%I4 (p < 0.001, Fig. 4.3, Table 1). However, measured

braking forces, β, were not significantly different among rotational inertias

(p = 0.08, Table 1), hence the hypothesis that increasing rotational inertia

would decrease braking force was rejected.

Most of the parameters within the turning model did not show

significant difference among rotational inertia conditions. Humans

maintained a constant AP foot placement (PAEP,imd, p = 0.17) among

different rotational inertia conditions (Table 1).

However, two of those parameters changed significantly. As rotational

inertia increased, ML foot placement decreased significantly (Pp, p < 0.05),

and stance duration increased significantly (τ, p < 0.01, Table 1).

However, the changes to ML foot placement were small and the increase

of stance duration would be expected to decrease braking force. So, they

80

were not the parameters that can explain why braking force remain

constant high among different rotational inertia conditions.

However, initial rotational angular speeds were significantly different

among rotational inertia conditions (ω0, p < 0.05, Table 1). Although ω0

decreased at higher rotational inertias, it prevented the decrease of

braking force with higher rotational inertias. ω0 caused a rotational angle,

ω0τ, toward turning direction, and ignoring it would under estimate braking

force. Adding the effect of ω0 to the original turning model Eq. 3 predicted

braking force F1 close to the measured braking force in each rotational

inertia condition (Fig. 4.3). However, the difference between F1 and β were

not constant among different rotational inertia conditions. This also

reflected from the difference of intercepts and slopes in each rotational

inertia conditions when regression was performed between F1 and β.

Further, it resulted in the non-perfect prediction of braking force between

F1 and β when all rotational inertia conditions were pooled in (Fig. 4.6B).

(

) (3)

ω0 was adjusted among different rotational inertia conditions to

maintain constant braking force. Without the adjustments of initial angular

speed among rotational inertia conditions braking force was over

estimated (Fig. 4.3, F1,0). Compared with straight running the adjustment

of ω0 in turning was more obvious that in each rotational inertia condition

81

in TURN ω0 was toward turning direction (p<0.001, simple compare in Fig.

4.7A).

82

DISCUSSION

We rejected the hypothesis that braking force would decrease as

rotational inertia increase. I found that initial rotational angular speed was

significantly altered to maintain nearly-constant braking force.

Updated model (Eq. 3) overestimates braking force (F1). To

accurately predict braking force during turning, it is also necessary to

account for another factor: the initial pre-rotation angle, θi, and it results in

that body rotation (θr) tends to be less than COM speed deflection (θd)

(Fig. 4.4A). At the beginning of turning body orientation preceded COM

velocity direction causing a pre-rotation (θi). Although pre-rotation

maintained unchanged among rotation inertia conditions (p = 0.35, Table

1), it was significantly different from zero (p < 0.001). Humans also control

body pre-rotation in straight running when compared with sidestep cutting

turns (Fig. 4.7B). Ignoring pre-rotation would underestimate braking force

because it is toward turning direction (Fig. 4.5, F1 (+θi)). When pre-rotation

was included it reduced the difference between predicted braking force (F1

(+θi)) and measured braking force (β) to a positive constant bias across

rotational inertia conditions and improved pooled-in regression (Fig. 4.6C).

However, due to the positive bias, braking was over estimated by a fixed

constant.

The non-perfect match between F1 and β in Fig. 4.6B is also caused

by some simplification in creating the turning model. In the original

83

equation it was assumed that COM kinematics in AP direction maintains a

constant speed by obeying Pimd(t) = PAEP,imd – VAEP,imd·t in stance, which

represents a zero net force (Jindrich et al., 2006). When Pimd(t) is

upgraded by taking both alpha and beta components in Fimd(t) into

consideration (A.3), two additional rotational angels, θα and θαFp are added

(Turning model A.10). θα were negative indicating against initial turning

direction while θαFp were positive (Table 1, Fig. 4.4B). The net effect of θα

and θαFp was against turning direction and reduced braking force. Ignoring

them would definitely overestimate the braking force. Finally, when both of

them were included in predicting braking force the positive biased

intercept were removed (Fig. 4.5, F'1).

These two sets factors, initial pre-rotation angle (θi) and angles

introduced by refined model (θα + θαFp), improve prediction of braking

force. Consequently, all the adjustments in braking force could be

considered as an “R” term of the equation (Eq. 5). Finally, by taking every

component into consideration F1' predicted braking force better (Eq. 4)

(Fig. 4.6D).

′

(

) (4)

where

( ) (5)

84

The “R” term lays out the foundation for studying the contribution of

other effects to braking force. For example, free moment (Tz) dominated in

vertical jump with a concomitant rotate (D. V. Lee, Walter, Deban, &

Carrier, 2001). Also, in walking it determined the body horizontal plane

rotation (Orendurff et al., 2006). However, the rotational angle (θTz)

caused solely by Tz was negligible compared to θr or θd (Table 1, Fig.

4.4B). Then including Tz by adding θTz in Eq. 5 did not significantly

improve predicting braking force (comparing Fig. 4.6DE).

Interplays of other parameters with increase of rotational inertia.

In locomotion one parameter change can simultaneously incur adaptations

from other variables (Hackert, Schilling, & Fischer, 2006). For example,

increase AP foot placement (PAEP,imd) or reduce ML foot placement (Pp)

will increase body rotation (A.10). However, increase PAEP,imd results in

increase of beta components in Fimd(t), and reduce Pp will reduce Fpmax in

Fp(t) because foot placement affects GRF (Patla, Adkin, & Ballard, 1999;

Raibert, 1986). Hence, more deceleration in AP and less acceleration in

ML would incur change to COM deflection. As rotational inertia increases

humans chose to reduce ML foot placement and maintain a constant AP

foot placement to maintain unchanged COM deflection.

Locomotors switch to different maneuver strategies when constraint by

the environment (Losos & Irschick, 1996). However, the constraint on

COM deflection and body rotation from the turning model does not

85

challenge human sidesteps cuttings. When rotational inertia is increased

turning becomes difficult (Eilam, 1994), then additional strategies of initial

rotational speed (ω0) and pre-rotation (θi) not included in the original

turning model emerged. In the study developing the original turning model,

participants cannot predict the turning direction until a visual cue was

available. As a result they might maintain zero values of ω0 and θi (Jindrich

et al., 2006). Anticipation in walking turns directed foot placement

(Orendurff et al., 2006; Patla et al., 1999), while in current turning it was

manifested as a pre-rotation (θi) between body orientation and COM

velocity direction resulting in the match of body direction and orientation

by the end of turning. ω0 and θi were initiated before the stance phase of

turning by anticipation as a feed forward control (Taylor, Dabnichki, &

Strike, 2005), otherwise improvised parameter change as unanticipated

turning entailed the effort from the joint level (Patla et al., 1999).

The observation that body rotation preceded COM velocity at the

beginning of turning is reversed to the strategies from insects turning

(Jindrich & Full, 1999; Schmitt & Holmes, 2000). It is also different from

that in human walking turns where COM velocity direction precede rotation

where rotation were defined by the chest markers rather than current hip

markers (Patla et al., 1999). Moreover, adjusting initial rotational angular

speed (ω0) also has the advantage over pre-rotation (θi) because

86

increasing it toward turning direction will increase body rotation (θr(τ))

without affecting other variables (A.10).

Finally, when strategies as pre-rotation and initial angular speed were

not available and insufficient then turning does not necessarily need to

involve braking forces against AP direction and could involve acceleration

in AP direction, which is frequently observed in ostriches (Jindrich et al.,

2007).

Conclusion. In submaximal effort turning, when rotational inertia is

increased, humans adopt initial body pre-rotation and rotational angular

speed in turning to maintain an unchanged braking force. Hence, within-

stride turning performance was not affected as humans adopt those

between-stride strategies.

87

TURNING MODEL

Here a more detailed model describing human turning during

sidestep cuttings is given. Assuming the AP direction GRF, Fimd, is given

by (A.1), then AP direction speed during turning is a function of time (A.2).

( )

(A.1)

( )

[ (

) (

)] (A.2)

Integrate Vimd(t) with respect to time obtains AP direction COM

displacement (A.3).

( )

(

) (

) (A.3)

The projection of GRF along ML direction is approximated by (A.4).

( )

(A.4)

According to the definition COM velocity at TD is perpendicular to

ML direction, then COM speed along ML direction as a function to time is

given in (A.5).

( )

(

) (A.5)

Integrate it again with respect to time results in the COM

displacement in ML direction (A.6).

( )

(

)

(A.6)

Free moment is approximated by a half sine wave in stance phase

(A.7).

88

( )

(A.7)

Hence, the net moment applying to COM in stance phase is (A.8).

( ) ( ) ( ) ( ) ( ) ( ) (A.8)

Integrate it with respect to time results in the angular speed in

stance phase (A.9).

( )

{ (

) (

) (

)

(

) (

)

(

)

[ (

)

(

)

(

)]} (A.9)

Finally, integrate ( ) during stance phase results in the angular

displacement by the end of turning at TO (A.10).

( ) ∫

∫ (∫ ( )

)

(

)

(A.10)

The 1st item on the right side of equal sign in (A.10),

(

) , is equal to θFp. The 4th item,

, is equal to θβ. The 5th item,

, is θαFp, and it is the angle

caused by the interaction between alpha component and Fp(t). The 6th

89

item,

, is θα, and it is the angle caused by alpha component in

Fimd(t). The 7th item,

, is the angle caused by free moment, θTz.

Rearranging the items in A.10 by leaving

to one side of the

equal sign, then it shows the format in Eq. 5 and 6 where additional effect

in predicting braking force could be added by the rational angle it causes.

90

Table 4.1

Variables measured in difference rotational inertias in TURN tasks

variables Unit p

value M0%I1(I) M15%I3(II) M15%I3.5(III) M17%I3.5(IV) M17%I4(V)

TD speed VAEP,imd 0.32 2.94±0.244 2.69±0.197 2.8±0.201 2.77±0.285 2.72±0.241

COM velocity deflection θd (°) 0.49 26.6±3.68 25±6.18 25.1±2.77 24.5±3.75 24.8±4.64

Body rotation θr (°) 0.97 12.6±7 13.2±5.71 13.3±2.72 12.3±3.31 12.3±3.38

Leg effectiveness # ε < 0.001 3.13±0.775(II,III,IV,V)

1.42±1.25 0.966±0.308(V)

0.817±0.558 0.562±0.427

Predicted braking force Fhmax (N) < 0.001 136±40.5(III,IV,V)

27.6±95.3 2.1±51.3(V)

-27.6±103 -74.4±72.5

Measured braking force β (N) 0.08 130±35.7 88±88.4 104±36.6 76.6±84.1 68.4±98.9

AP foot placement PAEP,imd

(m) 0.17 0.422±0.0245 0.418±0.0694 0.433±0.0242 0.405±0.0622

0.386±0.0574

ML foot placement Pp (m) < 0.05 0.247±0.024 0.213±0.0186 0.224±0.0151 0.229±0.031 0.219±0.025

1

Initial rotational angular speed

ω0 (°/s) < 0.05 65±37.2 32.8±11 40.8±5.96 42.5±9.79 37.9±8.73

Stance duration τ (s) < 0.01 0.275±0.0255(II)

0.32±0.0231 0.31±0.0182 0.303±0.0255 0.31±0.0254

Angle caused by ω0 ω0τ (°) 0.17 17.6±9.99 10.8±3.43 12.6±2.08 13.1±3.76 11.6±3.35

Initial pre-rotation θi (°) 0.35 8.48±8.51 2.57±4.6 3.99±4.8 5.93±6.33 3.37±5.3

Angle caused by alpha θα (°) < 0.01 -42.4±6.21(III,IV,V)

-22.5±16 -14.4±1.24(V)

-14.1±2.57 -12.4±1.59

Angle caused by interaction

θαFp (°) < 0.05 17.6±9.99(III,IV,V)

10.8±3.43 12.6±2.08 13.1±3.76 11.6±3.35

Angle caused by free moment

θTz (°) < 0.05 -8.03±7.92(II)

1.14±4.14 0.0238±3.67 -1.3±3.04 0.179±2.78

mean±std. Significant difference in post-hoc compare are indicated by superscript.

91

Figure 4.1 (A) Body orientation at TD (upper) and TO during sidestep

cutting turn (lower) (Jindrich et al., 2006). Coordinates are relative to the

initial COM velocity at TD (VAEP,imd) and TO (V1). During stance body

rotates θr while COM deflects θd. At TD there is a pre-rotation between

body orientation and COM velocity (θi). Positive θi indicates that body

rotation precedes COM velocity direction, and negative indicates lag, it is

assumed that θd = θi + θr. (B) Harness used to change body rotational

inertia (Izz).

92

Figure 4.2 Force profile ensembles for different rotational inertias in stance

phase in TURN. Fimd (A) and Fp (B) are the GRF projection along and

perpendicular to initial COM velocity at TD (VAEP,imd). Different rotational

inertias are different colors, M0%I1 black, M15%I3 red, M15%I3.5 blue,

M17%I3.5 magenta, and M17%I4 green. Each line is the ensemble

average of all trials within the same rotational inertia then averaged across

participants. For clarity the shade for standard deviation are not included.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

-200

0

200

stance duration (s)

Fim

d (

N)

A

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

200

400

stance duration (s)

Fp (

N)

B

93

Figure 4.3 The effects of rotational inertia and prediction equation on

braking forces. For braking force positive values indicates against initial

COM velocity direction. Fhmax from Eq.2 black solid, β, measured peak

braking force, red dashed, F1 from Eq. 3 blue dashed and dotted, and F1,0

from Eq. 3 with ω0 from all rotational inertia conditions set as the value at

M0I1, pink dotted, mean±std

M0%I1 M15%I3 M15%I3.5 M17%I3.5 M17%I4

-100

0

100

200p

AB < 0.05

Bra

kin

g fo

rce

(N

)

Fhmax

F1

F1,0

94

Figure 4.4 (A) Components of body angle (θr + θi) at TO compared with

COM deflection (θd). (B) Body rotation (θr) and its components caused by

ML force (θFp), initial body rotational angular speed (ω0τ), braking force

(θβ), free moment (θTz), alpha component in Fimd (θα), the interaction

between alpha component and Fp (θαFp). mean±std.

M0%I1 M15%I3 M15%I3.5 M17%I3.5 M17%I4-10

0

10

20

30

40

ang

le (

0)

i

r

d

A

M0%I1 M15%I3 M15%I3.5 M17%I3.5 M17%I4-100

-50

0

50

100

150

ang

le (

0)

0*

Fp

Tz

Fp

r

B

95

Figure 4.5 Influence of rotational inertia, and pre-rotation (θi) and angles

introduced by model refinement (θα and θαFp) on braking force. Predicted

braking force from Eq. 3 with only pre-rotation included (F1 (+θi)) black solid,

F'1 from Eq. 4 blue dash and dotted, and measured (β) braking force, red

dash.

M0%I1 M15%I3 M15%I3.5M17%I3.5 M17%I4

0

100

200

300p

A < 0.001

Bra

kin

g fo

rce

(N

)

F1 (+

i)

F1'

96

Figure 4.6 The evolution of prediction equation on braking force. The relationships between predicted braking force Fhmax

(A), F1 (B), F1 (+θi) (C), F'1 (D), F'1 (+θTz) (E) and recorded braking force (β). Symbol colors follow the definition of Fig. 4.2,

and each symbol represents an individual participant.

-100 0 100 200

-200

0

200

400

slope = 1.3 intercept = -103.7

R2 = 0.56

p < 0.001

(N)

Fhm

ax (

N)

A

-100 0 100 200

-200

0

200

400

slope = 1.5 intercept = -111.2

R2 = 0.65

p < 0.001

(N)

F1 (

N)

B

-100 0 100 200

-200

0

200

400

slope = 1.1 intercept = 66.4

R2 = 0.81

p < 0.001

(N)

F1 (

+

i) (N

)

C

-100 0 100 200

-200

0

200

400

slope = 1.1 intercept = 9

R2 = 0.86

p < 0.001

(N)

F1' (

N)

D

-100 0 100 200

-200

0

200

400

slope = 1.1 intercept = -5.3

R2 = 0.92

p < 0.001

(N)

F1' (

+

Tz)(

N)

E

97

Figure 4.7 Initial rotational angular speed (ω0) (A) and pre-rotation (θi) (B)

under the influence of gait and rotational inertia. A factorial repeated

ANOVA was performed with the significant main factor (Factor A: gait with

two levels, TURN and RUN; Factor B: rotational inertia with 5 levels,

M0%I1, M15%I3, M15%I3.5, M17I13.5, and M17%I4) indicated by upper

case letter A and B. AB means the interaction effect. Letter without *

means significant level p<0.05, * means p<0.01, ** means p<0.001. For

example, AB means a significant interaction effect with p<0.05. mean±std.

M0%I1 M15%I3 M15%I3.5 M17%I3.5 M17%I4-50

0

50

100

150

pAB

< 0.01

0 (

o/s

)

ATURN

RUN

M0%I1 M15%I3 M15%I3.5 M17%I3.5 M17%I4-10

0

10

20

pA < 0.05

i (

o)

B

98

Figure 4.8 A comprehensive horizontal plane human turning model with

body posture at TD and TO. AP force Fimd(t) is approximated by full sine

wave, alpha component, and half sine wave, beta component, the braking

force. ML force Fp(t) is approximated by another half sine wave with peak

Fpmax. Free moment Tz(t) is fitted by a half sine wave with peak Tmax. In the

current figure Tz(t) is negative and against turning direction. Each gray tile

in the ground is a 0.25 × 0.25 m square. All COM trajectories and body

postures were averaged across all rotational inertia levels and

participants.

99

Chapter 5

SUMMARY

Humans controlled sagittal plane running by obeying the control

laws of the monopod robot. Specifically, humans increased leg force

during thrust phase in stepping up, and stepping down incurred the

increase of compression force. Humans used a pogo-stick strategy to

control running speed rather than a unicycle. This supports that in fast

locomotion the spring-mass template dominates the COM dynamics. The

different leg stiffness between loading and unloading phase during stance

provided a net area in the work loop, hence, mechanical energy could be

added or removed. This also challenges the design of prostheses due to

the lack of adaptability of stiffness in the spring in maneuverability tasks

(McGowan, Grabowski, McDermott, Herr, & Kram, 2012). Humans

adjusted foot placement to change running speed that acceleration

resulted in foot placement behind neutral point and more propelling GRF.

Foot placement initiated from the retraction of hip prior to TD enhances

running stability (Seyfarth et al., 2003). The optimal lag in the PD

controller in describing the relationship between both pitch angle and hip

moments, the summation of both hips' extension moment, is close to the

time of pre-programmed action. This indicates the current hip moment is

determined from the previous instant. Such a lag also changes the

dynamic response of the whole system because the unstable proportional

100

parameter, stable derivative parameter, together with the delay in the

controller does not clearly indicate a stable or unstable controller. Humans

are always stable in running or walking. It is still possible that before the

deviation of the unstable system develops further a reset is initiated at the

beginning of the following stance phase (Dingwell & Kang, 2007). In this

study I only focused on the stability of body pitch angle in stance phase.

However, longer duration and continuous cyclical running would be more

promising in understanding the underlying control on body pitch attitude.

It seems that the Central Nervous System (CNS) first activates the

muscles close to the perturbations then the muscles near that vicinity will

be excited (Winter, 1995). The optimal lag is also critical to injury

prevention because in some cases it is the too late for muscle to develop

appropriate force to prevent tissues from over loading (Williams et al.,

2001). Loading acceptance practice may help to shift such a feedback

control to a feed forward control by choosing appropriate foot placement

by aligning GRF along the leg orientation to reduce the effective muscular

mechanical advantage (Biewener, 1989).

The joints in the lower extremities have functional preference which

is determined by the muscular-tendon architectures spanning the joints.

Proximal joint in the lower extremities is spanned by muscular-tendon

units with larger fiber and shorter tendon portion favoring power

generation (Alexander, 1992; Biewener, 1998). This is then reflected by

101

the work loop between hip moment and angle during a cycle in which

positive work is generated. Distal joint is spanned by the muscular-tendon

units with longer tendon portion favoring elastic energy storage (Biewener

& Daley, 2007; Biewener, McGowan, et al., 2004). Moreover, the arc in

the foot forms a spring facilitating human running (Ker et al., 1987). The

muscular-tendon architectures determine the functional preference that

proximal joint favors power generation while distal joints behaves as a

spring. However, the labor division is different from functional preference

and it is determined by the segmental structure of the lower extremities.

Hip contributes COM speed control over elevation because hip moment

propels COM anterior or posterior rather than vertically. Ankle favors COM

elevation control because GRF applies at the ball of the foot. Dorsi- or

plantar flexion only propelled COM vertically rather than horizontally. The

decoupling between anterior-posterior and vertical propelling are the

results of the leg posture.

Moreover, the existence of the bi-articular muscles, such as

gastrocnemius and quadriceps, transfers energy among proximal and

distal joints. For example, in early stance during running the energy

absorbed by ankle spring is transferred to proximal joint via gastrocnemius

(Prilutsky & Zatsiorsky, 1994). The additional energy can be added to

ankle in later stance. Hence, ankle can also contribute to the speed

increment in some extent (McGowan, Baudinette, & Biewener, 2005;

102

Peterson et al., 2011). This also explains the lower amount of knee work

than hip or ankle because knee work is the effect of energy transferred in

and out of it. However, the function of knee may primarily be in stabilizing

movement rather than powering because it determines the entire leg

length in negotiating terrain perturbation (Rummel & Seyfarth, 2008).

COM speed deflection and body rotation can be separated in

turning. COM deflection contains both deceleration in AP direction and

acceleration in ML direction. Hence, the translation of COM can be

determined by choosing appropriate foot placement (Raibert, Brown, &

Chepponis, 1984). How to regulate body rotation to match the COM

deflection then determines the requirement of turning. Humans choose the

initial angular speed and body pre-rotation to meet the task goals without

affecting translational movement. These strategies are due to the

anticipation of the turning direction and force platform locations when pro-

action in used by a feed forward control. This may also reflect the injury

prevention mechanism because by using visual anticipation there is no

difference of joint moments in the lower extremities between straight

running and sidestep cutting turns (Houck et al., 2006).

103

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APPENDIX A

INSTITUTIONAL REVIWE BOARD/HUMAN SUBJECT APPROVAL

FORMS ON DATA COLLECTION IN CHAPTER 2, 3, and 4

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APPENDIX B

STATEMENT ON AUTHORS' PERMISSION

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Chapter 2 is the study submitted to journal PLoS ONE and it is

under review. Chapter 3 and 4 will also be submitted to peer-reviewed

journals. The only co-author for these publications is Prof. Devin Jindrich. I

have obtained his permission to publish these results in the dissertation.

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BIOGRAPHICAL SKETCH

Mu Qiao was born on Dec 5th, 1981 in Benxi, Liaoning province in China. He graduated from Benxi senior high school in 2000. After that he entered Beijing University of Aeronautics and Astronautics majoring Man-Machine and Environment Engineering in the Department of Flight Vehicle Design and Applied Mechanics. He received his Bachelor of Engineering in 2004. He began his PhD in the Kinesiology program at Arizona State University from fall 2007. His study was about how humans control maneuverability and stability with emphasis on the functions of joints in the lower extremities. He is a student member of the American Biomechanics Society. Currently, he is a post-doc research associate at University of Nebraska at Omaha.