Efficient Robotic Walkingby Learning

Gaits and Terrain Properties

Sandeep Manjanna

Master of Science

School of Computer Science

McGill University

Montreal,Quebec

2013-08-12

A thesis submitted to McGill University in partial fulfillment of requirementsfor the degree of Master of Science in Computer Science

c⃝Sandeep Manjanna, 2013

DEDICATION

I dedicate this work to my parents, Annapurna and Manjanna, my granny,

my teachers, my brother Ajju and my girlfriend Rashmi.

ii

ACKNOWLEDGEMENTS

Studying at McGill has been a wonderful experience and I would like

to thank all the people who have made the course of my graduate studies

memorable. Foremost, I would like to express my gratitude to my super-

visor Gregory Dudek for his encouragement, knowledgeable inputs, support

and guidance throughout the research. I want to take this opportunity to

thank every member of the Mobile Robotics Lab: Dave, Malika, Juan, Flo-

rian, Anqi, Yogi, Yiannis, David, Jimmy, Junaed, Mike, Arnold, Isabelle and

Greg, for being helpful and inspiring me during the course of my research in

the lab. I thank Philippe Giguere for his patience, kind tutoring and helping

me understand the internals of the Aqua robot. I thank Bikram for his help

in conducting experiments and sharing his knowledge about the mechanical

design of the Aqua robot. I would like to thank my friends in Montreal who

made it a very pleasant experience: Aditi, Aparna, Hari, Rohini; all my friends

in India for all the encouragement they have given. Finally, I want to thank

my mom, my dad, my granny, my brother and my girlfriend for being there

when I needed them and supporting me with every decision I made.

iii

ABSTRACT

In this thesis, we investigate the question of how a legged robot can walk

efficiently, and take advantage of its ability to alter its gait. This work targets

the issue of increasing the efficiency of legged vehicles on different challeng-

ing terrains. We decompose the problem into three sub-problems: walking

gait problem, physical adaptation problem, and terrain identification and gait

adaptation problem. In the walking gait sub-problem, we investigate the ef-

fects of gait parameters on the performance of the robot. In particular, we

assess the ground speed, power efficiency and terrain sensibility of the robot

at varying leg cycle frequencies. In the physical adaptation sub-problem, we

investigate the effects of different kinds of legs on the robot’s performance. We

also look at the influence of leg-compliance on walking behavior. In the terrain

identification and gait adaptation sub-problem, we design a gait adaptation

algorithm to identify the terrain by initially classifying the proprioceptive in-

formation collected over different terrains and then adapt its gait accordingly.

Identifying the terrain in real-time helps the robot plan its gait on that terrain

and effectively increase the walking efficiency in real-time. We use a cost-based

unsupervised learning algorithm [28] to classify the terrain data. In our exper-

iments, we use proprioceptive sensor data collected by running the robot on

four different terrains. We also use synthetic data for verifying our algorithm.

We conclude with an analysis of the data and validate the performance of our

algorithm.

iv

ABREGE

Dans cette these, nous etudions les problemes lies a l’efficacite de marche

des robots a pattes et construisons des solutions algorithmiques et physiques

pour les regler. Ce travail vise a accroıtre l’efficacite, en termes de mobilite,

des vehicules a pattes sur differents terrains difficiles. Cette problematique

est decomposee en trois sous-problemes: la facon de marcher, l’adaptation

physique, et l’identification de terrains associee a l’adaptation de la demarche

des robots. Dans le premier cas (la facon de marcher), nous etudions les effets

des parametres de la demarche sur la performance du robot. Nous evaluons

plus particulierement la vitesse au sol, le rendement energetique et la sensibilite

du robot vis-a-vis du terrain et ce, en fonction de la vitesse de deplacement des

jambes. Dans le cas du deuxieme sous-probleme, soit l’adaptation physique,

nous etudions les effets de differents types de jambes sur la performance du

robot. Nous examinons egalement l’influence de la flexibilite des jambes sur

la marche du robot. Troisiemement, le sous-probleme d’identification de ter-

rains et d’adaptation de la demarche des robots est l’un des problemes les

plus importants pour les vehicules capables de marcher. Identifier le ter-

rain en temps reel permet au robot de planifier sa demarche sur ce terrain

et d’augmenter efficacement son rendement de marche. Nous concevons un

algorithme permettant d’identifier le terrain en classant d’abord les informa-

tions proprioceptives recueillies sur differents terrains pour ensuite adapter la

demarche en consequence. Dans nos experiences, nous utilisons un algorithme

d’apprentissage non supervise pour classer les donnees de terrain, de meme

que les donnees issues de capteurs proprioceptifs collectees en employant le

robot sur quatre types de terrains differents. Nous utilisons egalement des

donnees synthetiques afin de verifier notre algorithme d’identification. Dans

v

les resultats, nous presentons une analyse des donnees et validons les perfor-

mances de notre algorithme.

vi

TABLE OF CONTENTS

DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . iii

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

ABREGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

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

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

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problems Addressed . . . . . . . . . . . . . . . . . . . . . . 21.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Contribution of this Work . . . . . . . . . . . . . . . . . . 71.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Background and Related Work . . . . . . . . . . . . . . . . . . . 9

2.1 Walking Gaits and Performance . . . . . . . . . . . . . . . 92.2 Amphibious Adaptations in Robots . . . . . . . . . . . . . 102.3 Terrain Sensing and Identification . . . . . . . . . . . . . . 132.4 Gait Adaptation . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Gait and Performance of the Robot . . . . . . . . . . . . . . . . . 18

3.1 Walking gaits and Gait parameters . . . . . . . . . . . . . 183.2 Performance Factors . . . . . . . . . . . . . . . . . . . . . 213.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . 233.3.2 Data Collection . . . . . . . . . . . . . . . . . . . . 23

3.4 Results and Observations . . . . . . . . . . . . . . . . . . . 253.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4 Physical Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1 Ninja Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.1.1 Design Approach . . . . . . . . . . . . . . . . . . . 314.1.2 Mechanical Properties . . . . . . . . . . . . . . . . . 32

vii

4.2 Experimental Results and Observations . . . . . . . . . . . 344.2.1 Performance Evaluation . . . . . . . . . . . . . . . . 354.2.2 Effective Arm Length . . . . . . . . . . . . . . . . . 374.2.3 Linear Variant of Tripod Gait . . . . . . . . . . . . 38

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5 Terrain Identification in Real-time And Gait Adaptation . . . . . 43

5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.1.1 Sensor Data . . . . . . . . . . . . . . . . . . . . . . 445.1.2 Feature Selection . . . . . . . . . . . . . . . . . . . 455.1.3 Classification Methodology . . . . . . . . . . . . . . 455.1.4 On-line Terrain Identification . . . . . . . . . . . . . 475.1.5 Gait Switch . . . . . . . . . . . . . . . . . . . . . . 47

5.2 Semi-supervised Gait Adaptation . . . . . . . . . . . . . . 495.2.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . 505.2.2 Implementation . . . . . . . . . . . . . . . . . . . . 50

5.3 Experimental Results and Observations . . . . . . . . . . . 525.3.1 Terrain Differentiability and Gait Parameters . . . . 525.3.2 Performance of the Classifier . . . . . . . . . . . . . 545.3.3 On-line Terrain Identification and Gait Adaptation . 56

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . 67

6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 696.3 Final Word . . . . . . . . . . . . . . . . . . . . . . . . . . 69

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

viii

LIST OF TABLESTable page

2–1 Comparison of the amphibious leg designs. . . . . . . . . . . . 12

3–1 Tabular representation of the experimental observations. Thetable presents a fc at which optimal performance is achievedon different terrains. . . . . . . . . . . . . . . . . . . . . . . . 28

5–1 Mapping of terrain types and optimal gaits . . . . . . . . . . . 48

5–2 An example for value of switching gaits with ground speed asutility function. The speed data is taken from the results ofChapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

ix

LIST OF FIGURESFigure page

1–1 Hexapod robots . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1–2 Amphibious Aqua robot equipped with Ninja legs [18]. . . . . 4

3–1 Graphical representation of Tripod Gait. . . . . . . . . . . . . 20

3–2 Plot showing the parameters of the tripod gait . . . . . . . . . 21

3–3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 24

3–4 Ground speed of the robot plotted against fc . . . . . . . . . . 26

3–5 RMS of power consumed per unit distance walk of the robotplotted against fc . . . . . . . . . . . . . . . . . . . . . . . . 27

4–1 Surf entry exit experiment with Ninja legs . . . . . . . . . . . 31

4–2 Ninja leg behaving as an offset wheel. . . . . . . . . . . . . . . 32

4–3 Illustrated diagram of the Ninja Leg. . . . . . . . . . . . . . . 33

4–4 Comparison of the effective arm length between the semi-circular walking legs and the Ninja legs . . . . . . . . . . . . 33

4–5 Mechanical properties of Ninja legs . . . . . . . . . . . . . . . 34

4–6 Trial runs of the Aqua robot on tiled surface. . . . . . . . . . . 35

4–7 Ground speed plotted against fc . . . . . . . . . . . . . . . . . 36

4–8 RMS power consumption plotted against fc . . . . . . . . . . . 36

4–9 Depiction of Aqua robot going from sit mode to stand mode.Both the Ninja legs and the RHex legs are shown. . . . . . . 38

4–10 Performance variation with effective arm length . . . . . . . . 38

4–11 Two variants of tripod gait. . . . . . . . . . . . . . . . . . . . 40

4–12 Comparing the performance of variants of Tripod gait . . . . . 41

5–1 Block diagram of Gait Adaptation Algorithm . . . . . . . . . . 44

5–2 Effect of gait on data distribution . . . . . . . . . . . . . . . . 49

x

5–3 RosNodes for simulating the Gait Adaptation algorithm . . . . 52

5–4 Leg motor current and vertical acceleration (Az) plotted as afunction of Leg angle . . . . . . . . . . . . . . . . . . . . . . 53

5–5 Plots showing terrain differentiability . . . . . . . . . . . . . . 54

5–6 Plot showing variation in performance of the classifier with fc 55

5–7 Classification results on data from four terrains. . . . . . . . . 56

5–8 Data simulating two terrains . . . . . . . . . . . . . . . . . . . 58

5–9 Robot traversing from terrain 1 to terrain 2 only once. . . . . 59

5–10 Terrain transition for every 20 steps (Ts = 20). . . . . . . . . . 60

5–12 Terrain transition for every 2 steps (Ts = 2) . . . . . . . . . . 60

5–11 Terrain transition for every 3 steps. . . . . . . . . . . . . . . . 61

5–13 Error in choosing right gait plotted against transition steplength (Ts). . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5–14 Classification plotted against distance between the mean ofGaussian distributions. . . . . . . . . . . . . . . . . . . . . . 63

5–15 Robot sensor dataset collected from two terrains : dry sandand grass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5–16 Results of classification and gait adaptation plotted againsttime samples. . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5–17 The step length is changed to 3 (Ts=3) and this simulates achange in terrain for every 3 steps. . . . . . . . . . . . . . . 65

5–18 The step length is changed to 2 (Ts=2) and this simulates achange in terrain for every 2 steps. . . . . . . . . . . . . . . 66

xi

CHAPTER 1Introduction

1.1 Introduction

In this thesis, we investigate the question of how a legged robot can walk

efficiently, and take advantage of its ability to alter its gait. Autonomous ter-

restrial vehicles find applications in various fields including search and rescue

operation, agricultural land survey, geological debris exploration, payload car-

riage on difficult terrains, outdoor surveillance, remote inspection, and secu-

rity mission. These applications call for a robot that is able to walk effectively

through challenging terrains (e.g., ice, sand, gravel, snow, and wooded lands),

climb steep hills, walk over small obstacles (e.g., lumps of mud, logs, sand

piles, and rocks), climb stairs, and achieve many other maneuvers.

Legged robots are a kind of terrestrial robots which use legs for their loco-

motion. The mechanical ability of legged robots to navigate through different

kinds of terrains is one of their major potential benefits over other wheeled or

tracked mobile robots. Legged robots are highly capable of walking on rough,

rocky, sandy, steep and undesired terrains. These robots can also use different

kinds of leg movements to jump or step over an obstacle, climb stairs and

crawl on highly inclined surfaces. Energy efficiency while walking, generation

of an effective gait (a pattern of movement of limbs in animals, used for lo-

comotion) to move efficiently on challenging terrains, maintaining static and

dynamic stability of the system while walking are few of the challenges faced

by legged robots. Energy efficiency, higher locomotion speeds, robust walk-

ing capabilities on difficult surfaces, versatility and adaptability to different

walking environments are the key ingredients that will encourage a wide range

1

utilization of legged locomotion in autonomous systems. In this thesis, we try

to address some of these challenges and strive to maximize the effectiveness of

legged robots.

We used an amphibious Aqua family robot [20] (Fig. 1–1a) for our ex-

periments. This is a hexapod, built based on the design of RHex robot [57]

(Fig. 1–1b). We recorded the proprioceptive measures from the robot using

the inertial measurement unit and actuators aboard the robot. One of the

important characteristics of Aqua class robots is their use of robust open-loop

walking, which allows for robust walking across many terrain types with a very

simple mechanical design and control mechanism.

(a) Aqua robot [20] (b) RHex Robot [57]

Figure 1–1: Hexapod robots

1.2 Problems Addressed

In this work, we concentrate on some of the challenges in the mobility

of legged robots. We investigate the walking efficiency and estimate the per-

formance of legged robots when operated with different walking gaits and in

varied environments. We also investigate the capacity of autonomous vehi-

cles to sense their environment using proprioceptive measurements recorded

during their interaction with the environment. We also assess the impact of

mechanical changes on the walking performance of the robot. Through this

2

work, we address some of the mobility issues in legged robots, operating on

challenging terrains, by building algorithmic and mechanical solutions.

We decompose this problem into three sub-problems: a walking gait prob-

lem, physical adaptation problem, and terrain identification and gait adapta-

tion problem. For example, considering the walking efficiency problem in

humans: different gaits (e.g., walking, running, and jumping) affect their mo-

bility, physical adaptations (e.g., shoes, slippers, and spikes) aid in effortless

walking on different terrains, and finally, knowledge about the terrain will help

in planning the walking style compatible to that terrain.

The walking gait sub-problem aims at analyzing gaits and gait param-

eters and their effects on the performance of the robot. A walking gait is a

combination of different movements of limbs to achieve locomotion and is de-

fined by a set of properties, called gait-parameters, that alter the locomotion

trajectories of the mobile system. For example, a human walking gait is de-

fined by parameters, such as step length, stride length, speed, and foot angle.

In this work, for our analysis of walking gaits in legged robots, we consider the

gait parameter - leg rotation frequency. The robot is operated with varying

leg rotation frequencies and its performance is estimated as a function of this

frequency change, which turns out to have a profound effect on the robot’s

performance. For investigation, we quantize the performance into factors such

as ground speed and energy efficiency of the robot. In this sub-problem, we

also investigate the impact of the environment on the walking performance of

the robot by driving the robot on different terrains. For our experiments, we

chose terrains with varied properties including granular terrains like wet and

dry sand, soft terrain like grass, and hard terrain like concrete surface.

The second sub-problem is physical adaptation problem. A physical adap-

tation to the kind of terrain can enhance the walking experience. For example,

3

walking on ice surface is much easier with spiked shoes than with the flat sole

boots. Thus, a good physical equipment can help one in achieving better per-

formance as a walker. As an approach to this sub-problem, we inspected the

effect of different kinds of limbs on the walking performance of the robot. We

designed and verified the legs which enhanced the capabilities of the robot be-

yond walking. In this work, we explore different gaits that could be achieved

with the newly designed Ninja legs and analyze the performance of the robot

on various terrains, when equipped with these new legs. We look into few

mechanical aspects of the robot legs that would help the robot walk efficiently

and elegantly.

(a) Ninja legs used for terrestrial locomo-tion.

(b) Ninja legs used for swimming under-water.

Figure 1–2: Amphibious Aqua robot equipped with Ninja legs [18].

The last sub-problem is terrain identification and gait adaptation in real-

time. Identifying the terrain by tactile sensing has been an interesting problem

for many years. Sensing the terrain and getting to know the terrain well

in advance helps to plan one’s walk on that terrain. If one knows that the

terrain type is deep snow, then a gait - lifting the leg completely out of snow

on every step - can be planned. This kind of planning improves the walking

efficiency on the identified terrain. Similarly, in robots, good walking plan

based on the knowledge about the terrain helps in improving the efficiency of

the robot and aids the robot in choosing a terrain specific walking gait. Based

4

on our analysis in the walking gait sub-problem, we map walking gaits onto

terrains by considering a trade-off between performance factors. Once the

terrain is identified in real time, the robot looks up in this map to choose

a near-optimal high performance gait for that terrain. We have designed

an algorithm to identify the terrain in real time and autonomously change

the walking gait to suit the terrain identified. We achieve this by initially

classifying the proprioceptive measurements from different terrains using one

of the cost-based unsupervised classification techniques.

We also combine the sub-problems and investigate the interplay between

the gait parameters and the terrain classification accuracy, and the effects of

gait-parameters on the gait adaptation algorithm.

1.3 Motivation

Walking robots are gaining importance in many critical applications in-

cluding rescue mission, and exploring debris. All these applications pose diffi-

cult challenges for the robot to adapt to rough environments. A robot capable

of walking only on flat indoor surfaces will be of limited utility on complex

irregular terrains. Hence, it is important to endow the robot with the ability

to infer terrain classes and thus moderate its behavior accordingly. A legged

robot walking with high leg speed can get stuck in deep snow, but lower leg

speeds allow the robot to walk without digging into the snow. For walking on

hard concrete surfaces, however, the robot can be efficient and achieve better

ground speeds at higher leg speeds. These observations motivated us to study

gait and terrain relationships more deeply.

Walking robots have the potential to function over a wide range of ter-

rain types, such as sand, mud, grass, snow, and ice. But different terrains

imply different optimal walking behaviors; a phenomenon well known to any

person who has had to walk across an ice-covered sidewalk during a Canadian

5

winter. Similarly, terrain-specific gait changes in legged robots are needed to

optimize performance. The gait transition from walking to running in humans

and other animals has been the subject of extensive prior research. There are

several analyses of the transition from walking to running in biological sys-

tems as the speed of motion increases [19, 1]. One possible explanation for

gait transitions is that the shift to a new mode of locomotion occurs at the

mechanical limit of whatever locomotion mode is being used [2]. That is, once

the mechanical limit of the legs, walking in particular gait, has been reached

due to the speed of motion, the system must switch to a new gait to go any

faster. Another explanation proposes that gait transitions occur in order to

minimize the total metabolic cost, switching mechanism known as an ener-

getic trigger. The transition can be predicted by observing when the rate of

energy expenditure for walking surpasses that for running; this is equivalent

to the speed at which running becomes more efficient than walking in terms

of energy expenditure per unit distance. Human data indicates this speed to

be 2.2-2.3 m/s [45] [23]. These established observations suggested us to study

the different gait parameters and their effects on energy efficiency and ground

speed of the robot.

The Aqua family robots are amphibious robots. As we work with an

amphibious robot, we are also motivated by swimming to walking and walking

to swimming problems. The problem of transition between swimming gait

and walking gait poses several challenges - the robot should be capable of

identifying the difference between the shore and the wave, it should be capable

of deciding when to switch the gaits to have a smooth transition. These

challenges motivated us towards concentrating our study on identifying the

terrains and gait optimizations in real-time.

6

The walking robot gets a response back from the terrain. This response

provides the proprioceptive measurement for our experiments. This response

from the terrain depends on not only the terrain properties, but also the com-

pliance and other properties of the robot’s legs. Any changes in the properties

of legs affect the performance of the robot and also the features measured

for terrain identification. Hence, we considered studying different physical

adaptations of the robot and measure their effects on the performance of the

robot.

1.4 Contribution of this Work

There is a vast literature available on legged robots and their walking be-

haviors, however, substantial study needs to be done on the impact of walking

gaits on the robot’s performance and adaptation of walking gaits to the terrain

properties. In this study, we address few of the issues related to the efficient

walking of legged robots.

The major novel contribution of this work is an algorithm for on-line gait

adaptation, in which the robot’s behavior is altered as a function of observed

terrain properties. We present an analytical study of the interplay between

the gait parameters and the performance of the robot. Then, we add ter-

rain variations to this problem to make it more interesting and investigate the

response from the terrain to varying gait parameters. From the results, we

try to develop a mapping between the terrains and near-optimal gait proper-

ties. Optimal gait properties are the set of parameters which yield optimal

performance of the robot.

In a continued study of interaction between terrain and robot, we try

to take advantages of physical modifications to the robot. As an another

novel contribution, we present the design of an amphibious robotic leg (Ninja

leg), that enhances the capabilities of our robotic platform. These new legs

7

possess different properties and have an effect on the performance of the robot

and proprioceptive measurements from the robot. We analyze the impact of

physical alteration on the performance of our algorithm and terrain properties.

1.5 Thesis Outline

The thesis is organized into key important chapters, one for each of the

core sub-problems mentioned above. As a preliminary, however, Chapter 2

introduces the background to gait and terrain identification problems. We

discuss some previous work related to walking gaits and performance in legged

robots, tactile sensing and classification of the terrains.

Chapter 3 presents a detailed discussion of the walking gaits we use, and

the associated gait parameters. We describe the approach used to address our

first sub-problem and discuss the results and observations of our experiments.

In Chapter 4, we discuss the mechanical aspects of the newly designed legs for

the robot. We also present a set of behaviors and observations of the robot

equipped with different kinds of legs. Chapter 5 introduces the terrain identifi-

cation and gait adaptation problem and discusses the algorithm to identify the

terrain properties in real time and adapt to an optimal walking gait. In this

chapter, we provide results with a simulated setup to verify the performance

of our algorithm.

We also discuss the possible interplay between the sub-problems and pro-

vide the related results. Finally, we conclude the thesis with Chapter 6,

wherein we discuss the contributions of the work to the field of robotics and

probable future work.

8

CHAPTER 2Background and Related Work

Since this thesis touches on different subjects including walking gaits,

terrain clustering, gait transitions, performance of the robot, and physical

adaptations, this chapter reviews some of the previous work done in these

different areas.

2.1 Walking Gaits and Performance

The details of a walking gait have a great influence on the overall perfor-

mance of locomotive systems. Being able to select an effective combination of

gait parameters benefits the mobile system by delivering better performance.

Gait studies in terrestrial mammals show a species-specific bias for the speed

these animals use, although they are capable of utilizing and sustaining a wide

range of speeds [47]. Studies discovered that the domestic horse has a pre-

ferred speed within each gait [33], and many species have been observed to use

certain speeds much more frequently than others [11, 32, 48]. Prior research

shows that the preference for certain specific speeds associated with each gait

is due to the fact that at these speeds, energy efficiency is maximized [33].

Studies also show that a particular locomotion mode can achieve only certain

finite maximum speed within the system’s mechanical limit [2]. That is, once

the mechanical limit of the legs, walking in particular gait, has been reached

due to the speed of motion, the system must switch to a new gait to go any

faster. Thus the gait parameters in animals affect their mobility.

There has also been a body of prior work on the walking capabilities and

efficient gaits in legged robots. One of the earliest legged robots to demonstrate

impressive obstacle climbing ability, and good mobility in difficult terrains is

9

GE Quadruped [62, 21]. Other notable early results are the speed evaluation

tests on six legged robots such as Atilla [6] and Genghis [5]. The gait related

properties including leg placement, and stride frequency are also discussed in

these robots. Saranli et al. [57] proposed a speed analysis on a hexapod robot,

RHex. In their work, the gait of the robot is split into slow and fast swings

and the robot uses a tripod gait for locomotion. The parameters of the gait,

such as stride angle, stance angle, and stride period, are varied and the speed

achieved is estimated. The effects of the terrain properties on the velocity

of the robot are considered as well. They also concentrate on evaluating the

performance of the robot in terms of power consumption and specific resistance

of the terrain.

Another performance evaluation conducted by Cham et al. [13], on the

Sprawlita hexapod, investigates the stride frequency optimization to achieve

maximum performance. This study captures the effects of stride period on the

performance measures such as hopping height and velocity. In a recent paper,

Garcia Bermudez et al. [25] discuss the maximum velocity achieved by the

OctoRoACH robot on distinct rough terrains. Here, the authors concentrate

on the effects of stride frequency and measure the performance in terms of

maximum velocity and vibrational terrain signatures. In our work, we quantify

the performance in terms of ground speed and energy efficiency over different

terrains. We conduct the performance evaluation over two variable spaces:

the gait-parameters and the terrain properties.

2.2 Amphibious Adaptations in Robots

Amphibious robots have the potential for many applications in coral reef

studies, terrain mapping, and search and rescue operations. Amphibious legs

equip the robot with a capability to explore diverse locations in the world

encompassing those that are on the ground as well as underwater.

10

Recently, there have been amphibious robots designed to operate with

legs to walk and swim effectively. The design by Boxerbaum et al. [9] has

six propeller legs which can be used as wheels on land and propellers under

water. The propeller legs in this design have 2DOF, to achieve translational

and yawing motions of the robot underwater, increasing the complexity of

the controller and probably have a negative impact on cost and robustness

relative to the design proposed by us. An alternative design by Yu et al. [70]

is equipped with four circular legs and two flippers for swimming. The circular

legs are used as wheels for land locomotion and as propellers for underwater

mobility. In these designs, the legs have more than one degree of freedom which

is achieved by using multiple actuators per leg. Increased number of actuators

in these designs complicate the robot’s operations. A major drawback of

propeller based legs is the plausible harm propellers could cause to delicate

marine creatures.

The amphibious six-legged AmphiHex-robot, in the study by Liang et al.

[43], uses six adaptable legs which can adapt to both swimming and walking.

This design has a limitation on the strength of the legs to support the weight

of heavier robots. A good estimate of swimming capabilities of the robot in

actual underwater environments is missing in their work. Also the strength of

the legs is not discussed in detail. The Ninja leg [18], which we discuss in later

chapter, is a mechanically simple design with 1 degree of freedom per leg and

allows the Aqua robot to achieve complex maneuvers with 5DOF trajectories.

Table 2–1 presents a comparison between different amphibious leg designs.

The gait used for different maneuvers of the robot affects the power effi-

ciency and range of physical speed of the robot. Several research groups have

addressed the development of efficient tripod gait walking for legged robots

[34, 15, 58, 26]. Several studies have also been conducted on swimming gaits

11

Table 2–1: Comparison of the amphibious leg designs.

Platform Used Terrestrial Underwater Thrust Complexity

Mode Mode (N) per Leg

Alexander SBoxerbaum,Philip Werk,Roger D Quinn,and RaviVaidyanathan.[9] (2005)

Whegs IV Wheel Propeller 34 2DOF

Jiancheng Yu,Yuangui Tang,Xueqiang Zhang,and ChongjieLiu. [70] (2010)

. Wheel Propeller 30 2DOF

Xu Liang, MinXu, Lichao Xu,Peng Liu, Xi-aoshuang Ren,Ziwen Kong,Jie Yang, andShiwu Zhang.[43] (2012)

AmphiHex Legged Oscillatory 27 1DOF

Bir BikramDey, SandeepManjanna, andGregory Dudek.[18] (2013)

Aqua Legged Oscillatory 36 1DOF

12

for legged robots. A study by Plamondon et al. [49] discusses the develop-

ment and performance properties of swimming gaits, for Aqua-class vehicles,

with names such as “middle-off”,“ hovering”, “sinusoid”, “alternate”, each of

which provides a trade-off between stability, speed, and other factors. We use

middle-off swimming gait for our experiments in this work.

One of the open questions in amphibious legged robots is the adaptive leg

that enables the robot to run on terrestrial surfaces and swim underwater. We

try to address this issue by presenting a design (Ninja legs) that amalgamates

the walking abilities of legs and swimming abilities of the flippers. We evaluate

our design not only for performance, but also for practical robustness, by

posing challenging tasks like entering and exiting surf in the ocean.

2.3 Terrain Sensing and Identification

Terrain identification has the potential to increase the efficiency of nav-

igation in mobile vehicles. Once the terrain is identified, mobile vehicles can

use this information to adapt their gaits based on prior knowledge about the

terrain, avoid certain terrain types that would pose challenges, improve the

walking abilities and performances. To be able to identify the terrain, one

should be capable of sensing its properties. Many sensors like cameras, and

range sensors, can be considered for terrain identification purposes, but tac-

tile sensing provides information directly related to the mechanical properties

of the terrain. Tactile sensing is an economical and robust solution for sur-

veying the terrain properties. In this work, we sense and identify the terrain

through tactile feedback. Similarly, many animals use tactile feedback for

navigation through challenging environments. For example, whiskers on the

body of some animals act as tactile sensors and aid them in functionalities

including exploration, locomotion, gather information about surface textures

and shapes [50, 63, 42].

13

One of the earliest research to mention tactile sensors in robots is Grey

Walter’s study on tortoise robot [64]. The tortoise robot uses a touch sensor

to avoid obstacles and navigate through the environment to reach its reward.

Some of the popular ways to achieve tactile sensing are using artificial whiskers,

tactile probes or vehicle-mounted sensors. In the literature, the deflections of

artificial flexible whiskers, measured using a potentiometer, are used to esti-

mate the distance to an obstacle [37, 16] or recognize an object [55]. These

whiskers are not sensitive to the texture of the surface and thus are not very

much suitable for terrain sensing. A study by Roy et al. [54] presents surface

texture classification technique using the acoustic response obtained by tap-

ping a probe against a surface. Another work using a tactile probe, presented

by Giguere et al. [29, 26], analyzes the acceleration patterns induced at the

tip of the probe while it is dragged over a surface. They present classification

results over ten different surfaces including both indoors and outdoors.

Yet another efficient way to sense a terrain is by considering the dynam-

ics of overall system when the robot is traversing different terrains. This can

be achieved by measuring the inertial estimations captured by inertial sensors

mounted on the robot’s body. In this model, wheels or the legs of the vehicle

act as tactile probes. In [56], Sadhukhan proposed a terrain classification tech-

nique using the internal sensors on a wheeled vehicle. This technique relied on

vertical acceleration of the chassis of the vehicle to perform terrain identifica-

tion. DuPont et al. [22] present a terrain identification technique for wheeled

vehicles by considering the vibration signatures represented by angular veloci-

ties such as pitching and rolling, and vertical accelerations. They make use of

a probabilistic neural network to differentiate between three terrains such as

grass, gravel and asphalt. Brooks et al. [10] use linear separator and Weiss et

14

al. [67] use support vector machines on the vibrational signatures produced

by chassis vibrations when the vehicle traversed different terrains.

The problem of terrain identification by legged vehicles was studied ini-

tially in the context of research on enhancing the mobility of planetary rovers.

Krotkov et al. [40] proposed the modeling of terrain to plan the leg placements

of the Ambler rover [7]. In their subsequent work, Krotkov et al. described

the estimation of terrain characteristics from leg contact forces [39]. Giguere

et al. [28, 26] proposed an unsupervised machine learning algorithm to clas-

sify the inertial sensor data from different terrains. This algorithm exploits

the time-dependencies between the samples and is able to cluster data from

fast-switching terrains. An advantage of this technique is that the method

works by finding a set of parameter values for any user-specified classifier that

minimizes a cost function. We use this elegant methodology [28] in our gait

adaptation algorithm for on-line terrain identification.

2.4 Gait Adaptation

Humans naturally adapt their gait to the environment they are walking

on. For example, people are able to walk on both grass and ice, even though

they require substantially different gaits to avoid falling. Thus, the subsystems

in our brains adapt in order to achieve a stable gait on different terrains.

Similarly, the legged robotic vehicles need to walk through difficult terrains

without becoming unstable or painfully inefficient.

There has been a body of prior work on achieving stable locomotion with

legged vehicles on rough terrains. One of the approaches is to deliberately and

carefully plan every footfall of the robot [68, 14]. A paper by Shih et al. [61]

discusses the gait adaptation by modeling the states of the robot to maintain

its stability. This approach divides the environment into permitted and non-

permitted cells for leg placement. This study presents three approaches such

15

as body motion adaptation, leg sequence adaptation, and leg position adap-

tation. Footfall planning algorithms are very difficult to achieve on a small

mobile platform because of the need for accurate sensor information, accurate

constraint modelling, and huge computation power. Another recent work on

the BigDog robot [52] proposes a control system that adapts to terrain changes

through terrain sensing and posture control. This control system determines

the desired load on each leg and actuator, and the contact with the ground us-

ing joint sensor information. A posture algorithm coordinates the kinematics

of legs with their ground reaction forces to produce a desired body position.

An alternative approach for gait adaptation is to have explicitly designed

gaits for specific purposes. These individual gaits are stored and activated

based on the current purpose. For example, if the current purpose is to climb,

then the gait with ability to climb stairs is selected from stored gaits. There

are several studies conducted to improve the robustness and the performance

of this approach by applying learning techniques [59]. Weingarten et al., in

their study to achieve automated gait adaptation [66], use a modified version

of Nelder-Mead descent to adapt the gait parameters of the robot. They also

conclude that Nelder-Mead tuning yields better performing gaits as compared

to those achieved by manual tuning.

We use a similar approach to map the gait parameters against the terrain

type. Instead of purpose, we have a terrain type based on which a suitable

gait is picked. With a large set of possible gaits, the task to transition between

the gaits becomes challenging. Haynes et al. [15] present acyclic feed-forward

motion patterns that allow a robot to switch from one gait to another. As

we have a limited set of gaits, we have not yet considered the complex gait

transition challenges in this work.

16

In our work, we try to bridge the gap between terrain sensing and gait

adaptation. We propose an algorithm to adapt the walking behavior of the

robot based on the proprioceptive feedback received from the terrain.

17

CHAPTER 3Gait and Performance of the Robot

In this chapter, we discuss our approach towards the walking gait problem,

wherein, we analyze the influence of gait parameters and terrain properties

on the performance of walking robots. We evaluate our approach through a

set of experiments on four different flat terrains: grass, dry sand, wet sand,

and concrete surface. Some parts of this chapter are published in one of our

publications [44].

3.1 Walking gaits and Gait parameters

Walking gait in terms of legged robots can be defined as a periodic pattern

of leg movements that propel the body mass center of the mobile system. The

repetition of this periodic pattern provides locomotive ability to the robot.

Besides stable locomotion, another important aim of a stable gait is to provide

balance or stability to the system. Walking gait of the legged system depends

on various factors, such as the physical structure of the system, number of legs

it has, its center of mass, the environment, and the constraints of the current

task.

Some of the legged vehicles like SIL04 [17], Athlete [69], and humanoid

HRP-3 [38] compute the trajectories for their legs and feet to achieve a stable

locomotion [31, 40]. These trajectories depend on the properties of the terrain,

the vehicles are planning to navigate through. Hence, the computation of

these trajectories need many sensory feedback from the environment. These

vehicles should use sensing equipments, such as visual sensors, stereo vision

cameras, laser range finders, to estimate the terrain properties along with lot

of computing resources to compute actual trajectories. Some motion planners

18

also use force transducers to assess the characteristics of interactions between

the robot’s feet and the terrain surface [24]. The gait generated by this kind

of computed trajectories and foot-placement strategies can be referred to as

closed-loop gait. It is called closed-loop because the trajectories depend on

the sensory feedback from the environment. Thus, to operate with a stable

gait, the system requires a robust and detailed profiling of the ground surface.

This increases the complexity and potentially makes the system fragile.

Contrary to closed-loop gait, open-loop gait provides predetermined foot

trajectories for navigation of the mobile system. Here, the trajectory is inde-

pendent of the environment. Many legged robots use open-loop strategies for

land locomotion [12, 51, 53]. As Aqua robot is built based on RHex design,

similar to Rhex, Aqua’s land locomotion is inspired by the principles of cock-

roach locomotion. Biological studies on the locomotion of cockroaches suggest

that the lag between neural signal propagation from cockroach’s brain to its

leg and the speed of its gait is relatively large. This lag forces high speed

cockroach runners to employ an open-loop feed-forward gait [36]. Following

this model, even Aqua employs open-loop gait mechanism. In Aqua robot, the

PD controller regulates the hip actuators and thus controls the torque to its

leg shaft. The controller aims at eliminating the differences between its clock

signal and actual shaft position, and the velocity. The local hip feedback does

not provide any information about the true state of the leg or the body, thus

making the robot to operate in a task open-loop manner [65]. In our experi-

ments, we use a forward alternating tripod gait [57]. In this mode of walking,

the three legs, two on one side and one on the other side of the robot, form a

stable tripod. While one tripod formation is in contact with the ground and

propelling the robot forward, the other tripod formation is circulated rapidly

around to be ready for the next support phase [66] (Fig. 3–1). This quick

19

alternation of support, coupled with the compliant nature of the legs, results

in a complex dynamic interaction between the robot and the ground.

Figure 3–1: Graphical representation of Tripod Gait. The triangle representsthe tripod support produced by three legs in the tripod gait.

Every gait has a set of variables which define the physical trajectory

followed by components of the system. These properties are referred to as gait

parameters. For example, walking gait of a human is characterized with gait

parameters such as step length, stride length, speed, and foot angle. Similarly,

even the tripod gait is defined by gait parameters such as total stride period,

stance period, and stance angle. Before introducing the details of parameters

for the tripod gait, here is a brief introduction to the Buehler clock, which

is an essential part of walking gait of the Aqua robot. Buehler clock is a

computational analog of the central pattern generator [8, 35] in animals. The

Buehler clock was originally developed for RHex [57, 4] and is based on a

study which shows that cockroach legs are excited by a strongly stereotypical

clock reference signal [41]. As the Aqua is based on RHex, it follows a similar

pattern for walking. To achieve the tripod-gait, this clock uses a piece-wise

linear angle vs. time reference trajectory characterized by four parameters[60]:

the total stride or cycle period tc, the duty factor (the ratio of a single stance

period over the cycle period) ts/tc, the leg angle swept during the stance Φs

and an angle offset to break symmetry in the gait Φ0.

Fig. 3–2 depicts the feed-forward clock signal that is fed into the robot’s

legs to achieve the stable gait. In the alternating tripod mechanism, this same

20

Figure 3–2: Plot showing the parameters of the tripod gait. Angular signalsare plotted against the clock signals of the rotation of a leg.

reference signal is supplied to each leg, except that the left tripod is 1800 out

of phase with the right tripod. The grey region in Fig. 3–2 represents the

part of the leg rotation at which the leg is touching the ground, i.e., the stance

phase of the gait. As it can be seen, there are several parameters to this sim-

ple gait. Optimizing the gait refers to optimizing all the gait parameters. It

gets complex and non-converging if all the parameters are considered at once.

Hence, for the initial set of studies, we consider the performance of the robot

over varying cycle frequency (fc). Cycle frequency is the frequency of the

robot’s leg rotation (i.e. number of leg rotations per second). In our experi-

ments, we record the walking data at various cycle frequencies and estimate

the performance of the robot over different terrains.

3.2 Performance Factors

One of the significant aims of a gait is to provide balance or maintain

stability of the system and robustness for walking through different environ-

ments. It does not seem feasible to analyse the effects of gait changes on the

stability or robustness of the system. Hence, we need to derive measurable

quantities which will affect the stability, fitness and robustness of the robot.

21

We chose to assess the performance factors that increase the overall capabili-

ties of the robot and thus provide better robustness and stability to the robot

for operating on different terrains.

We considered few of the performance factors such as: ground speed (ac-

tual speed achieved by the robot on a walk), on-spot rotation capabilities

(ability to rotate on the spot when operating on different terrains), energy

efficiency (power consumed by the robot per unit distance walk), alignment to

a straight path (measure of deviation of path from straight line), and terrain

tear (measure of tear caused to the terrain). Among these factors, with a

constraint on equipment and test environment, we considered measuring two

performance factors, ground speed and energy efficiency. We had to reject the

on-spot rotation factor as the robot failed to rotate on certain surfaces (e.g.,

grass and sand) because of a high back emf on the robot’s leg when operated

in reverse mode. We also dropped the straight path factor as the test envi-

ronments (e.g., beach areas) were not perfectly flat to consider the deviation

from straight path. Measuring the terrain tear was difficult due to the lack of

equipment, however, we would like to consider these factors in future studies.

The ground speed gives the actual speed that the robot is able to attain on

a particular terrain. Analyzing this performance factor will give an estimation

of capabilities of the robot when operated in different environments. This

factor facilitates us to estimate a near-optimal cycle-frequency per terrain, at

which the robot can cover maximum distance in given time. Secondly, the

energy efficiency of the robot gives a measure of sustainability of the robot

on difficult environments. This performance factor will help us investigate the

energy efficient cycle frequency for operations on a particular terrain. Thus,

we estimate the performance of the robot by evaluating its ground speed and

energy efficiency on various terrains.

22

In specific terms, the problem is to optimize the cycle frequency - for a

particular terrain - at which the robot achieves either highest ground speed,

or power efficient operations, or a trade-off between both.

3.3 Experiments

We investigated this problem by conducting walking trials of the robot

on four different terrains with five different cycle-frequencies. We computed

the ground speed of the robot by measuring the time from recorded videos

and the distance between the flag posts. We also recorded the battery current

and battery voltage during the trials and computed the power consumed by

the robot for every run. Thus, we have an estimate of the ground speeds

and power consumption of the robot on different terrains, when operated with

different cycle-frequencies (fc).

3.3.1 Experimental Setup

The experiments were conducted on four terrains (Fig. 3–3a), namely dry

sand, wet sand, grass, and concrete floor. The setup as seen in Fig. 3–3b was

used on these terrains and Aqua was made to walk from the start point till the

end point. Video of all the trials was recorded from a fixed distance as shown

in Fig. 3–3a. This video was used to compute the time taken by the robot

to cover the experimental path distance. This time is precise and is used for

computing the ground speed of the robot.

3.3.2 Data Collection

The cycle-frequency (fc) is controlled by changing the speed levels in the

graphical interface of the Aqua robot. Five different values of fc - 1.146, 1.187,

1.332, 1.703 and 2.05 Hz, are achieved by changing the speed control setting

to five levels - 0.1, 0.2, 0.4, 0.6 and 0.8, on the graphical speed bar of the

interface. For each speed control setting and every terrain, five trials were

conducted.

23

(a) Different terrains and graphical representation of experimental setup.

(b) The field setup indicating the robot’s path and the markers. Taken at Bellairs lab,Barbados.

Figure 3–3: Experimental Setup

The data collected is a mixture of many sensor measurements. The rela-

tive leg rotations are measured using optical encoders attached to the motor

shafts and a MSI-P400 quadrature decoder card is used to decode the signals

from light receivers. Leg motor electrical current are estimated using carefully

calibrated motor models [46]. These models compute an electrical current

estimate based on physical parameters of the motors, voltage commands to

the motors and their angular velocities. The robot is equipped with a 3-axis

24

Inertial Measurement Unit (3DM-GX1TM), which carries 3 Micro-Electro-

Mechanical Systems (MEMS) acceleration sensors, 3 MEMS rate gyroscopes

and 3 magnetometers. Accelerometers measure the accelerations of the robot’s

body, inm/s2 and rate gyroscopes measure the angular velocities of the robot’s

body in rad/s. The data is collected from these sensors at a rate of 50 Hz, i.e.

50 sensor readings per second.

3.4 Results and Observations

This set of experiments was conducted to investigate the effects of chang-

ing leg cycle frequency (fc) on the performance of the Aqua robot. As dis-

cussed in previous sections, in this work, the performance is measured in terms

of ground speed and power consumed per unit distance of walk. In Fig. 3–4,

we see that the ground speed of the robot increases with cycle-frequency for

soft-granular terrains (dry sand and wet sand), whereas the ground speed of

the robot on hard terrains (grass and concrete surface), decreases at higher

fc value of 2.05 Hz. We suspect that the robot’s legs start to slip from the

surface of the terrain, when rotated at very high speeds on hard terrains. On

soft granular terrains, the granularity of the terrain provides grip to the legs

and helps the robot achieve higher ground speeds even at an increasing cycle

frequency. Thus, the results show that, to achieve higher ground speeds on

hard terrains, the fc value should be capped to the range 1.703 Hz to 2.05 Hz

and to achieve the same on soft granular terrains, the robot needs to operate

at its highest fc values. Results of these experiments clearly show that the

terrain type has a strong influence on the velocity of the robot, at fixed gait

parameters.

25

1 1.151.187 1.332 1.703 2.05 2.20.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cycle−frequency (Hz)

Gro

und

Spe

ed (

m/s

)

ConcreteDry SandGrassWet Sand

Figure 3–4: Ground speed of the robot plotted against fc. The plot shows thevariation found over different terrains. Plot also displays the errors occurredduring different trials.

Another result in Fig. 3–5 shows the variation of power consumed by the

robot per unit distance of walk against varying cycle-frequency. The power

consumed by the robot is measured by recording the battery current and

battery voltage over the robot’s run. From the results, it is evident that the

robot reacts differently to hard and soft granular terrains. We take a trade-off

between the performance factors, ground speed and power consumption, as an

optimal performance. The fc value at which the robot consumes less power yet

achieves acceptable ground speeds is considered as near-optimal fc value. For

example, on wet sand, the robot operating at high fc value of 2.05 Hz achieves

highest ground speed, yet maintain low power consumption compared to other

terrains. On dry sand, however, it is very power inefficient to operate at high

fc values.

26

1 1.151.187 1.332 1.703 2.05 2.2535

40

45

50

55

60

65

Cycle frequency (Hz)

RM

S P

ower

con

sum

ed p

er m

eter

(J /

ms)

ConcreteDry SandGrassWet Sand

Figure 3–5: Root mean square of power consumed per unit distance walk ofthe robot plotted against fc. The plot shows the errors in the readings overfive trials for each speed and terrain.

Using both the ground speed results and the energy efficiency results, we

build a table (Table 3–1), presenting the fc values at which optimal perfor-

mance can be achieved by the robot. Here, we consider optimal performance

as a trade-off between the ground speed and the power consumption, higher

ground speeds achieved at not very expensive power consumptions. The Ta-

ble 3–1 presents a mapping of the terrain and fc values at which the highest

ground speed is achieved and fc values at which an acceptable measure of

power is consumed. The fourth column presents the fc values at which an

optimal performance can be expected.

27

Table 3–1: Tabular representation of the experimental observations. The tablepresents a fc at which optimal performance is achieved on different terrains.

Terrain fc fc Optimal Performance

(max Ground Speed) (acceptable Power Consumption)

Concrete 1.703 Hz 1.332 Hz 1.332 < fc < 1.703

Grass 1.703 Hz 1.703 Hz fc = 1.703

Dry Sand 2.05 Hz 1.703 Hz 1.703 < fc < 2.05

Wet Sand 2.05 Hz 2.05 Hz fc = 2.05

3.5 Summary

In this chapter, we introduced walking gaits and gait parameters of the

robot. We also discussed the performance factors that will be affected by the

gait used for walking. Through experiments, we analyzed the effects of gait

parameters and terrain properties on the performance of the robot. Finally,

we estimated the optimal gait settings in the Aqua robot to achieve better

performance on various challenging terrains.

One of the limitations of our analysis in this chapter is the study over only

one gait parameter (fc). We would like to enhance our analysis by considering

different gait parameters in future. We would also like to explore the cycle-

frequency domain thoroughly, instead of just five frequency values. We also

have plans to incorporate other performance factors mentioned in Section 3.2.

28

CHAPTER 4Physical Adaptation

In this chapter, we address the problem of improving the walking perfor-

mance of the robot by physically adapting to the environment. One of the

ways to improve the mobile efficiency is to employ physical modifications suit-

able to the environment. This chapter introduces a physical adaptation of the

Aqua robot in the form of new robotic legs called “Ninja legs”.

4.1 Ninja Legs

Ninja legs are a class of robotic legs that enable amphibious operation,

both walking and swimming, of the Aqua class hexapod robots. We refer

to these amphibious legs as Ninja legs as the design resembles a spinning

ninja star. Fig. 1–2 shows the Aqua robot equipped with the Ninja legs.

The mechanical design for these legs was developed by Bir Bikram Dey and

Gregory Dudek. A detailed discussion on the mechanical aspects of this design

can be found in our recent paper [18].

As discussed before, legged mobility has often been envisioned as the

most versatile locomotion strategy possible for terrestrial robots. Likewise,

the use of actuators with flippers can provide an exceptionally large degree of

mobility and versatility in the underwater domain. What has proven elusive to

date, however, is a simple leg design that exhibits the advantages of terrestrial

walking legs as well as the motile efficiency of flippers when underwater. It

is this type of hybrid that we discuss and evaluate in this chapter. The leg

design and associated assembly we propose has the attributes of flippers, legs

as well as wheels.

29

Several different classes of leg design have been previously developed for

Aqua-class vehicles, including both robust all-terrain legs for walking, and

efficient flippers for swimming. Notably, however, the walking legs have ex-

tremely poor efficiency and limited thrust when used for swimming in the

water, and the flippers are completely unsuitable for terrestrial locomotion

since they are unable to bear the physical load of the robot due to the flexibil-

ity they require for efficient swimming. A long standing problem is to develop

robust robotic legs designed to perform both effective terrestrial and efficient

underwater maneuvers. With the design of Ninja legs, we have attempted to

address the problem of adapting to different modes of locomotion.

We also evaluated the qualitative performance of the robot using Ninja

legs in terms of entering and exiting the open ocean, through surf with a wave

height of roughly 1 m (Fig. 4–1). Under these circumstances, we observed

that the robot was able to swim to shore, switch (under manual controls) to

walking mode upon contact with the beach, and walk onto the shore. It was

similarly able to walk into the surf, enter the water, and swim out in the

open water. Executing this maneuver depends critically on a sequence of gait

transitions to time various actions relative to wave action, and this challenging

behavior was executed under manual control. The legs, however, were clearly

sufficient to perform this activity.

In the scope of this thesis, the rest of the chapter concentrates only on

evaluating Ninja legs and their properties for terrestrial locomotion. As the

thesis concentrates on the terrestrial mobility of legged robots, we will not

discuss further the swimming efficiency and capabilities of Ninja legs. More

on swimming abilities of Ninja legs can be found in [18].

30

(a) Surf Entry-Aqua walks to the ocean and starts swimming once it is in water.

(b) Surf Exit-Aqua swims to the shore and starts walking on the beach

Figure 4–1: Surf entry exit experiment with Ninja legs

4.1.1 Design Approach

As discussed before, our aim is to design a set of legs with properties

suitable for both terrestrial walking and underwater swimming. We propose a

31

design in which a structure encloses the flipper, in order to protect the flipper

during terrestrial operations. The enclosing structure also performs as the

walking legs for terrestrial locomotion.

Figure 4–2: Ninja leg behaving as an offset wheel.

An enclosure of circular shape is designed to contain the flippers used for

generating thrust underwater (or on the water surface). This whole structure,

consisting of a circular enclosure along with the flippers, will rotate at an offset

from the center as seen in Fig. 4–2. This allows us to have the advantages

and some disadvantages of an offset wheel. This offset-wheel design of the

enclosure is effective as it provides the advantages of traditional semi-circular

walking legs in both forward and backward directions. Since the enclosure is

a cage-like structure, with an extensive open area for water to flow through,

the flippers inside can still generate enough thrust for the robot’s swimming.

4.1.2 Mechanical Properties

The Aqua robot, while using tripod gait for walking, needs three legs to

be able to support the weight of the robot. The robot weighs about 16 kg to

18 kg, with the batteries. For safety and robustness, we fabricated Ninja legs

with enough strength so that one leg can take the weight of the whole robot.

The property of a material to undergo elastic deformation is called the

compliance. Compliance of the leg is a critical property for an efficient walking

of a robot, hence, we need the Ninja legs to be compliant. The enclosure is

32

the part which acts as leg when the robot is in walking mode. Hence, we used

bent spring steel rods to make the circular shaped enclosure. Carbon fiber

plates are used to reinforce the structure as they increase the strength of the

legs and are light-weight and slender. Fig. 4–3 shows the detailed structure

of the Ninja legs.

Figure 4–3: Illustrated diagram of the Ninja Leg.

As shown by the arrow in Fig. 4–4, Ninja legs have shorter effective arm

length due to the increase in their diameter. Shortening of arm length reduces

the leg motor current required for the robot to go from sit mode to stand

mode. We will verify this claim in our results section.

Figure 4–4: Comparison of the effective arm length between the semi-circularwalking legs and the Ninja legs. The arrows represent the effective arm length.

The semi-circular walking legs have compliance for 78.390 of the motor

rotation (Fig. 4–5a). Whereas, Ninja legs have compliance for about 120.90

33

of the motor rotation (Fig. 4–5b). The remaining 239.10 of rotation does not

permit compliance because of presence of the carbon fibre plate.

(a) Compliance span forNinja legs.

(b) Compliance spanfor semi-circular walk-ing legs.

(c) Effective armlengths of the Ninjalegs on granular terrain.

Figure 4–5: Mechanical properties of Ninja legs

One of the major concerns was the capability of the robot to walk on

granular terrains (e.g., sand, and snow) with the Ninja legs. As the rods

are thin, there is a chance of “digging” into the terrain. Hence, we added

the walking supports to increase the area of contact between the legs and

the terrain. The placement of walking supports on the rods determines the

effective arm lengths (Fig. 4–5c).

4.2 Experimental Results and Observations

We conducted three sets of experiments to evaluate the effectiveness of

the Ninja legs for terrestrial locomotion. The first set of experiments were

to evaluate the performance of the robot equipped with Ninja legs. We also

conducted experiments to evaluate the claim regarding advantages of a shorter

arm length (Fig. 4–4). We compare the performance of the Ninja legs against

the RHex legs as these are widely used in legged robots for terrestrial loco-

motion [57, 4, 58, 3] and provide a combination of simplicity, load bearing

34

capacity, compliance and robustness. Finally, we use a variant of standard

tripod gait and compare the performance of the robot.

4.2.1 Performance Evaluation

In this section, we present the results of performance evaluation exper-

iments on the Aqua robot equipped with both RHex semi-circular legs and

Ninja legs. The experiments conducted are similar to those explained in Sec-

tion 3.3, with the difference being that the data was collected with both RHex

legs and Ninja legs. We conducted experiments on one terrain so that we can

compare the two leg designs, keeping the terrain constant. The terrain used

is a tiled surface (Fig. 4–6). The performance factors measured are ground

speed and energy efficiency.

(a) Aqua is equipped with Ninja legs. (b) Aqua is equipped with RHex legs.

Figure 4–6: Trial runs of the Aqua robot on tiled surface.

The plot in Fig. 4–7 shows the ground speeds achieved by the robot when

operated with varied leg-cycle frequencies (fc). Ninja legs, due to the reduced

compliance of their building materials, achieve better physical speeds at higher

values of fc. The semi-circular walking legs, however, make the robot’s motion

irregular (i.e. bumpy) at higher values of fc because of higher compliance of

their component materials.

35

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.50.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cycle Frequency (Hz)

Gro

und

Spe

ed (

m/s

)

RHex Legs

Ninja Legs

Figure 4–7: Ground speeds for both RHex legs and Ninja legs plotted againstcycle frequency of leg rotation.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.545

50

55

60

65

70

75

Cycle Frequency (Hz)

RM

S P

ower

Con

sum

ed p

er u

nit w

alk

(J/m

s)

RHex LegsNinja Legs

Figure 4–8: The Power consumed per unit distance walk plotted against thecycle frequency of the leg rotation. The plot shows the readings for both RHexlegs and Ninja legs.

36

Fig. 4–8 represents the power consumed per unit distance of walk plotted

against varying cycle frequency (fc) of the robot legs. The plot indicates that

the robot consumes more power when walking with the Ninja legs than with

the RHex walking legs. We suspect this is because of the added weight of the

Ninja legs. Even though the power consumption is slightly higher than the

usual semi-circular RHex legs, the Ninja legs achieve higher ground speeds.

In future, we plan to reduce the weight of Ninja legs by replacing the

heavy spring steel rods with other light weight and more compliant material.

Reducing the weight of the legs will definitely have an impact on the power

consumption as we will be reducing the load on the motors.

4.2.2 Effective Arm Length

Effective arm length is the length measured from the arm-joint on the

body till the contact point of the arm with the ground. With respect to our

robot, the effective arm length is the distance between the leg-hip joint of the

robot and the leg-ground contact point. The arrows in Fig. 4–4 depict the

effective arm lengths of both Ninja legs and semi-circular RHex legs. This

experiment was conducted to justify our claim in Section 4.1.2 - shortening of

arm length reduces the current through the leg motors when the robot transits

from sit mode to stand mode (Fig. 4–9). Fig. 4–4 shows that the effective

arm length of Ninja legs is shorter than that of semi-circular RHex legs. The

robot was made to go from sit mode to stand mode and current through the

leg motors was recorded. Four trials were conducted with both RHex legs and

Ninja legs. From the average of four trials, we found that Ninja legs draw 0.65

Amperes of current which is significantly lesser than 1.96 Amperes drawn by

RHex legs. Plot in Fig. 4–10 shows the peaks in the leg motor current. It can

be observed that the RHex legs draw a significant load of current to attain the

stand position.

37

Figure 4–9: Depiction of Aqua robot going from sit mode to stand mode. Boththe Ninja legs and the RHex legs are shown.

1 1.5 2 2.5 3 3.5 4 4.5 5−4

−3

−2

−1

0

1

2

3

4

5

6

Time (Sec)

Leg

Mot

or C

urre

nt (

A)

RHex LegsNinja Legs

Figure 4–10: The robot was made to go from sit mode to stand mode with bothRHex legs and Ninja Legs. Figure shows leg motor current plotted against theclock.

Also the plot shows that the RHex legs consume a sustained current even

when the robot is idle. This can be attributed to the semi-circular shape of

these legs which do not permit a completely stable static stance, and thus a

torque is applied continuously. Ninja legs, however, achieve a stable static

standing because of their circular wheel shape. Thus Ninja legs draw zero

current as long as the robot is idle.

4.2.3 Linear Variant of Tripod Gait

As discussed in Section 3.1, to achieve the tripod gait, the central pattern

generator of Aqua robot uses a piece-wise linear angle vs. time reference

38

trajectory. For the first two experiments, we used a tripod gait, in which the

angular velocity of the leg varies accordingly whether the leg is in aerial phase

or stance phase, demonstrating the salient features of Buehler clock. Hence, we

refer to this kind of tripod gait as Buehler clock based tripod gait (Bc-tripod).

In this experiment, we tried a variant of the tripod gait by making the angle vs.

time reference trajectory linear. This variant is called wheel mode tripod gait

because the legs rotate with constant angular velocity similar to wheels. Since

the stance is still a tripod, three legs rotate out of phase with the remaining

three legs as in standard tripod gait. Fig. 4–11 shows a comparison between

the angular trajectories of Bc-tripod and wheel mode tripod gait. As it is seen

in the plot, Bc-tripod gait has a stance phase in which the angular velocity

of the leg is slower, whereas the angular velocity of the leg is constant over

period in wheel mode tripod gait.

As before, we recorded the current through leg motors in both Bc-tripod

gait and wheel mode tripod gait. Fig. 4–12 shows leg motor current plotted

against the clock time. We can see that the Bc-tripod gait has large current

spikes. This peak in current arises due to the forceful impact of the robot leg

onto the ground after a fast aerial phase. In wheel mode, however, there is

no different aerial and stance phase, thus preventing a high impact at the leg-

ground contact. We would like to further analyze this new variant of tripod

gait in future.

39

1 1.5 2 2.5 3 3.5 4−4

−3

−2

−1

0

1

2

3

4

Clock (sec)

Leg

Ang

le (

Rad

ians

)

(a) Trajectory plot for Beuhler-clock based tripod gait.

1 1.5 2 2.5 3 3.5 4 4.5−4

−3

−2

−1

0

1

2

3

4

Clock (sec)

Leg

Ang

le (

Rad

ians

)

(b) Trajectory plot for wheel mode tripod gait.

Figure 4–11: Two variants of tripod gait.

40

1 1.5 2 2.5 3 3.5 4 4.5 5

−8

−6

−4

−2

0

2

4

6

8

Time (Sec)

Leg

Mot

or C

urre

nt (

Am

p)

Wheel Mode

Beuhler Mode

Figure 4–12: Leg motor current peaks recorded on the robot when operatedwith both Bc-tripod and wheel mode tripod.

4.3 Summary

This chapter introduced a new physical adaptation of the robot which

enhances the capabilities of the robot. We demonstrate experimentally that

the Ninja legs have clear advantages in terms of their ability to achieve high

ground speeds as well as their reduced power consumption in standing mode.

We also investigated the behavior of the robot when operated in several vari-

ants of the tripod gait.

Some of the limitations of our design are the weight of the legs resulting

in high power consumption, rigidity of the legs affecting the leg motor current

peaks, and the material used for walking supports in the legs that is responsible

for slipping of the robot on smooth surfaces. We plan to address these issues

by looking in depth into the materials used in manufacturing the legs. We

would like to get valid inputs from experts in the field of material composition

to have a clear idea on the materials to be used. In future, we would like to

41

analyze the response from different terrains when the robot is operated with

Ninja legs (similar to our experiments in Section 3.3).

42

CHAPTER 5Terrain Identification in Real-time And Gait Adaptation

Terrain identification and gait adaptation to suit the terrain are some

of the important qualities that help the robot walk efficiently in its environ-

ment. In this chapter, we propose an algorithm to enable the robot to adapt

its open-loop walking gait to the terrain. The algorithm consists of terrain

classification, terrain identification in real-time and gait adaptation. We will

discuss the overview of the algorithm followed by a detailed description. In

the experiment section, we analyze the effects of gait parameters on terrain

sensing and terrain classification. At the end, we evaluate our algorithm with

both semi-synthetic data and robot sensor data.

5.1 Overview

The block diagram in Fig. 5–1 shows the data flow and processes in our

gait adaptation algorithm. The whole process is divided into two phases: a

training phase and an execution phase. The training phase is indicated by the

dotted line rectangle in the block diagram (Fig. 5–1). In the training phase, we

collect proprioceptive data from different terrains and build classifiers using

an unsupervised cost-based learning technique [28]. At the end of training

phase, we have classifier parameters and classes with labels. In the execution

phase, we classify the data coming from the robot’s sensors in real-time and

identify the terrain class. Once we know the terrain, we make the decision

on appropriate gait for that terrain and feed the gait into the robot. Thus,

the algorithm enhances the robot’s abilities by making it capable of adapting

its gait in real-time. Each block in the diagram (Fig. 5–1) and the data flow

between the blocks is discussed further in this section.

43

Figure 5–1: Block diagram of Gait Adaptation Algorithm

5.1.1 Sensor Data

The robot is made to walk on different terrains and multiple sensors on-

board are used to collect proprioceptive data. We record the leg positions,

current through the robot’s legs, linear accelerations, angular velocities, bat-

tery current and voltage drawn. The leg positions of the robot are obtained by

relative leg rotations measured using optical encoders attached to the motor

shafts. Leg motor electrical current are estimated using carefully calibrated

motor models [46], that compute an electrical current estimate based on the

44

physical parameters of the motors, the voltage command to the motors and

their angular velocities. The robot is equipped with a 3-axis Inertial Measure-

ment Unit (3DM-GX1TM), which houses 3 Micro-Electro-Mechanical Systems

(MEMS) acceleration sensors, 3 MEMS rate gyroscopes to measure angular

velocities and 3 magnetometers. The data is collected from these sensors at a

rate of 50 Hz, i.e. 50 readings of sensor data are recorded per second.

5.1.2 Feature Selection

The feature selection block is responsible for generating the vector xt

as an input to the classifier. The data vector xt represents the data from

one complete leg cycle. Thus, data vector xt consist of data collected by

sampling 13 sensors - comprising of 3 accelerometers, 3 rate gyroscopes, 1

leg angle encoder and 6 motor current estimators - at a rate of 30 samples

per one cycle of the leg. Thus, each feature vector xt is of size 13x30. In

this work, the dimensionality of the dataset is reduced by applying Principal

Component Analysis and only the top Nf = 2 main features are selected

for the classification. It was shown by Giguere et al. [27, 26], that the two

main components are sufficient to discriminate between the terrain classes.

We plan to consider other components to achieve more discrimination in our

future work. The features selected in this step are fed into the classifier.

5.1.3 Classification Methodology

We use an elegant methodology developed by Giguere et al. [28] for un-

supervised clustering of proprioceptive data samples. These samples represent

sequences of consecutive measurements from the robot as it traverses the ter-

rain. Since the samples are generated through a physical system interacting

with a continuous or piece-wise continuous terrain, time-dependency will be

present between consecutive samples. The clustering algorithm [28] explicitly

45

exploits this time-dependency. It is a single-stage batch method, eliminating

the need for a moving time-window.

The algorithm works by minimizing a cost function which minimizes the

variation of classifier posterior probabilities over time, while simultaneously

maintaining a wide distribution of posterior probabilities. The aim of the

algorithm is to search for the parameters θ that minimizes the following cost

function,

argminθ

Nc∑i=1

∑T−1t=1 (p(ci| xt+1, θ)− p(ci|xt, θ))

2

var(p(ci|X, θ))2

The dataset needed for the algorithm are,

• A sample set X = {xt}, generated by a Markovian process with Nc (No.

of Classes) states, where xt is a feature vector produced at some time t

ϵ {0, T}.

• A classifier with parameters θ used to estimate the probability P (ci|xt, θ),

that the sample belongs to class ci ⊂ C, where C is a set of all possible

Nc classes.

• A set of parameters θ that is able to classify the data set X reasonably

well.

The classifier is fed with the data vector xt from feature selection step.

The advantage of this algorithm is that it can be evaluated with different

kinds of classifiers, such as k-nearest neighbors (k-nn), linear separator and

mixture of Gaussian, based on the knowledge about the class distributions. In

this work, we use linear separator and k-nn classifier with this unsupervised

learning technique. At the end of this step, we have a vector of classifier

parameters θ that define the classes. Once we have the classifier parameters,

we make use of true labels of the data to produce classes with labels and the

classifier.

46

5.1.4 On-line Terrain Identification

The objective of the training phase is to (efficiently) produce a classifier

and an associated small set of class labels. Next, the aim is to identify the

terrain using the real-time data from the robot when it is walking. Initially, a

random gait is selected for the robot to walk. The sensor data from the robot

is split into feature packets, each packet comprising of data samples from one

complete leg rotation as mentioned in Section 5.1.2. The feature packets are

then fed into the classifier. The classifier classifies each feature packet to its

terrain class and generates a list of class labels representing all the feature

packets.

The terrain identification block identifies the terrain by employing deci-

sion making strategies on the list of class labels. Different decision strategies,

such as maximum appearance strategy (a class label that appears most fre-

quently in the list is decided to be the terrain class), certainty of the class

strategy (a class with least uncertainty is chosen as the current terrain class),

and consecutive similarity strategy (a class with maximum consecutive ap-

pearances will be chosen as the terrain class), could be employed in making

the decision about the terrain class. Due to its simplicity and efficiency, in

this work, we employ maximum appearance strategy.

5.1.5 Gait Switch

This algorithm selects a gait based on the identified terrain. Initially a

mapping of terrains against walking gaits is built from the information avail-

able about the effectiveness of different gaits on the terrains. We build such

a map from the results of our experiments in Chapter 3. By considering a

trade-off between ground speed and energy efficiency, we create a terrain vs.

cycle-frequency (fc) mapping as shown in Table 5–1.

47

Table 5–1: Mapping of terrain types and optimal gaits

Terrain Label Terrain Gait Label Optimal Cycle-frequency (Hz)

A Concrete Gait A fc = (1.332 + 1.703)/2

B Grass Gait B fc = 1.703

C Dry Sand Gait C fc = (1.703 + 2.05)/2

D Wet Sand Gait D fc = 2.05

Once we have identified the terrain, the task is to look up this table and

pick the corresponding gait. The decision to change the gait has to be taken

with a strategy such as the cost of switching strategy (switch the gait only if

the cost is minimal), and the value of switching strategy (compute the value

in terms of a utility function). For example, if we consider the ground speed

achieved as a utility function, then the value of switch is the ratio of ground

speed achieved by right gait on the terrain (Gait B on Terrain B) to that

achieved by wrong gait on the terrain (Gait D on Terrain B). If this ratio is

more than certain threshold, then the gait will be switched. The Table 5–2

shows an example for value of switching gaits between terrain B (Grass) and

terrain D (Wet Sand), using ground speed as the utility function.

Table 5–2: An example for value of switching gaits with ground speed as utilityfunction. The speed data is taken from the results of Chapter 3

Terrain Class / Gait Class Gait B Gait D Value of Switch

Terrain B (Grass) 0.816 m/s 0.717 m/s 0.816 : 0.717 = 1.138

Terrain D (Wet Sand) 0.516 m/s 0.666 m/s 0.666 : 0.516 = 1.290

As the robot changes its walking style, the response from the terrain

changes and this affects the data collected by the robot’s sensors. Thus, every

gait will give different readings from the terrains. For example, Fig. 5–2

48

shows similar features sampled from two terrains with two different gaits. The

feature values are clearly different for both the gaits. It is evident from the

plots that different classifiers are needed for different gaits used. Consider

the data in Fig. 5–2, an advanced classifier, such as k-nn, trained with the

Dataset1, will fail to classify the data samples from Dataset2. For example, a

data-point (-1, -0.6) will be classified as Terrain B by a classifier trained with

Dataset1, whereas the same data-point will be classified into Terrain C by a

classifier trained with Dataset2. Hence, we use gait-specific classifiers. That

means, if we have n gaits, we will repeat the training phase of the algorithm n

times with the data generated by each of these n gaits to generate n classifiers.

−1 0 1 2 3 4−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

Feature 1

Fea

ture

2

Dataset 2 : fc = 1.703 Hz

−1 0 1 2 3 4−1

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−0.5

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Feature 1

Fea

ture

2

Dataset 1 : fc = 1.332 Hz

00.511.50

0.51

Terrain C (Dry Sand)

Terrain B (Grass)

Figure 5–2: Plot showing the effect of gait on data distribution. It shows thedifference in the sample space of the data collected by the robot running ontwo terrains with different gaits. This makes it necessary to have a classifiertrained for each of the gaits.

5.2 Semi-supervised Gait Adaptation

In the previous section, we discussed a detailed overview of the gait adap-

tation algorithm. Different strategies and decision making mechanisms were

49

also discussed. Here, we present pseudo code for the algorithm and discuss

the implementations made for validating this algorithm.

5.2.1 Algorithm

We present a semi-supervised gait adaptation algorithm to aid the robot

achieve better walking on rough and varying terrains. We call it gait adap-

tation because this algorithm enhances the robot with an ability to adapt

its walking gait according to the terrain. The algorithm is deemed semi-

supervised because we use the true class labels in training phase to build the

classifiers and terrain classes. The pseudo code in Algorithm 1 presents step-

wise details for the computational stages in the block diagram ( Fig. 5–1),

presented in the previous Section. Here, the training phase can be executed

off-line or on-line, however, the execution phase is always run on-line.

5.2.2 Implementation

For this work, we have implemented the simulation version of the gait

adaptation algorithm. This is the initial phase of the algorithm validation

which serves to permit more controlled and rigorous analysis than the real

system, and to allow pre-configuration before deployment on the real system.

As part of initial implementation, we use ROS nodes to replace the actual robot

sensors. The real-time data from on-board sensors is simulated by a publisher

node which publishes the data on to a ROS topic. The gait adaptation node,

representing our algorithm, subscribes to this ROS topic and processes the

data vectors that are published.

Fig. 5–3 shows the ROS publisher and subscriber nodes, and the ROS

topic used to stream data. Node robotSensors publishes the sensor data onto

topic DataStream. GaitAdaptation node, subscribed to DataStream topic,

50

Algorithm 1 Semi-supervised Gait Adaptation Algorithm

Input: Set of n terrain classes, T = {t1, t2, ......tn}.Set of n gaits, G = {g1, g2, ......gn}.Data collected with every gait gi in G, XG = {Xg1 , Xg2 , ......Xgn}.Where,Xgi = {Xt1 , Xt2 , ....., Xtn}, Data from each terrain ti.

Xti = {x1, x2, ....., xm}, m data samples in every vector.xi = {s1, s2, .....s13}, Readings from 13 Sensors.

Output: tcurr : Current terrain identified.gnew : Optimal gait chosen for terrain tcurr

Training Phase:

1: Map {T ← G} ◃ A map of Gaits to Terrains2: for each gi in G do3: classifier parameters: θgi ← UnsupervisedCostBasedClassifier(Xgi)

4: cgi ← Classifier (θgi ,T )5: gi ← {gi,cgi} ◃ Every gait is assigned with its own classifier6: end for

Execution Phase:

7: initialize current gait: gcurr ← Random(G)8: define: switchThreshold9: while (True) do

10: online sensor data from terrain: Xti = {x1, x2, ....., xm}◃ k data samples belong to one complete cycle of leg rotation. Each

feature packet is made of k samples11: feature packets: F : {f1, f2, ....., fm/k} ← sampling(Xti)

12: terrain labels: t : {t1, t2, ......, tm/k} ← classify(F )

13: current terrain: tcurr ← max(t)14: gnew ← lookUp(Map{T ← G},tcurr)15: if (valGaitSwitch(gnew, gcurr, tcurr) ≥ switchThreshold) then16: gcurr ← gnew17: end if18: end while

51

processes the sensor data. For validation of the algorithm, we use both syn-

thetically generated data and real data collect by the robot over multiple runs

on different terrains.

Figure 5–3: RosNodes for simulating the Gait Adaptation algorithm.

5.3 Experimental Results and Observations

We present three sets of experiments to evaluate the interplay between

walking gaits and terrain sensing ability of the robot. These experiments were

conducted with the Aqua robot equipped with semi-circular legs. Initially,

we investigate the effects of gait parameters on the terrain differentiability. In

this problem, we define terrain differentiability as the distance between terrain

classes in the feature space. If the terrain classes are farther apart, then those

classes are more differentiable. In our second experiment, we evaluate the

performance of the classification methodology with the data collected by the

robot operated with different walking gaits. Lastly, we validate the semi-

supervised gait adaptation algorithm proposed in this chapter.

5.3.1 Terrain Differentiability and Gait Parameters

In this subsection, we analyze the effects of cycle-frequencies on the dif-

ferentiability of the terrain classes. We created a feature set by considering the

leg motor currents (I0) and vertical accelerations (Az), as these features are

most affected by physical interaction with the terrains. The dimensionality of

the feature set is reduced by sampling the data at one particular angle of the

leg rotation cycle, at which the separation between the terrain classes is the

highest [30]. In Fig. 5–4, the features Il and Az are plotted as a function of

leg angle. The plot also shows the optimal angle (1.25 radians) at which the

classes are well separated. The optimal angle is computed by considering the

52

angle at which the average distance between the classes is maximum. Then

the data is sampled at leg angle of 1.25 radians and used for further results.

−4 −3 −2 −1 0 1 2 3 4−8

−6

−4

−2

0

2

4

6

8

Leg Angle (radians)

Leg

mot

or c

urre

nt

−4 −3 −2 −1 0 1 2 3 4−4

−3

−2

−1

0

1

Leg Angle (radians)

Ver

tical

acc

eler

atio

n

GrassConcreteDry SandWet Sand

Leg Angle = 1.25 rad

Figure 5–4: Leg motor current and Vertical acceleration (Az) plotted as afunction of Leg angle. The plot also shows the angle (1.25 radians) at whichthe data sets collected from different terrains are well classifiable.

The results in Fig. 5–5 show the data from different terrains, sampled

at the leg angle of 1.25 radians. The data samples were collected over all

five fc values. In Fig. 5–5, the data samples are plotted on the same scale.

It is observed that the terrain samples collected at different fc values are

distributed differently in the feature space. Moreover, this class separation

is terrain-dependent. For example, the terrains grass and dry sand are well

separated at the fc setting of 1.146 Hz, but not separated at an fc value of

2.05 Hz. Similar observations can be made for different pairs of terrains. This

again stresses the impact of terrains on the robot’s dynamics.

These results exemplify how difficult it is to distinguish the classes at

different fc values. They can also be used to verify the terrain identified by

the robot. For example, if the robot identifies a terrain to be concrete surface

while walking with fc set to 1.146 Hz, it can switch the fc value to 2.05 Hz

53

−1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

Leg Current (I0)

Ver

tica

l Acc

eler

atio

n (

Az)

fc = 1.146 Hz

−1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

Leg Current (I0)

Ver

tica

l Acc

eler

atio

n (

Az)

fc = 1.187 Hz

−1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

Leg Current (I0)

Ver

tica

l Acc

eler

atio

n (

Az)

fc = 1.332 Hz

−1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

Leg Current (I0)V

erti

cal A

ccel

erat

ion

(A

z)

fc = 1.703 Hz

−1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

Leg Current (I0)

Ver

tica

l Acc

eler

atio

n (

Az)

fc = 2.05 Hz

00.511.50

0.51

Wet Sand

Concrete

Dry Sand

Grass

Figure 5–5: Terrain Differentiability : Distribution of sensor measurements infeature space (motor current Il, vertical acceleration Az) sampled at leg angle1.25 rad, with changes in fc. The data shows four terrain classes.

and re-run the identification to more reliably estimate the terrain. Thus, these

results are useful in real-time gait adaptation.

5.3.2 Performance of the Classifier

One of the critical parts of our algorithm is the classifier. In these ex-

periments we try to evaluate the performance of the classifier and the effect

of changing fc on the classifier. The results indicate that there are specific

cycles-frequencies (fc) at which the discrimination between different sets of

54

terrains becomes more accurate. As illustrated in Fig. 5–6, a fc value of 1.332

Hz is optimal for many pairs of terrains; however, for dry sand and grass, fc

of 2.05 Hz gives better classification success rates and for grass and concrete,

fc of 1.187 Hz gives better classification success rates. The classifier performs

better when the speed factor is taken into account. The success rate for two-

class classifier is estimated around 90% at the optimal speed. This is more

efficient than the success rate of 73.75% in [28].

Figure 5–6: Plot showing variation in performance of the classifier with fc. Itshows a comparison between different pairs of terrains.

The previous results suggest that the fc value of 1.332 Hz is optimal for

classification of most of the terrains we examined. Hence, we classified the data

from four different terrains collected at the fc of 1.332 Hz. The top 2 (Nf ) PCA

features from the data were used. We see from Fig. 5–7 that the performance

is very good and comparable to the similar experiments conducted by Garcia

et al.[25] with an overall success rate of 92.11%. Our advantage is that by

using unsupervised machine learning we have only a weak dependence on the

55

availability of training data. The training was achieved with unlabeled data

and the feature set used is also very small.

−20 −10 0 10 20−30

−25

−20

−15

−10

−5

0

5

10

Labeled Data

Feature 1

Fea

ture

2

−20 −10 0 10 20−30

−25

−20

−15

−10

−5

0

5

10

Labels comming from Clusering Algorithm

Feature 1

Fea

ture

2

00.511.500.51

Wet SandConcreteDry SandGrass

00.511.5

Wet SandConcreteDry SandGrass

(a) Results of classification algorithm run on data collected from four terrains.

(b) Confusion matrix of the classification re-sults.

Figure 5–7: Classification results on data from four terrains.

5.3.3 On-line Terrain Identification and Gait Adaptation

We validated our gait adaptation algorithm with two types of datasets

- semi-synthetic dataset: data samples are generated by two Gaussian dis-

tributions, and robot sensor dataset: data samples collected by running the

robot through different terrains. The samples in these data are segmented

56

and stitched to create scenarios of transitions between two terrains. We con-

ducted multiple experiments with each dataset by changing the frequency of

transitions between terrain classes.

In our algorithm, the terrain is not identified on every data packet, that

means the terrain identity is not decided on every step of the robot. Instead,

we consider a group of packets to decide on a particular terrain id. In this

section, for all the experiments, we consider a fixed data packet length (DPs).

We use DPs = 3 in the experiments presented here.

Experiments with Semi-Synthetic Dataset

In these experiments, the dataset is generated by two Gaussian distri-

butions, each representing a terrain. Here, we are simulating the scenario

of robot traversing between two terrains. We refer to this dataset as semi-

synthetic because the Gaussian distributions used to generate this dataset are

derived from the real sensor data collected from the robot running on two

different terrains - dry sand and grass. The two distributions used are shown

in Fig. 5–8. For experiments in this section, we use a linear separator gener-

ated through cost minimization methodology explained in Section 5.1.3. We

consider four different cases, in which the transition between the terrains is

at different step lengths. For example, if the robot is walking on grass and

enters a tilled area after 50 steps, then the transition step length has a value

of 50. We use the notation Ts to represent the transition step length. Four

cases we consider are with values Ts = {100, 20, 3, 2}. Ts gives a notion of

the frequency of terrain transitions, lower the value of Ts higher will be the

terrain transition frequency.

57

The results are presented by plotting the class labels : from ground truth,

classifier output and gait adaptation algorithm output, against the time sam-

ples. Fig. 5–9 shows the data samples over 200 time samples. A transition be-

tween two terrains is shown by a switch after 100 time samples. It is observed

that at few time samples at which the terrain labels are wrongly classified

because of the overlap between the classes. The gait adaptation algorithm,

however, performs efficiently as the gait decision is made by considering 3

(DPs) consecutive data packets and not every data packet.

−25 −20 −15 −10 −5 0 5 10 15−30

−20

−10

0

10

20

30

Feature 1

Fea

ture

2

Gaussian 1

Gaussian 2

Figure 5–8: Data simulating two terrains. The samples are generated fromtwo Gaussian distributions that represent two terrains in real data collectedfrom robot.

58

0 20 40 60 80 100 120 140 160 180 200

Gait A

Gait B

Class A

Class B

Terrain A

Terrain B

Traversal in time

Ground TruthClassifier OutputGait Adaptation Output

Figure 5–9: Robot traversing from terrain 1 to terrain 2 only once.

Data samples are altered by splitting and stitching to simulate a scenario

of frequent terrain change. We generated similar results as before, with the

difference being the frequency of the terrain transitions. Fig. 5–10 shows the

results for dataset with transition step, Ts = 20. The results for experiments

using dataset with a value of Ts = 3 is shown in Fig. 5–11. It is observed that

the gait adaptation algorithm performs exceedingly well when the transition

step is set equal to data packet length (Ts = DPs). The gait adaptation

algorithm performs poorly if the terrain transition occurs more frequently

than the length of the data packet list considered. That is, if Ts < DPs, the

algorithm fails to choose the appropriate gait. This is observed in Fig. 5–12.

59

0 20 40 60 80 100 120 140 160 180 200

Gait A

Gait B

Class A

Class B

Terrain A

Terrain B

Traversal in time

Ground TruthClassifier OutputGait Adaptation Output

Figure 5–10: Terrain transition for every 20 steps (Ts = 20).

0 20 40 60 80 100 120 140 160 180 200

Gait A

Gait B

Class A

Class B

Terrain A

Terrain B

Traversal in time

Ground TruthClassifier OutputGait Adaptation Output

Figure 5–12: Terrain transition for every 2 steps (Ts = 2). In this test, tran-sition step length is lesser than the data packet length considered by gaitadaptation algorithm.

60

0 20 40 60 80 100 120 140 160 180 200

Gait A

Gait B

Class A

Class B

Terrain A

Terrain B

Traversal in time

Ground TruthClassifier OutputGait Adaptation Output

Figure 5–11: Terrain transition for every 3 steps. In this test, transitionstep length is equal to the data packet length considered by gait adaptationalgorithm (Ts = DPs = 3).

We evaluated the performance of the gait adaptation algorithm and plot-

ted the percentage error in the choice of gait against the terrain transition

step length (Ts). Fig. 5–13 presents the variation of percentage error in gait

adaptation with terrain transition step length. It is observed that the error in

the choice of gait increases with the reduction in terrain transition step length,

that is, the performance of the algorithm is better if the frequency of terrain

transition is low. The plot also shows a drop in the error when the transition

step length is equal to data packet length (Ts = DPs = 3).

61

13510203050801000

10

20

30

40

50

60

70

Transition Step Length (Ts)

Err

or in

Gai

t Ada

ptat

ion

(%)

Figure 5–13: Error in choosing right gait plotted against transition step length(Ts).

Fig. 5–14 presents the variation in the percentage error of classification

over the variation in the distance between means of Gaussian distributions

used for dataset generation. Here, we observe that the classification error

reaches minimum as the Gaussian distributions are moved apart. The results

are in accordance with the expectation, farther the sample distributions better

is the performance of the linear separator.

62

5 7 10 12 15 17 20 250

10

20

30

40

50

60

70

80

90

Distance between the mean of Gaussian distributions

Err

or in

Cla

ssifi

catio

n (%

)

Figure 5–14: Classification plotted against distance between the mean of Gaus-sian distributions.

Experiments with Robot Sensor Data

We also present similar results with the dataset created by the robot

sensor samples. We collected the sensor samples as the robot walked over

two different terrains - Dry Sand and Grass. These sensor samples were split

into data packets (each data packet containing the samples from one complete

leg rotation), and then processed by PCA feature extractor to generate the

dataset. Fig. 5–15 show the distribution of data packets from two terrains,

dry sand and grass.

63

−40 −30 −20 −10 0 10 20−15

−10

−5

0

5

10

15

20

25

30

Feature 1

Fea

ture

2

Dry Sand

Grass

Figure 5–15: Robot sensor dataset collected from two terrains : dry sand andgrass.

Similar to previous experiments, with robot sensor data, we evaluate the

algorithm with three test cases by varying the transition step length (Ts). In

these experiments with robot sensor data, however, we use k-nearest neigh-

bor classifier generated through cost minimization methodology explained in

Section 5.1.3. We use three neighbors (k = 3) for classification. Fig. 5–16,

5–17, and 5–18 present the classifier and gait adaptation algorithm results

for a transition step length of 22, 3, and 2 respectively. As observed in pre-

vious experiments, the performance of the gait adaptation algorithm is poor

when the terrain transition step length is lesser than the data packet length

(Ts < DPs).

64

0 5 10 15 20 25 30 35 40

Gait A

Gait B

Class A

Class B

Dry Sand

Grass

Traversal in time

Ground TruthClassifier OutputGait Adaptation Output

Figure 5–16: Results of classification and gait adaptation plotted against timesamples.

0 5 10 15 20 25 30 35 40

Gait A

Gait B

Class A

Class B

Dry Sand

Grass

Traversal in time

Ground TruthClassifier OutputGait Adaptation Output

Figure 5–17: The step length is changed to 3 (Ts=3) and this simulates achange in terrain for every 3 steps.

65

0 5 10 15 20 25 30 35 40

Gait A

Gait B

Class A

Class B

Dry Sand

Grass

Traversal in time

Ground TruthClassifier OutputGait Adaptation Output

Figure 5–18: The step length is changed to 2 (Ts=2) and this simulates achange in terrain for every 2 steps.

5.4 Summary

In this chapter, we presented a semi-supervised algorithm to achieve real-

time gait adaptation based on the cost-based unsupervised classifier. We

demonstrated the efficiency of the algorithm on two different datasets, semi-

synthetic dataset and robot sensor dataset. We also analyzed the performance

of the classifier and the gait adaptation algorithm, in terms of errors in clas-

sification and errors in the selecting the right gait, respectively. The future

work on our algorithm and analyses will be discussed in the next chapter.

66

CHAPTER 6Conclusion and Future Work

6.1 Summary

In this thesis, we presented an analytical study and algorithmic approach

to provide an autonomous robot with the ability to infer terrain classes and

thus moderate its behavior to enhance performance. We centered our focus

on improving the walking capabilities of the robot by evaluating the styles

of walk, response from the terrain, decisions based on terrain feedback, and

palpable adjustments to the robot’s body.

Initially, we measure the effects that gait parameters can have on the per-

formance of a robot when it walks on different terrains. Our results suggest

that the optimal speed of leg rotation for energy consumption is tied to the

terrain type. Thus, by controlling the cycle-frequency, one can achieve a trade-

off between the ground speed and power consumption of the robot. We also

presented the design of a new class of multi-purpose leg to be used for walk-

ing robots, and specifically for the Aqua hexapod vehicle. These legs allow

amphibious operation: that is both swimming and walking, providing efficient

swimming underwater, on the surface, maneuverability underwater allowing 5

DOF motion and complex trajectories in 6 DOF, as well as efficient walking

on land. We evaluated the effectiveness of these legs for walking on a variety

of terrain types and with variants of the tripod walking gait. In the field, we

also verified that these legs are suitable for swimming through moderate surf,

walking through the breakers on a beach (and thus through slurry), and onto

wet and dry sand. To our knowledge, this level of versatility is comparable to,

67

and apparently exceeds, what has been previously demonstrated with prior

walking vehicles.

We proposed a semi-supervised gait adaptation algorithm to identify the

terrain in real time and adapt the walking gait accordingly. We made use of an

unsupervised classification technique to first categorize the terrain features into

terrain classes and then used this information to identify the current terrain

and adopt a near optimal gait accordingly. We evaluated this algorithm in a

simulated environment, but with real data collected by the robot on a variety of

terrains. We also demonstrated that the terrain identification sensitivity of the

robot, and thus the error margin of the classifier differs when the robot walks

with different cycle-frequencies. This implied that active gait selection should

improve classification accuracy. In fact, we observed a significant increase in

efficiency of the terrain classification algorithm by varying the cycle-frequency

of the leg rotation. Thus through our algorithm, we endow the robot with an

ability to select its actions based on the response from the environment.

Our methodologies in this work have some limitations which we would

like to address in near future. We limit our study of gait parameters to only

one of the parameters, which is cycle-frequency. Other gait parameters, the

stance angle and the stance period, also have an impact on the performance

of the robot and adding more parameters and performance factors elaborate

the experiment domain.

The algorithm we propose requires a predetermined set of terrain classes

to successfully train the classifiers. There is a limitation with respect to the

kinds of terrains that the algorithm is capable of adapting. Also, our algorithm

does not explore the entire space of gait parameter as we only use a set of

fixed gaits. It would be more elegant to adapt to any new untrained terrain

by optimizing over gait parameter space, however, the complexity in the gait

68

space made us choose a set of predetermined gaits for our initial attempt with

gait adaptation.

6.2 Future Work

The classification problem is highly dependent on the set of features se-

lected. We would like to experiment with the larger feature sets and evaluate

the results. The classifier accuracy need to be tested with different feature

selection algorithms to choose better features that position the terrain classes

farther apart in feature space. We also plan to extend and generalize our re-

sults to a more diverse set of terrain types, more rugged non-flat terrains like

gravel, and rocky paths.

In the near future, we would like to conduct real-time outdoor testings

of our gait adaptation algorithm to further validate its performance. We plan

to conduct more experiments with the robot running on rough terrains and

adapting its behavior accordingly. The real-time outdoor tests on the robot

would provide more insights on better strategies for terrain class decisions and

value of gait switch. We also plan to enhance the gait adaptation algorithm

to optimize the gait parameters of the robot, on the run.

Amphibious mobility being one of our motivations, we hope to fully ex-

amine the space of both available gaits as well as preferred gait transitions that

can be used for locomotion on complex terrains and specifically on land/water

interfaces. We would like to conduct more experiments in littoral regions

to analyze the gait transition decisions so that a smooth transition between

walking and swimming gaits and vice-versa is ensured.

6.3 Final Word

In this thesis, we presented an approach to enhancing the walking expe-

rience of an autonomous system by learning its environment through propri-

oceptive sensing and the moderation of its actions based on the environment.

69

We experimentally observed a clear connection between the environment, the

robot’s performance, and the gait, and demonstrated that this connection can

be exploited to enhance performance relative to prior approaches which did

not adapt dynamically. We also explored the behavior of autonomous vehi-

cles in complex environments that require amphibious operations. Finally,

the simulation results validated the effectiveness of the algorithm proposed for

autonomous gait adaptation based on the terrain feedback.

70

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