Mobility Evaluation of Wheeled All Terrain Robots Metrics and Application

8/14/2019 Mobility Evaluation of Wheeled All Terrain Robots Metrics and Application

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DISS. ETH NO. 18160

Mobility evaluation of wheeled all-terrain robots

Metrics and application

Dissertation submitted toEidgenssische Technische Hochschule Zrich

for the degree of Doctor of Technical Sciences

presented by

Thomas THER

Dipl. Masch.-Ing. ETHborn October 28, 1977

citizen of Altsttten (SG), Switzerland

accepted on the recommendation of Prof. Roland Siegwart, principal adviser

Prof. Kazuya Yoshida, member of the jury

ZurichJanuary 8, 2009


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Abstract

Numerous concepts of mobile robots for rough terrain applications, rovers,have been proposed in robotics literature. Unfortunately, in most cases, thelocomotion performance of these systems was not properly evaluated or themethodology is not consistent between publications and thus, the results arenot comparable. This is a problem because the real value of new concepts ishard to estimate. Therefore, this thesis aims at providing a common basisfor evaluation and comparison of the mobility performance in rough terrainwhich includes: denition of metrics with relevance to mobility; developmentof tools for performance evaluation according to these metrics; compilationof a catalog of existing systems; carrying out a performance comparison;

validation of the metrics by means of experimental testing.The evaluation methods applied in this work focus on simple models forcomparative analyses. They are meant to support designers during earlyphases of development when details of a new mechanism are not yet denedand the selection of candidate systems is large.

Several mobility metrics are discussed in this work with emphasis on sta-bility, friction requirement at the wheel ground contact, maximum motortorque, and the rovers ability to comply with kinematic constraints on un-even terrain in order to avoid slip. These metrics are complementary becausethey cover different aspects of mobility, and they provide valuable informa-tion like stability margins while driving on sloped terrain, the risk of gettingstuck in an unknown environment due to excessive slippage or insufficienttorque during obstacle climbing, or an indicator for loss of energy caused byslip.

Since comparison of several rovers requires a tremendous modeling efforta software tool was developed which enables extensive comparison througheasy modeling and fast processing of simulations. This tool is used here toconduct a performance analysis of a collection of existing rovers based on astatic model. On the one hand, this analysis demonstrates the usefulness of such a tool. On the other hand, signicant differences in performance between


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the rovers were detected and show the need for comparative analysis.A novel metric, based on a simple kinematic model, is formulated to

predict the level of slip caused by the suspension mechanism of a rover. The

link between the metric and the effective slip is shown by means of a dynamicsimulation.For validation of the simulation results, a modular hardware system was

developed which allows for conguration of four different suspension types.The correlation of measurements from testing and simulation results is highlysatisfying and shows the validity of the proposed metrics for performanceprediction of real systems.


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Kurzfassung

Zahlreiche Konzepte fr mobile Roboter, die sich in unebenem Gelnde be-wegen knnen, so genannte Rover, sind aus der Literatur bekannt. Leiderist die Fortbewegungsfhigkeit dieser Systeme in den meisten Fllen nichtrichtig evaluiert worden oder die zugrunde liegende Methodik ist nicht kon-sistent ber die verschiedenen Publikationen hinweg, weshalb ein Vergleichder Resultate verunmglicht wird. Dies ist problematisch, weil dadurch dereigentliche Wert eines neuen Konzepts nur schwer abzuschtzen ist. Da-her ist es das Ziel dieser Arbeit, die Grundlagen fr eine gemeinsame Basisfr Evaluation und Vergleich der Fortbewegungsfhigkeit von Robotern inunebenem Gelnde zu schaffen. Dazu gehren folgende Punkte: Denition

von Metriken mit Relevanz bezglich Gelndegngigkeit; Entwicklung vonSoftware zur Evaluierung von Systemen gemss diesen Metriken; Auistungvon bekannten Rovern und Durchfhrung eines Vergleichs ihrer Performance;Validierung der Metriken durch Messungen an Hardware.

Der Fokus dieser Arbeit ist auf Evaluationsmethoden gerichtet, welcheauf einfachen Modellen basieren und vergleichende Analysen ermglichenDiese sollen dazu dienen, Entwickler in frhen Phasen eines Projekts zu un-tersttzen, wenn die Details eines Entwurfs noch nicht bekannt sind und dieAuswahl an potentiellen Lsungen gross ist.

Unterschiedliche Metriken fr die Gelndegngigkeit werden in dieser Ar-beit ausfhrlich diskutiert mit den Schwerpunkten Stabilitt, Anforderungan die Reibung zwischen Rad und Boden, maximales Motormoment, sowieFhigkeit des Roboters sich an unebenes Gelnde anzupassen ohne Schlupf,der durch die Kinematik der Aufhngung bedingt wird, zu verursachen.

Diese Metriken sind komplementr, weil sie unterschiedliche Aspekte derGelndegngigkeit abdecken und sie liefern usserst hilfreiche Informationenwie die Stabilittsmarge whrend der Fahrt auf geneigtem Untergrund, dasRisiko in unbekannter Umgebung stecken zu bleiben aufgrund von starkemSchlupf oder ungengendem Motormoment sowie eine Kennziffer fr En-ergieverlust durch das Auftreten von Schlupf.


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Der Vergleich zahlreicher Systeme bedingt einen grossen Aufwand anModellierungsarbeit. Deshalb ist eine Software entwickelt worden, die um-fassende Vergleiche durch einfaches Modellieren und schnelles Abarbeiten

von Simulationen ermglicht. Diese Software wurde hier fr die Analyseder Gelndegngigkeit verschiedener, existierender Rover basierend auf einemstatischen Modell eingesetzt. Zum einen zeigt diese Analyse die Ntzlichkeiteiner solchen Software, zum anderen konnten erhebliche Unterschiede bezglichGelndegngigkeit zwischen den Systemen festgestellt werden.

Des Weiteren wurde eine neuartige Metrik, die auf einem einfachen kine-matischen Modell basiert, deniert, um das Mass an Schlupf abschtzen zuknnen, welcher durch den Aufhngungsmechanismus des Rovers verursachtwird. In einer dynamischen Simulation wird der Zusammenhang zwischen

dieser Metrik und dem effektiven Schlupf aufgezeigt.Fr die Validierung der Simulationsresultate ist ein Hardwaresystem en-twickelt worden, welches erlaubt, vier verschiedene Aufhngungen zu kon-gurieren. Die Korrelation von Testmessungen und Simulationsresultatenist sehr hoch und zeigt, dass sich die vorgeschlagenen Metriken fr die Ab-schtzung der Gelndegngigkeit von realen Systemen gut eigenen.


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Contents

Abstract i

Kurzfassung iii

1 Introduction 11.1 Locomotion for rough terrain. . . . . . . . . . . . . . . . . . 11.2 Motivation and objectives. . . . . . . . . . . . . . . . . . . . 21.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Performance evaluation 5

2.1 General considerations. . . . . . . . . . . . . . . . . . . . . . 52.2 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 General metrics in literature. . . . . . . . . . . . . . 9

2.2.1.1 System metrics. . . . . . . . . . . . . . . . . 92.2.1.2 Control metrics. . . . . . . . . . . . . . . . 102.2.1.3 Operational metrics. . . . . . . . . . . . . . 10

2.2.2 Mobility metrics. . . . . . . . . . . . . . . . . . . . . 102.2.2.1 Friction requirement. . . . . . . . . . . . . . 112.2.2.2 Maximum torque. . . . . . . . . . . . . . . . 132.2.2.3 Maximum obstacle height. . . . . . . . . . . 142.2.2.4 Slip. . . . . . . . . . . . . . . . . . . . . . . 142.2.2.5 Stability . . . . . . . . . . . . . . . . . . . . 162.2.2.6 Velocity constraint violation (VCV ) . . . . . 232.2.2.7 Additional metrics. . . . . . . . . . . . . . . 24

2.3 Normalization and requirements. . . . . . . . . . . . . . . . 262.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3 Systems 293.1 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35


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v i C o n t e n t s

3.3 Rover breadboard. . . . . . . . . . . . . . . . . . . . . . . . . 383.3.1 Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . 383.3.2 Electronics. . . . . . . . . . . . . . . . . . . . . . . . 41

3.3.3 Software. . . . . . . . . . . . . . . . . . . . . . . . . . 423.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4 Modeling and analysis 434.1 Simulation tools. . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1.1 Overview of simulators. . . . . . . . . . . . . . . . . . 434.1.2 2D static tool. . . . . . . . . . . . . . . . . . . . . . . 46

4.1.2.1 Overview. . . . . . . . . . . . . . . . . . . . 474.1.2.2 2DS kinematics module. . . . . . . . . . . . 48

4.1.2.3 2DS statics module. . . . . . . . . . . . . . 494.1.3 Working Model 2D. . . . . . . . . . . . . . . . . . . . 504.2 Static analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2.1 Approach and metrics. . . . . . . . . . . . . . . . . . 524.2.2 Static models. . . . . . . . . . . . . . . . . . . . . . . 544.2.3 Simulation results. . . . . . . . . . . . . . . . . . . . 57

4.2.3.1 Stability analysis. . . . . . . . . . . . . . . . 574.2.3.2 Obstacle climbing. . . . . . . . . . . . . . . 614.2.3.3 Sensitivity analysis. . . . . . . . . . . . . . 68

4.2.4 Conclusion of the static analysis. . . . . . . . . . . . 704.3 Kinematic analysis. . . . . . . . . . . . . . . . . . . . . . . . 714.3.1 Approach and metrics. . . . . . . . . . . . . . . . . . 714.3.2 Improvements. . . . . . . . . . . . . . . . . . . . . . . 724.3.3 Simulation environment. . . . . . . . . . . . . . . . . 734.3.4 Kinematic models. . . . . . . . . . . . . . . . . . . . 75

4.3.4.1 Simplications. . . . . . . . . . . . . . . . . 754.3.4.2 Kinematic equations. . . . . . . . . . . . . . 76

4.3.5 Simulation results. . . . . . . . . . . . . . . . . . . . 784.3.6 Conclusion of the kinematic analysis. . . . . . . . . . 81

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5 Experimental validation 835.1 Test setup and measurements. . . . . . . . . . . . . . . . . . 835.2 Validation of the static analysis. . . . . . . . . . . . . . . . . 85

5.2.1 Summary. . . . . . . . . . . . . . . . . . . . . . . . . 865.2.2 General results. . . . . . . . . . . . . . . . . . . . . . 875.2.3 Torque requirement. . . . . . . . . . . . . . . . . . . 905.2.4 Friction requirement. . . . . . . . . . . . . . . . . . . 91

5.3 Validation of the kinematic analysis. . . . . . . . . . . . . . 92


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C o n t e n t s v i i

5.3.1 Approach. . . . . . . . . . . . . . . . . . . . . . . . . 935.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.4 Conclusion of the experimental validation. . . . . . . . . . . 96

6 Conclusion and outlook 996.1 Conclusion and contributions. . . . . . . . . . . . . . . . . . 996.2 Outlook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Acknowledgements 103

Bibliography 105

Curriculum Vitae 115


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v i i i C o n t e n t s


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List of Tables

2.1 The problem of scaling rovers for comparison.. . . . . . . . . 26

3.1 Wheeled passive locomotion systems: overview part I.. . . . 303.2 Wheeled passive locomotion systems: overview part II.. . . . 313.3 Wheeled passive locomotion systems: overview part III.. . . 323.4 Main parameters of the modular hardware system.. . . . . . 40

4.1 2DS models of existing rovers part I.. . . . . . . . . . . . . . 554.2 2DS models of existing rovers part II.. . . . . . . . . . . . . 564.3 2DS models of additional rover concepts part I.. . . . . . . . 564.4 2DS models of additional rover concepts part II.. . . . . . . 574.5 Static stability results.. . . . . . . . . . . . . . . . . . . . . . 594.6 Impact of CoG on SS.. . . . . . . . . . . . . . . . . . . . . . 604.7 Results for friction requirement and maximum torque.. . . . 634.8 Impact of payload on performance of PEGASUS.. . . . . . . 644.9 Simulation results kinematic analysis on sine terrain.. . . . . 784.10 Simulation results kinematic analysis on sinestep terrain.. . . 79

5.1 Pass/fail results of step climbing on different surface types.. 865.2 Pass/fail results of step climbing with different torque limits.865.3 Torques of RCL-E: measurements and prediction.. . . . . . . 905.4 Mean torque measurements of CRAB, RB, and RCL-E.. . . 955.5 Comparison of relative performance of T and V CV . . . . . . 95


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x L i s t o f T a b l e s


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List of Figures

2.1 Wheel ground interaction.. . . . . . . . . . . . . . . . . . . . 122.2 Wheel torque measurement during step climbing motion.. . . 132.3 Types of slip.. . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Longitudinal (left) and lateral (right) stability.. . . . . . . . 172.5 Support polygon of the force-angle stability measure.. . . . . 182.6 Comparison of models for stability evaluation.. . . . . . . . . 192.7 Stability results from static model.. . . . . . . . . . . . . . . 202.8 Inuence of the simplications applied by Slade on stability.. 212.9 Stability metrics based on dynamic model.. . . . . . . . . . . 22

2.10 Ideal velocities in rough terrain.. . . . . . . . . . . . . . . . . 232.11 Ideal velocities for two different reference wheels.. . . . . . . 24

3.1 Comparison of ExoMars and RB.. . . . . . . . . . . . . . . . 343.2 Comparison of Nexus 6 and RCL-E.. . . . . . . . . . . . . . 343.3 Suspension of the CRAB.. . . . . . . . . . . . . . . . . . . . 363.4 The four congurations of the modular hardware system.. . 393.5 Hardware coordinate system.. . . . . . . . . . . . . . . . . . 403.6 Rover electronics.. . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1 Modules of the performance optimization tool POT.. . . . . 474.2 2DS architecture.. . . . . . . . . . . . . . . . . . . . . . . . . 484.3 2DS: node update.. . . . . . . . . . . . . . . . . . . . . . . . 494.4 WM2D user interface.. . . . . . . . . . . . . . . . . . . . . . 514.5 Common features of 2DS models.. . . . . . . . . . . . . . . . 544.6 Benchmark terrain: step of 0.11 m (wheel diameter).. . . . . 614.7 Normal forces on PEGASUS.. . . . . . . . . . . . . . . . . . 644.8 Minimum normal force during step climbing.. . . . . . . . . 654.9 Friction requirement during step climbing.. . . . . . . . . . . 664.10 Wheel torques and normal forces during step climbing.. . . . 67


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x i i L i s t o f F i g u r e s

4.11 Bogie types.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.12 Sensitivity of static stability on Z position of CoG.. . . . . . 694.13 Sensitivity of friction requirement and maximum torque.. . . 69

4.14 Terrain types: (a) sinestep, (b) sine.. . . . . . . . . . . . . . 734.15 Interaction WM2D-Matlab and control architecture.. . . . . 744.16 Motor model implemented in Matlab.. . . . . . . . . . . . . 744.18 Motion comparison regular and parallelogram bogie.. . . . . 774.19 Wheel movement on different bogie types.. . . . . . . . . . . 794.20 Simulation results for metrics r on the sine terrain.. . . . . . 804.21 Simulation results for metricsa on the sine terrain.. . . . . . 81

5.1 CRAB on sine terrain.. . . . . . . . . . . . . . . . . . . . . . 84

5.2 Torque measurements on step obstacle.. . . . . . . . . . . . . 885.3 RB problem during step climbing.. . . . . . . . . . . . . . . 895.4 Torque and encoder measurements (torque requirement).. . . 915.5 Torque and encoder measurements (friction requirement).. . 925.6 Traction margin before slip occurs.. . . . . . . . . . . . . . . 935.7 Wheel torque measurements on sine terrain.. . . . . . . . . . 94


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Chapter 1

Introduction

1.1 Locomotion for rough terrain

There is an increasing need for mobile robots which are able to operate inunstructured environments with highly uneven terrain. These robots aremainly used for tasks which humans cannot do and which are not safe. Suchtasks include search and rescue in the debris of buildings after an earthquake

where humans are not able to pass and danger due to unstable structurespersists. In highly polluted areas which are not accessible to humans dueto the risk of intoxication, robots can be sent to gather information withvarious kinds of sensors. But the application that has received the most mediaattention in recent years is planetary exploration. Human space missions toMars are not possible at the moment, therefore, mobile robots are employedto explore the Red Planet and return data to Earth.

All these applications have in common that the robot is an intermediarythat primarily gathers information for human operators or provides mobil-ity to scientic instruments to approach targets of interest. To accomplishthese tasks successfully, the robots have to have means to adapt to uneventerrain and climb over obstacles, this means, they need increased mobilitycapabilities.

Different types of locomotion have been identied, the most importantones being wheeled, legged, and tracked locomotion. The adaptation to un-even terrain can be active or passive. Tracked vehicles have become thefavorite type in search and rescue scenarios where the environment is highlyunstructured. A lot of research was done in the eld of legged robots whichhas lead to signicant progress, and legged locomotion has a very high po-tential. The same applies to actively articulated suspensions. But, various


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2 1 . I n t r o d u c t i o n

considerations have lead to the choice of focusing this research on wheeled,passive locomotion.

Integration in related research at the Autonomous Systems Lab (ASL)of the Swiss Federal Institute of Technology in Zurich (ETH Zurich)concerning investigation and usage of wheeled, passive systems.

Link to ongoing projects of the European Space Agency (ESA), primar-ily the ExoMars mission which aims at sending a wheeled rover withpassive suspension to Mars.

Reliability and energy efficiency are key parameters in rover design

and the performance of wheeled, passive systems is superior to otherlocomotion types.

The control complexity of vehicles with passive suspension is very lowwhich makes them suitable for applications requiring a high degree of autonomy and robustness. On the one hand, only a small number of sensors is required. On the other hand, simple control algorithms canbe used. This means that the mobility performance is achieved bymeans of well thought out mechanics.

1.2 Motivation and objectives

The development of a rover, from rst ideas to the nal vehicle, is a complexprocess which can be split into several phases. At the beginning, ideas forsolving the mobility issue are searched. The promising ideas are transformedinto preliminary designs. At this point, trade-offs have to be conducted inorder to enable an objective, methodological selection of the best design.Then, the details have to be specied and simulations are run to determinethe expected performance. Multiple iterations of detailed design, prototypemanufacturing, and testing might be necessary before the nal specicationscan be dened such that the rover ts the requirements.

In literature, numerous ideas and rst prototypes of rovers can be foundas well as sophisticated models for accurate simulation of complex systems.Unfortunately, there is almost no work that shares a common basis and al-lows for comparison of the results. The denition of performance varies inliterature, direct comparison of several systems is rare, and the validation of simulation results is uncommon. Therefore, the following objectives were setfor this thesis:


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1 . 3 . O u t l i n e 3

Collect existing and introduce new metrics which dene the perfor-mance of wheeled, passive locomotion systems. The focus is on performance evaluation of preliminary designs which means that the details of

the nal design are not known yet and several candidate systems haveto be evaluated and compared in the frame of trade-offs for selection of the best design option.

Compile a catalog of existing rovers to provide an overview of the stateof the art. The term rover is used to refer to the respective suspensionmechanism which is responsible for the mobility performance in roughterrain.

Apply important metrics in a performance comparison of several sys-tems. The primary objective of this comparison is to show the utilityof these metrics whereas the comparison results are of subordinate rel-evance.

Since the level of detail of preliminary designs is low, it is not usefulto employ complex models for simulation. Therefore, the performanceevaluation is to be based on simple approaches and the results have tobe validated by means of experimental testing.

1.3 Outline

This thesis is split into four main parts. In chapter 2, the general need forperformance evaluation and the intrinsic benets for the robotics communityare argued, new mobility metrics are dened, and commonly used ones arediscussed in detail. An overview of existing systems, which are used in theanalysis sections, is provided in chapter 3, along with a description of thehardware for experimental validation. Chapter 4 starts with a brief overview

of existing software for simulation of rough terrain robots and continues withcomprehensive analyses based on static and kinematic models. The validationof the simulation results is provided in chapter 5. The conclusion summarizesthe work and highlights the contributions of this thesis.


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4 1 . I n t r o d u c t i o n


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Chapter 2

Performance evaluation

The evaluation of a systems performance is addressed in this chapter. Thisincludes a discussion about value and necessity of performance evaluationand its currently low but emerging importance in the robotics community.New and commonly used metrics are presented; they are needed to deneperformance and qualify it as good or bad. Then, a normalization is proposedbecause the systems have to have a common denominator to be comparable.Finally, the importance of requirements, which specify the capabilities theevaluated system is expected to have, is highlighted.

2.1 General considerations

Performance evaluation is a crucial part of system development. It pro-vides the necessary information to answer the following fundamental ques-tions which have to be asked at the end of each project:

Does the new system have superior capabilities compared toexisting solutions? In the case of a research project the value of a new system, as well as the benet for the research community, liesin its superiority with respect to the state of the art. Otherwise, theinvestment in the project cannot be justied. Thus it is important toprovide evidence for the gained value through performance evaluation

Does the new system comply with the performances asked forin the requirements document? If the project is not pure research,a client might be satised with a performance similar to the one of existing systems. However, the client will only pay if he gets what he


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6 2 . P e r f o r m a n c e e v a l u a t i o n

asked for at the beginning. Performance evaluation is the tool for theresearcher or engineer to prove that he did his work as specied, andfor the client to check if he gets what was agreed on.

While performance evaluation already is an integral part of industrialprojects, probably because it has a direct impact on payments, it still seemsto be widely neglected in the robotics community, at least among the peopleconcerned with system design. Unfortunately, many researchers limit theirpublications to a pure description of their system and a demonstration of the systems capabilities, instead of a thorough evaluation. The authorsstress the strengths of their system, mostly with respect to very specicsituations, but no benchmarks are performed. Even though it is desirable toshow the performance of a new system on real hardware, the experimentalresults usually remain very qualitative and do not allow a comparison withother systems. This weakness was already stressed in (Gat, 1995) and thecriticism remains valid. Gat called it anecdotal experimental results fromimplemented systems with little or no formal theoretical foundation. Theresearchers approach results in working systems, but it does not yield anunderstanding of the limitations of these systems.

Reasons for this common approach may be plentiful. While one couldargue that this is just the simplest solution and that people fear direct com-

parison of their work with the work of other researchers, it must not beforgotten that the availability of several platforms at the same place is rareand that hardware testing is a very demanding process in terms of time,infrastructure, manpower, or costs. Therefore, it is of highest importanceto standardize test procedures and to introduce commonly accepted metricswhich describe the performance of a system. (Sukhatme and Bekey, 1996)stated that progress in mobile robot evaluation will come to fruition whendifferent metrics are proposed and debated and some standardization ensues.Consequently, developers must test their systems accordingly and discuss the

results in their publications. The approach of (McBride et al., 2003) is evenbetter where the system is not tested by its developers themselves whichshould make the results less biased.

According to (Jacoff et al., 2002) not only researchers would benet fromstandardized tests but also sponsors and end users of robotic systems. Po-tential major benets for the robotics community include the following:

The best system for a specic application could be determined easilyand in an objective way.

Reviewers would be provided with an objective tool to estimate thevalue of a new system with respect to the state of the art.


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2 . 1 . G e n e r a l c o n s i d e r a t i o n s 7

Instead of participating in competitions, developers could test theirsystem at home and know immediately how it performs with respect toother systems. In that sense, performance rankings could be interpreted

as continuous competitions. This approach should by no means replaceregular competitions because they usually have positive side effects.For example, competitions often lead to a collective effort that resultsin signicant progress.

Standardized tests and binding norms are common in other elds of both research and industry. Even though roboticists have achievedremarkable accomplishments, standardized metrics and performanceevaluation could still contribute to increased reputation of the robotics

community among researchers in other domains.Despite the above criticism, it has to be stressed at this point that there

are ongoing efforts in the robotics community to standardize metrics and toestablish benchmarks. The part of the community that is concerned withalgorithms seems to be more active in this area. In SLAM (SimultaneousLocalization And Mapping), the dataset of Victoria Park in Sydney by Guiv-ant and Nebot (Guivant et al., 2002) has become a de facto standard onwhich algorithms have to be tested before publication. Caltech 101 (Fei-

Fei et al., 2004) contains pictures of objects belonging to 101 categories.They are used for benchmarking algorithms in many scientic publications,as well in robotics as in pure computer vision. Another interesting project isRadish: The Robotics Data Set Repository (Howard and Roy, 2003) whichaims to facilitate the development, evaluation and comparison of roboticsalgorithms. It does not only provide existing datasets but also encourages re-searchers to actively contribute and ll the repository with their own datasets.

The American National Institute of Standards and Technology (NIST) hasalso made an effort towards standardization and benchmarking in roboticswith the introduction of the Performance Metrics for Intelligent Systems(PerMIS) Workshop (NIST, 2000) which is aimed towards dening mea-sures and methodologies of evaluating performance of intelligent systems.Even though the better part of the publications in the PerMIS proceedingsare concerned with algorithms, PerMIS appears to be the biggest initiativein robotics that covers standardization of benchmarks for hardware systems.While common benchmarks can be easily implemented for algorithms in theform of data sets, it turns out to be more complicated for hardware systems.NIST has developed and built Reference Test Arenas for Urban Search andRescue Robots where robots can be tested and competitions are held regu-larly. Such setups have been reproduced in other places all over the world


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8 2 . P e r f o r m a n c e e v a l u a t i o n

like Bremen, Germany(Birk et al., 2007). Different elements in these arenaswere standardized (Jacoff et al., 2003), e.g., step eld pallets which are re-peatable surface topologies with different levels of aggressiveness to test the

mobility of a robot. Step elds can be easily created anywhere to simulateuneven ground under standardized conditions.The rock distribution at the Viking 2 landing site (Golombek and Rapp,

1997) has also evolved into a standard which can be found in many works re-lated to Mars exploration. In the context of the development of the ExoMarsrover, for example, this rock distribution is used to benchmark candidaterover designs in simulation.

As with every standard or norm, standardized performance evaluation

cannot cover every aspect of any particular mission or application. Yet, itcould provide information about required core competences that would helpresearchers and engineers looking for potential solutions, e.g., because datafor necessary trade-offs would be available. The robotics community stillhas a long way to go in this direction. However, the increasing number of publications and workshops dedicated to this topic are promising and showthat the existing initiatives are gaining momentum.

2.2 Metrics

Numerous metrics have been proposed and used in literature. They all serveto quantify the performance of robotic systems. Metrics provide means toassign numerical values to a systems capabilities. Consequently, they allowfor an objective comparison of similar systems. However, not all metrics

are relevant to a specic application. The important ones can be deter-mined based on the requirements of a project. Therefore, metrics have to beweighted accordingly, and it has to be specied what is considered good orbad performance.

This whole process requires some sort of standard which is accepted andapplied by the larger part of the robotics community. Since mobile roboticsis a broad eld of research, publications related to metrics for mobile robotscover a wide range of aspects. To illustrate this diversity, a selection of metrics appearing in literature is briey discussed in the next subsection.Thereafter, the most important metrics concerning the mobility of a robotare analyzed in more detail.


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1 0 2 . P e r f o r m a n c e e v a l u a t i o n

for a scenario including 100 kg payload, compacted snow, level ground, andnominal traveling speed of 1ms .

Energy is a critical parameter for mobile robots because it usually is

available in limited quantities only. This holds true especially for solar pow-ered rovers like the MER. (Roncoli and Ludwinski, 2002) provide an energyusage scenario over the whole mission split up by consumers. It clearly showshow the mission is affected by the availability of energy.

2.2.1.2 Control metrics

The electro-mechanical design of a system has a big impact on the perfor-mance. However, good controls can push the performance level even further.

In this regard, there is also a need for metrics to evaluate the algorithmic partof a system. (Munoz et al., 2007) summarize different metrics for navigationevaluation, and a protocol for standardized testing is proposed. The metricsare sorted by different categories, such as smoothness and security, and theyprovide the user with more detailed information than just length of a pathand required time. For example, thesmoothness metrics evaluate theconsistency between decision-action relationship and the algorithms abilityto anticipate and respond to events and thesecurity metrics measurethe mean and maximum risk during the entire mission, e.g., based on theminimum distance to an obstacle.

2.2.1.3 Operational metrics

The focus of (Tunstel, 2006) is on metrics for operational performance of de-ployed rovers as opposed to metrics for robot systems that are in experimentalphases of development, verication, or validation. Tunstel states that theavailable set of engineering telemetry from the rover constrains what metricscan be formulated. Therefore, operational performance metrics should befunctions of telemetry or derived data products produced during operations.Examples are:total traverse distance and terrain-based autonomousnavigation speed for the category autonomous navigation;approacha-bility and positioning accuracy and repeatability for approach andinstrument placement.

2.2.2 Mobility metrics

For all-terrain robots the mobility performance is a pivotal criteria. Numer-ous metrics help to understand and evaluate the locomotion capabilities of mobile robotic systems.


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2 . 2 . M e t r i c s 1 1

Three terms that are widely used to subclassify performance of wheeledrobotic locomotion are discussed in great detail in (Apostolopoulos, 2001).Maneuverability refers to a robots ability to change its heading, avoid ob-

stacles and navigate through cluttered environments.Trafficability is usedto express the robots ability to generate traction and overcome resistances.Congurations with good trafficability should maximize soil thrust while min-imizing motion resistance. The performance index that is of highest impor-tance in the scope of the present work isterrainability . Apostolopoulosdenes terrainability as the locomotions ability to negotiate rough terrainfeatures without compromising the vehicles stability and forward progress.

In this sense, most of the metrics described below refer to the terrainabil-ity of a robotic vehicle. This selection extends the list of Apostolopoulos in

order to cover additional aspects of mobility.2.2.2.1 Friction requirement

One of the biggest issues for vehicles moving in rough terrain is the generationof traction. Given that all wheels touch the ground at all times, the loadon the wheels changes due to the unevenness of the terrain. Assuming aproportional relationship between load on a wheel and maximum tractionsupported by the ground, it is advisable to set the torques on the wheels

accordingly. If all wheels of the vehicle are powered, the system is oveactuated. With the appropriate technique the ideal torques on the wheels canbe calculated such that minimum friction is required by the vehicle to avoidslip. Theoretically, this solution corresponds to the vehicles best possibleperformance in terms of slip avoidance. Hence, this characteristic is wellsuited to evaluate the performance of a vehicle. The corresponding metric iscalled friction requirement.

The approach, minimization of required friction through selection of idealtorques, has been used and discussed in several works. (Sreenivasan andWilcox, 1994) introduces it in the control algorithm of the actively actuatedGofor rover in simulation to minimize slip. (Iagnemma and Dubowsky, 2004)shows its usefulness in a dual cost function of a controller to improve mobilityover rough terrain of a rocker bogie type rover. In (Lamon et al., 2004) theapproach is extended from 2D to 3D and applied to the more complex Shrimprover (Siegwart et al., 2002). Further, it is shown that the maximum perfor-mance of the rover is achieved if the required friction is equal for all wheelsIn related work (Lamon and Siegwart, 2005), the approach is integrated ina PID control loop to assign motor torques based on the actual state of therover which leads to a signicant reduction of slip. The rst work to use theapproach as a metric to compare different rovers is (Thueer et al., 2006a)


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which employs the rover performance optimization tool described in (Krebset al., 2006).

The calculation of the friction requirement is based on Coulombs friction

law: F T F N (2.1)

where F T : traction force,F N : normal force, : friction coefficient which depends on the materials of wheel

and ground.

The maximum traction force supported by the ground is equal to F N . If it is exceeded (F T > F N ), slip occurs.

However, it is very difficult to know the exact value of in a real environ-ment, and in the case of loose soil, the wheel ground interaction demands fora more complex contact model. Therefore, the friction requirement metricmakes use of a virtual friction coefficient which is dened as

=F T F N

=T/rF N

(2.2)

where the traction forceF T can be expressed as the ratio of motor torqueT to wheel radiusr (Fig. 2.1).Because of over-actuation of rovers, the torque can be selected freely whichimpacts . The target value of is the minimum because it denes theminimum friction required by the wheel before it slips. By minimizingthrough specic selection of the wheel torques, the probability is increasedthat the required friction coefficient is smaller than the available frictioncoefficient ( < ) in any real situation and that enough traction can begenerated to prevent slip.

Since the load on each wheelF N i (indexi indicating wheeli) depends onthe state of the rover, the minimization of i has to be coordinated on system

FT

F N

T

r

Figure 2.1: Wheel ground interaction.


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2 . 2 . M e t r i c s 1 3

level. According to (Lamon et al., 2004), the optimal solution corresponds tothe situation where alli are equal. This solution can be found by applyingthe optimization criterion

mini

(i )2 (2.3)

to the wheel torque selection process where is the mean of alli . Theresultingmin expresses the friction requirement of the evaluated rover inthe given situation. If the rover is analyzed over a full simulation run, theactual friction requirementreq [-] corresponds to the maximum of all(min )nwheren is the number of simulation steps.

req = max {(

min )n } (2.4)

2.2.2.2 Maximum torque

The example of a torque measurement during step climbing of a six wheelrover, as depicted in Fig.2.2, is used to emphasize the necessity to havean estimate of the required peak torqueT max [Nm] while designing a rover.The nominal torque is roughly 0.4 Nm but the peak values climb as high as

3.5 Nm. These differences are signicant and have to be considered whenselecting motor and gearbox to be sure that all dependent requirements, e.g.,obstacle climbing, maximum traveling speed, or mean power, can be met.

(Wilhelm et al., 2007) highlight the fact that climbing even small steps atlow speed might require maximum torque. Therefore, they propose a dynamicmodel for this specic situation. The model is able to handle exible wheelsand allows for comparison of different robot designs due to non-dimensionaparameters. The authors claim that better estimates of the torques through

0 5 10 15 20 25-1

0

1

2

3

4

Time [s]

W h e e l

t o r q u e

[ N m

]

rear wheelmiddle wheelfront wheel

Figure 2.2: Wheel torque measurement during step climbing motion.


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more accurate modeling lead to lower actuator requirements with associatedbenets for mass and power consumption.

2.2.2.3 Maximum obstacle heightThe metric maximum obstacle heighthmax [m] is closely coupled to the met-rics maximum torque and friction requirement.req and T max are specic toa given terrain geometry. If this geometry is changed systematically, e.g., theobstacle height is increased, friction and torque requirements change accord-ingly. The maximum obstacle height is reached when the friction or torquerequirement is in conict with soil characteristics or motor performance. Insome cases, however, it might turn out that ground clearance is the limiting

factor during obstacle negotiation.2.2.2.4 Slip

Various forms of slip exist. (Tarokh and McDermott, 2005) identify turn slip,side slip, and roll slip as in Fig.2.3. In the present work, only the latteris used as a metric because the suspension conguration has a signicantimpact on roll slip in rough terrain.

Roll slip is the relative motion between a rolling object and the surface onwhich it is moving. This slip is generated by the objectss rotational speedbeing greater or less than its free-rolling speed. In fact, real-world wheeled ortracked vehicles are capable of moving only because slip occurs. Nevertheless,slip is an undesirable effect due to several reasons:

If the traveled distance of a vehicle is measured only by means of wheelrotation, slip cannot be detected. This kind of odometry is inherentlyinaccurate to a certain degree depending on the environment. (Nagatani

side slip ()

x w

y w

x w

y w

(a)

turn slip ()

v

x w y w

(b)

roll slip ()

xw

zw

x w

z w

r +

(c)

Figure 2.3: Types of slip.


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2 . 2 . M e t r i c s 1 5

et al., 2007) describe a method to improve the odometry by consideringslippage in the model of a tracked vehicle, a locomotion type that iseven more susceptible to slip than wheeled locomotion. (Lamon and

Siegwart, 2003) show how to include the state of an articulated rovermoving on rough terrain to increase the accuracy of the odometry.

It is difficult to measure or estimate slip accurately. However, controlcan be signicantly improved if slip is accounted for through estimationand additional sensing(Helmick et al., 2005), or through modeling of the complex wheel ground interaction mechanics (Yoshida and Hamano,2002). Very recently, (Ishigami et al., 2008) reported impressive resultsfrom slope traversal along a given trajectory with online slip compen-

sation using visual odometry.Slip is a loss of energy because the energy put into the rotation of awheel cannot be completely transformed into the desired linear move-ment.

The vehicle gets stuck if 100% slip occurs.

Different denitions for slip exist. The most common one denes the slipratio s r [-] as follows:

s r =(r v)/r ; r > v (acceleration )

(r v)/v ; r < v (deceleration )(2.5)

where : rotational wheel speed,v : translational wheel speed,r : wheel radius.

With the same information, the absolute accumulated slipsa

[m] can becalculated as a measure for the total slip distance over the course of a testrun:

sa =n

i =1

r i vi t (2.6)

where n : number of measurements, t : sampling time.

Unfortunately, the measurement of one important parameter used in theabove formulas, the translational speedv of each wheel, is not easy in reality.In laboratory setups, it can be measured by means of vision systems. If no


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such tracking system is available, the above denitions of slip are not applica-ble. Then, the only measure of wheel slip is the difference between recordedwheel rotation and total traveled distance which is difficult to determine in

rough terrain too.2.2.2.5 Stability

Knowledge of the stability of a vehicle is pivotal, either to plan trajectories,to generate velocity commands, or to monitor the stability margin online.Depending on the traveling speed of a vehicle, the model used to calculatestability can be static or dynamic. For slow moving rovers, the static modelis usually considered sufficiently precise because inertial effects can be ne-

glected at these speeds. However, (Mann and Shiller, 2005) developed adynamic model for an articulated rover and dened a static stability margin(SSM) and a dynamic stability margin (DSM) which are based on the feasiblerange of speed and acceleration, i.e., the range of values which comply withthe stability constraints. Stability measures based on both types of modelsare discussed below.

I) Stability based on a static model

Different approaches of varying degree of complexity to calculate static sta-bility (SS) are presented next.

The simplest way to determine a vehicles stability is the geometric ap-proach which is commonly referred to in literature as stability margin.This term dates back as far as (McGhee and Frank, 1968) and is usedto evaluate the distance between the projection of the center of grav-ity (CoG) on the ground and the border of the polygon formed by thesupporting points of the vehicle on the plane. (Hirose et al., 2001) sum-

marize existing stability criteria and propose a classication with thefocus on walking machines. (Apostolopoulos, 2001) limits his work towheeled vehicles and identies the longitudinal and lateral gravitationalstability margin for a vehicle driving parallel to an uphill slope or alonga cross-hill slope, respectively. The maximum angleSS at which thestability margin becomes zero can be calculated based on the CoGsposition relative to the wheel ground contact points (Fig.2.4), e.g.,maximum longitudinal uphill stability is reached at

SS = atanx rear

z . (2.7)


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2 . 2 . M e t r i c s 1 7

xfront

rear

front

xrear

z

xvzv

yvzv

z

y left yright

left right

Figure 2.4: Longitudinal (left) and lateral (right) stability.

A more general form of the geometric approach, the force-angle sta-bility measure, was introduced by (Papadopoulos and Rey, 1996) andapplied in a slightly modied form by (Iagnemma et al., 2000). It isable to handle any kind of vehicle footprint at any angle relative tothe slope by considering the outermost wheel ground contact points p i (i = 1 ,...,m ) which form a convex support polygon when projectedonto the horizontal plane (Fig.2.5). The lines joining the wheel groundcontact points are referred to as tipover axesa i where i = a i / a i .Tipover axis normalsl i that intersect the CoG are given by:

l i = ( 1 i T i ) p i +1 (2.8)where(i + 1) has to be set to 1 if i = m in order to close the loop.Stability anglesi can then be computed for each tipover axis as theangle between the gravitational force vectorf g and the axis normall i :

i = i cos 1 ( f g l i ) (2.9)

withi = +1 if ( l i f g ) i < 0 1 otherwise (2.10)

The overall maximum vehicle stability angle is dened as the minimumof thei stability anglesi :

SS = min (i ), i = {1,...,m }. (2.11)

Both geometric approaches to calculate stability are simple and requirelow processing power which makes it possible to include them in controlalgorithms. (Iagnemma et al., 2000) and (Grand et al., 2004) have used the


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xy

z

f g

1 2

i

i+1

li ip 1

p 2

p i

p i+1

l1

Figure 2.5: Support polygon of the force-angle stability measure.

latter approach to recongure the actively articulated legs of their wheeledrobots by including the stability angles in an optimization criterion that aimsat maximizing stability.(Nakamura et al., 2007) pursue the same strategy byactively moving the center of mass of a wheeled robot.

Unfortunately, these approaches are not suitable to calculate the stabil-ity of passively articulated rovers where the suspension system has a non-negligible impact on the stability. In this case, the effective stability can becalculated by means of a static model. A 2D model, which outputs up- anddownhill stability, is considered next. Options to extend the approach to 3Dare discussed below.

First, a static 2D model of the vehicle on a at surface has to be devel-oped. Then, while the inclination angle of the surface is incremented inthe model, the contact forces are calculated at each step. The stabil-ity angle is dened as the angle when one of the wheels looses contactwith the ground, i.e.,F N 0. It has to be highlighted that this con-dition is mandatory for the static model to work but that a real roverdoes not necessarily tip over at this angle because a rover can be tem-porarily stable even if one wheel does not touch the ground. If allnwheels are motorized, as it is normally the case for rovers, the equationsystem is under-determined and has an innite number of solutions.The physical meaning of this situation is that(n 1) wheel torquescan be set as inputs or that an optimization has to be employed tond the wheel torques. However, on a at surface the selection of thewheel torques has no impact on the normal forces and hence, on theSS neither. Therefore, wheel torque selection is not discussed here but


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2 . 2 . M e t r i c s 1 9

a reasonable approach, which minimizes required friction, is describedin 2.2.2.1.

To demonstrate the impact of the suspension system on the SS, the geo-metric and static approaches are both applied to a simple rocker bogie typerover as depicted in Fig.2.6 (left) with equal wheel spacing (lfront = lrear ).The right side of Fig.2.6shows the derived models for the two approaches.

By considering only the position of the CoG and the distance betweenfront and rear wheel, the suspension system is completely neglected in thegeometric approach. Since the resulting model is fully symmetric, the ge-ometric approach yields identical stability anglesrear and front for up-and downhill stability, respectively. Using the same dimensions for both ap-

proaches, the geometric model predicts stability of +/- 61

.The static model which represents the mechanical properties of the roverin more detail suggests that identical up- and downhill stability is very un-likely due to the highly asymmetrical character of the suspension system.It predicts accordingly that the rover remains stable up to 55 uphill and42 downhill slope, which are by denition the angles where one of the nor-mal forces on the wheels becomes zero. These normal forces are plotted as function of the slope angle in Fig.2.7and show clearly distinct load distribu-tions for positive and negative inclination. This is caused by the asymmetricdesign of the suspension system and conrms the intuitive result of differentup- and downhill stability.

It might be surprising that the two approaches do not yield the same uphillstability even though the rear part of the models is identical. This is linkedto the fact that the geometric model is too simple and does not consider thefeatures of the suspension. The normal force plot helps understanding whathappens at the wheel ground contacts on a sloped terrain. It shows that

rear front

lfrontlrear

xvzv geometric model

lfrontlrear

static model

lfrontlrear

Figure 2.6: Comparison of models for stability evaluation. Left: originaldenition of rover; right: derived geometric and static models (scaled).


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-40 -35 -30 -25 -20 -15 -10 -5 00

10

20

30

40

50

Inclination angle []

N o r m a l

f o r c e

[ N ]

Downhill stability


0 5 10 15 20 25 30 35 40 45 50 550

10

20

30

40

50

Inclination angle []

N o r m a l

f o r c e

[ N ]

Uphill stability


Figure 2.7: Stability results from static model.

the middle wheel looses contact with the ground rst, for both positive andnegative inclination. This behavior leads to reduced stability. The geometricapproach cannot model such behavior and is therefore too optimistic forarticulated rovers.

Another drawback of the geometric approach is its inability to modelwheel ground contact angles which have a great inuence on the stability of a vehicle. Since the 2D static model considers this detail, it is able to providestability information on any terrain shape in general, not only on an inclinedplane.

Obviously, the static approach can only be used for the longitudinal direc-tion in which the suspension is acting. The lateral SS can be calculated witha geometric approach because most rovers do not dispose of a compliance inthis direction.

Extending the static model to 3D is desirable to gain information aboutthe stability for any heading angle with respect to the slope. However, thisis not possible by just adding forces in the third dimension to the modelbecause a rover is a statically indeterminate system in the lateral direction.This indeterminacy can not be handled by the proposed rigid body model.It cannot be determined how the lateral stresses are distributed within the

structure unless elasticity of the elements is considered which is in conictwith the objective of this analysis to employ simple models.Several simplications are possible to deal with this problem.

(Lamon, 2005) introduced additional degrees of freedom (DoF) in thelateral direction in the wheel ground contact model. Lateral forceswere considered only at the front and rear wheel of the SOLERO roverwhich is a pretty strong simplication. Nevertheless, the model servedits purpose to improve motion control.

Instead of introducing DoF, the contacts could be modeled as compli-ant components, i.e., springs. This is a commonly used approach in


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2 . 2 . M e t r i c s 2 1

40 30 20 10 0 -10 -20 -30 -400

50

100

150

200

250

Slope angle []

N o r m a l

f o r c e

[ N ]

Normal forces ExoMars (3-Bogie)

rear middlefront

3-Bogie Longitudinal Static Stability

C o n

t a c t

f o r c e

[ N ]

Source: (Slade et al., 2007)

Slope [] + ve down

Figure 2.8: Inuence of the simplications applied by Slade (left)on the stability results in comparison with the static model (right).

(note: different denition of slope angle)

dynamic simulations where contacts are modeled as compliant spring-damper systems(Sohl and Jain, 2005). This approach has not yet beeninvestigated to determine static stability.

Another approach is used in (Slade et al., 2007). By considering onlythe vertical component of the contact force (along the gravity vector),static indeterminacy can be avoided and the equation system resultsfrom regular force and torque equilibrium. The results for up- anddownhill stability (heading = 0 ) are compared to the output by thenormal static model in Fig.2.8. In general, the curves are very simi-lar but two main differences become apparent: the discrepancy growsbigger with increasing angles; the force values are bigger in the modelby Slade because it outputs the vertical component of the contact forcewhile the regular static model outputs the normal force only. Con-sequently, the model by Slade predicts better stability. However, the

simplicity of this approach can be a big advantage but further investi-gation is needed.

II) Stability based on a dynamic model

In the work of Shiller and Mann (Shiller and Mann, 2004; Mann and Shiller,2005) a dynamic 2D model is employed to determine stability. Thus stabilitydenitions and interpretation of the metrics are different than the ones above.Stability conditions are expressed in terms of constraints on then individual

ground forces.


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2 . 2 . M e t r i c s 2 3

2.2.2.6 Velocity constraint violation ( VCV )

V CV [-] is a measure for the risk of violation of kinematic constraints throughdeviation from the ideal velocity which leads to slip. If a vehicle is movingon a plane and the same speed is set to all wheels, no slip occurs under idealconditions. Under real world conditions slip can never be avoided but the sliplevel remains low on a plane because the ideal velocities are equal. In roughterrain, however, kinematic constraints require every wheel to rotate at anindividual speed (Fig.2.10), thus, deviation from the ideal velocity is morefrequent and the slip level increases. This problem was addressed by meansof control algorithms which assign individual wheel speeds based on the stateof the rover but sensing all the necessary information is difficult. Therefore,it is desirable to use a suspension system which complies inherently well withthe kinematic constraints.

Basic kinematics, which describes relative motion between the wheels, isused to calculate the ideal velocities. By imposing the terrain constraintson the wheel motion and selecting one wheel as reference where speed iinput, the ideal velocities of the remaining wheels result from the kinematicproperties of the suspension system. An example with ideal velocities of twocases with different reference wheels is depicted in Fig.2.11.

To calculateV CV , rst, the ratio between ideal velocityvideal and refer-

ence velocityv is dened for each wheel asV =

videalv

(2.15)

Since positive and negative deviations tend to even out the mean value of V over a full simulation run withn measurements, the standard deviation isused instead.

V =1n

n

i =1

V i V 2

12

(2.16)

V is calculated for every wheel except for the reference whereV = 0 . That is, a set of V consists of (m 1) values for anm wheel

Figure 2.10: Ideal velocities in rough terrain.


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2 . 2 . M e t r i c s 2 5

F Tmax = c A + F N tan (2.18)

where c : coefficient of soil cohesion,A : contact area,F N : normal force, : soil friction angle.

c and are soil specic parameters which are used in complex wheelground contact models based on terramechanical theory. Fundamen-tal information about terramechanics can be found in (Bekker, 1969)and (Wong, 1993). A broader denition of gradeability is discussed ingreat detail in (Apostolopoulos, 2001).Mainly two considerations lead to the exclusion of the slope gradeabilityfrom the performance comparison in this thesis. On the one hand, thehigh level of complexity of the terramechanical wheel ground interactionmodel is not in line with the objective to use simple models. On theother hand, the model makes use of several soil specic parameters.Since no precise application scenario exists for this work, there is nointerest to investigate the slope gradeability on a specic soil type.Instead, the more general formulation of the friction requirementreqat a certain angle could be used for comparison.Mean free path (MFP) (Wilcox et al., 1997) dene the MFP asthe expected distance which the vehicle can traverse on a straight linebefore it encounters a non-traversable hazard. They argue that in thecase of a large MFP value the hazard avoiding system can be simplewhich reduces costs and complexity of the rover while increasing thelikelihood for a successful mission. The MFP depends on rover lengthand width as well as on size and areal density of rocks (obstacles) atthe planned mission location.Coverability and crossability These two metrics were introducedby (Molinoy et al., 2007) with the objective to develop methods forquantifying the difficulty a robot would encounter traversing rough ter-rain. It is assumed that the terrain can be discretized like the NISTstep eld. Coverability reects the difficulty a robot would have tryingto move over the entire terrain. Crossability refers to the difficulty formoving from point A to point B.The authors state that the focus was on general formulation of themetric rather than on accuracy for specic robot congurations. In


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this sense, only the wheel diameter as well as one scalar value repre-senting the kinematics of the robot are contained in the formula forcoverability. It is questionable if this single value which has no direct

physical meaning is sufficient to objectively describe the obstacle climb-ing capabilities of existing rovers. Therefore, the metrics seem to bebetter suited for performance comparison of one rover on different ter-rains rather than for comparison of different rovers on the same terrainwhich is the objective of this thesis.

2.3 Normalization and requirements

One fundamental problem of comparing existing rovers is that they are alldifferent in several dimensions like footprint, wheel diameter, mass, or CoG.Scaling them by one factor is not possible because the factor varies dependingon the dimension as shown in Table2.1. Therefore, in the present case wherethe focus is on the comparison of the suspension systems, it was decided toapply some sort of normalization. This means that one set of dimensions waschosen for the key parameters and that the suspension systems were adaptedin size to t this standard. This is a pragmatic but reasonable choice in viewof the intended validation of the proposed metrics by means of experimentaltesting. The hardware system has to have one xed size and one set of wheelswhile the suspension can be recongured to different types.

A comparison can also use dimensionless parameters in order to relatethe performance of systems of different sizes. The friction requirement, forexample, can be expressed as a function of the ratio between track lengthL

Table 2.1: The problem of scaling rovers for comparison: the ratio depends onthe parameter.

CRAB 1 ExoMars 1

parameter ratiotrack length [m] 0.648 1.4 2.16

mass [kg] 35 93.5 2.67

wheel diameter [m] 0.18 0.25 1.39CoG Z [m] 0.215 0.554 2.58


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2 . 4 . C o n c l u s i o n 2 7

and obstacle heighth, req = f ( Lh ). These parameters are both important,track length for the design, obstacle height for the performance. This way,rovers of different length can be compared. However, this approach has three

main drawbacks which are of great importance in the frame of this work.First the available data about existing rovers does not enable conductinga comparison of this kind. As it was pointed out before, the evaluations wereall carried out based on different methodologies and metrics. Therefore, if acomparison was to be made, new models would have to be created anywayand it would be reasonable to normalize them as proposed above.

Second it has to be considered that the performance with respect to a spe-cic metric can be inuenced by more than one parameter which complicatesthis kind of comparison signicantly. For example, besides the length of therover the wheel diameter has a signicant impact on the friction requirementtoo. Therefore, rovers of different length can only be compared if they haveequal wheels.

Third the development of a rover is in most cases driven by requirementswhich constrain the dimensions of a candidate system. For example, if a roveris expected to carry a payload of 1 m length, a 0.65 m rover like NASAsSojourner does not t the requirements. However, it must be distinguishedbetween a real rover which has xed dimensions and the principle of thesuspension mechanism which can be adapted to the appropriate dimensionslike the rocker bogie suspension that was used for Sojourner, FIDO, andMER 1 .

Requirements are also important for the comparison of the systems. Assoon as all normalized rovers are evaluated with respect to the same metrics,performance rankings can be generated. However, the requirements dene theimportance of each metric which has a direct impact on the overall rankings.For example, if a rover is going to operate in benign terrain, the obstacleclimbing capabilities are of little relevance and a good climber is not the

right choice for such a mission. Obviously, metrics are used to evaluate theperformance of a system but requirements are needed to nd the systemwhich is most suited for a specic application.

2.4 Conclusion

Standardized performance evaluation is a powerful tool to compare and as-sess the value of robotic systems. Even though a lot of researchers have

used specic metrics in their work and several initiatives push for commonly1 A detailed description of the rovers can be found in chapter 3.


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accepted rules and benchmarks, standardized performance evaluation has along way to go in robotics.

A number of metrics were presented in this chapter as examples of the

diversity of mobile robotics as a eld of research. Since this work focuseson the performance of wheeled locomotion systems for rough terrain appli-cations, special attention was paid to mobility metrics which were discussedin great detail.

The most important mobility metrics, which are used in the analysis andvalidation sections below, are summarized here.

The friction requirement (req ) is a measure for the obstacle climbingcapability of a rover. If this values is small, the rover requires less fric-tion and is therefore more likely to overcome an obstacle in an unknownenvironment without getting stuck.

The maximum torque (T max ) is an important parameter for the roverdesigner for the selection of motor and gearbox. Situations like obsta-cle climbing require signicantly higher torques than regular motion inrough terrain. Therefore, the specications for electronic and mechan-ical components have to be adapted accordingly.

The static stability angles (SS ) help mission planners to determinenon-accessible areas, and rover drivers are provided with informationabout stability margins while driving on sloped terrain.

The V CV metric is an indicator of the amount of slip that could occurdue to violation of kinematic constraints in uneven terrain. This in-formation is valuable since slip has a negative impact on the odometryand causes loss of energy.

These metrics cover different aspects of mobility performance and provide

essential information about a rovers capabilities which is needed for properevaluation and comparison.The discussion about normalization and requirements recalled the need to

create a common basis for comparison and to precisely dene the objectives of a rover development. Metrics alone are of little use because their importancechanges depending on the application and in most cases the challenge is tond the right trade-off.


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Chapter 3

Systems

Numerous wheeled passive locomotion systems have been proposed in liter-ature. A comprehensive selection of them is analyzed to different extent inthis thesis. These systems are introduced next. First, an overview in listform is provided, followed by a more detailed description. For validationpurposes of the simulation results, modular hardware was developed whichallows exchanging the suspension conguration by maintaining importantsystem parameters. The hardware design is described in the last part of thischapter.

3.1 Overview

In Tables3.1 - 3.3, a brief description of all systems is given in alphabeticalorder. A similar overview was given by (Lauria, 2003) which included activesystems, too. The selection below, however, is limited to passive systemsand has been extended by new ones which have appeared in the roboticscommunity in recent years.


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Table 3.1: Wheeled passive locomotion systems: overview part I.

CJ-1 by Transportation College, Jilin UniversityCoupled positive and negativequadrilateral lever mechanismson each side.Differential to level body pitch.No steerings.

CRAB by ASL, ETH ZurichTwo parallelogram bogies on eachside with linkage at top.Differential to level body pitch.4 steerings.

ExoMars (3-Bogie) by ESA

Three regular bogies(2 longitudinal at side,1 transversal at rear). 2D modelidentical to RB.No differential required.6 steerings.Nexus 6 by Space Robotics Lab, Tohoku University

Coupled parallelogram bogies.Rear bogie only moves on asym-metric terrain because of link todifferential. 2D model identicalto RCL-E.Differential to level body pitch.4 steerings.

rigid link in 2D

Marsokhod by VNIITRANSMASH

Three pairs of wheels, joined to-gether by a three DoF passivelyarticulated frame.No differential required.Skid steered.


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3 . 1 . O v e r v i e w 3 1

Table 3.2: Wheeled passive locomotion systems: overview part II.

PEGASUS (Micro5) by AMSL, Meiji UniversityFour wheel drive with fth wheellinked to body by means of afreely rotating lever.Body split left/right, connectedby pivot.Skid steered.

RCL-C by RCLEarly design option for ExoMars.Rigid connection rear to centerwheel, articulated from center to

front.Differential to level body pitch.4 steerings.

RCL-D (ExoMaDeR) by RCLEarly design option for ExoMars.Complex suspension geometry,diagonally mirrored left/right.Differential to level body pitch.4 steerings.

RCL-E by RCL

ExoMars design option. Threeparallelogram bogies(2 longitudinal at side, 1 trans-versal at rear).No differential required.4 steerings.Rocker bogie (RB) by NASA/JPL

Versions: Rocky 7, FIDO,Sojourner, MER, MSL.Rocker and bogie on both sides.Differential to level body pitch.4-6 steerings.


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3 2 3 . S y s t e m s

Table 3.3: Wheeled passive locomotion systems: overview part III.

Shrimp/SOLERO by ASL, ETH Zurich

Wheels in 3 tracks (2 each), forkat front with internal spring, 1parallelogram bogie at each side,rigid link body-rear wheel.No differential required.2 steerings.

WMR by Korea Advanced Institute of Science and TechnologyFour bar linkage mechanism.Differential: N/A.No steerings.

Four wheel vehiclesNo longitudinal suspension. 2D model identical to 4WD car.Nomad by CMUPassive adaptation to uneven ter-rain through left/right averaginglinkage.Coordinated steering.

Dune-Explorer by SpaceRobotics Lab (Tohoku Uni.)Passive adaptation to uneven ter-rain through left/right averaging

linkage.4 steerings.

K11 by ASL/NASA AmesPassive adaptation to uneven ter-rain through longitudinal pivot atfront center.No steering.


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3 . 1 . O v e r v i e w 3 3

CRAB, RB, and RCL-E were evaluated in detail in this work becauseof their relevance with respect to ongoing research at ASL, and, in the caseof RB, because of its successful employment in Mars exploration missions

While the evaluation of most other systems was limited to the static analysis,two rovers were not explicitly considered in the analysis at all. Reasons forthis exclusion are given here.

ExoMars (3-Bogie)ExoMars (Michaud et al., 2008) is the suspension system selected byESA for the ExoMars mission. It evolved from the former design optionRCL-E. They only differ in bogie type. ExoMars has three regularbogies, thus the alternative name 3-Bogie, to provide mobility in rough

terrain, while RLC-E makes use of parallelogram bogies. The bogiearrangement, one on each side at the front and one at the rear, isadvantageous for the payload volume because no traversing differentialis required. However, the stability polygon is reduced to a triangle.The main reason why ExoMars is not explicitly included in the analysisis its equality in 2D with NASAs rocker bogie system. If looked at fromthe side (Fig.3.1 (right)), ExoMars and RB are identical. Since theanalysis in this work makes use of 2D models only, the same model rep-resents both rovers. Due to RBs status as quasi-reference system andits proven mobility performance, this conguration is always referredto as RB but the results are valid for ExoMars too.

Nexus 6The same applies to Nexus 6 (Yoshida and Hamano, 2002) which isidentical in 2D to RCL-E (Fig.3.2). RCL-E was given priority becauseof its role as an ExoMars design option and ASLs participation in ESAprojects.Nexus 6 has a suspension consisting of two coupled parallelogram bo-gies. However, the upper parallelogram is connected to the body andthe differential lever at the rear, rendering the parallelogram immobileas long as left and right suspension move over identical terrain geom-etry. This is common to both systems because the transversal rearbogie of RCL-E does not move either on such terrain. Because of theclear design analogies, the results of the 2D analysis of RCL-E are alsoapplicable to Nexus 6.


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3 4 3 . S y s t e m s

ExoMars (3-Bogie)

(a)

RB

(b)

Figure 3.1: Comparison of ExoMars and RB. Left: transversal bogie and dif-ferential are active which puts the front bogies at different heights; center/right:transversal bogie and differential are in initial position (inactive) and bogies there-

fore at the same height which leads to identical 2D models.

Nexus 6

(a)

RCL-E

(b)

Figure 3.2: Comparison of Nexus 6 and RCL-E. Left: differential and transver-sal bogie are active which puts the front bogies at different heights; center/right:

differential and transversal bogie are in initial position (inactive) and front bogiestherefore at the same height which leads to identical 2D models.


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3 . 2 . D e s c r i p t i o n 3 5

3.2 Description

The systems briey introduced above are described in more detail in this

section2

.CJ-1This rover was proposed in (Chen and Wang, 2007) as a candidate for aChinese lunar rover. Information about the system is generally sparse.According to the authors, the initial conguration had the drawbackto distribute load unequally to the wheels and to have low obstacleclimbing capabilities. The authors claim to have solved these problemsthrough optimization and show a schematic of the altered conguration.

Even a prototype of CJ-1 during obstacle negotiation is depicted butresults are provided for simulation only and in confusing format.The suspension consists of a coupled positive - negative (inverted)quadrilateral lever mechanism. Left and right suspension are identi-cal and linked by a differential.

CRABThe CRAB (Thueer et al., 2006b) was developed at ASL. The evolutionof the system and how simulation was used to improve the performanceis described in (Thueer et al., 2007). The CRAB is a functional researchplatform equipped with different types of sensors (IMU, camera) andis being used for work on terrain classication.The suspension consists of two parallelogram bogies which are con-nected by two joints (colored white in Fig.3.3). The top joint is anormal pivot while the lower one is a double-joint which connects thewheel as well. The distances between the vertical bars are set to13 and23 of the bogie length which leads to equal loading of all wheels. Left

and right suspension are identical and linked by a differential.MarsokhodMarsokhod (Kemurdjian et al., 1992) consists of an articulated framewith two segments that move relative to each other and three pairs of independently driven wheels. The steering capabilities are limited toskid steering.Due to the articulated frame, the payload area is segmented (front/rear).This is unfavorable because it limits the effective payload volume and

2 The level of detail in the description of the systems varies greatly due to availableinformation.


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1/3 L 2/3 L

Figure 3.3: Suspension of the CRAB.

maximum size of devices. Another disadvantage is that the CoG of each segment has to be at23 of the segment length towards the outerwheels to have equal load on all wheels.

PEGASUS (Micro5)PEGASUS (Kuroda et al., 1999) is basically a four wheel vehicle witha pivot at the front between left and right side to allow adaptation touneven terrain. In order to increase terrainability, the designers addeda fth wheel in the center which is also connected to the pivot by meansof a rigid bar.PEGASUS payload area is segmented (left/right) which is considered adisadvantage because it makes it difficult to accommodate the payload.

RCL-CTests with an RCL-C (Kucherenko et al., 2004) breadboard at ASLshowed awfully bad performance during obstacle climbing because of unfavorable kinematics, and the system was discarded as an ExoMarsdesign option even by the designers themselves. RCL-C is used in thestatic analysis anyway to investigate the cause for the bad performance.

RCL-DAt rst, concept D (Kucherenko et al., 2004) was considered the bestoption of RCLs rover study. Therefore, the ExoMaDer breadboardwas built for ESA. Testing was deemed successful with the rover show-ing good terrainability. However, due to the suspension systems highcomplexity, RCL-D was also discarded and the continued developmentresulted in the RCL-E design.


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3 . 2 . D e s c r i p t i o n 3 7

RCL-D has a multi-leverage suspension system which is designed toprovide vertical displacement of all wheels. Left and right suspensionare identical and linked by a differential.

RCL-ERCL-E (Kucherenko et al., 2004) was considered the best design optionfor the ExoMars mission until deciencies in stability were discoveredduring the chassis trade-off (Michaud et al., 2007). This problem wassolved by replacing the parallelogram bogies by regular bogies which re-sulted in the 3-Bogie design for ExoMars (Michaud et al., 2008). See3.1on ExoMars and Nexus 6 for more details about RCL-Es suspension.This study investigates more than the stability and it was started before

the ExoMars conguration was changed. Therefore, RCL-E is includedin the full analysis.

Rover bogie (RB)NASAs rocker bogie conguration (Lindemann and Voorhees, 2005;Fiorini, 2000) has already been successfully employed three times inMars missions in the form of the rovers Sojourner, Spirit and Opportu-nity. The next rocker bogie rover, the Mars Science Lab, is scheduledto launch in 2009. Test systems like Rocky 7 and FIDO have also been

mentioned in literature. Thus, RB has become the quasi-reference sys-tem to which other rovers have to be compared. Unfortunately, littledata is available about the mobility performance of RB and it has tobe considered that the various RB rovers of NASA differ signicantlyin size.The RB conguration consists of a rocker and a bogie. They are linkedby a pivot which allows the wheels to keep contact with the ground inuneven terrain. The wheel spacing is different on the various implemen-tations of RB. If the distances are not equal, the position of the centerof mass has to be chosen accordingly to get equal load on all wheels.Left and right suspension are identical and linked by a differential.

Shrimp/SOLEROShrimp and SOLERO, developed at ASL, are based on the same con-guration (Siegwart et al., 2002;Michaud et al., 2002) but they differin size. The spring in the fork at the front is used to distribute the loadequally to all wheels. This leads to excellent step climbing capabilities.Unfortunately, the wheels are aligned in three tracks. With two steer-ings only, front and rear, the lateral wheels are subject to skidding inorder to follow a curved trajectory. While small obstacles might pass


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3 8 3 . S y s t e m s

under a rover with two suspensions (left/right), this is not possible inthe case of the Shrimp.The Shrimp is one of the few rough terrain robotic platforms availableas a product (BlueBotics, 2008).The suspension consists of a quadrilateral mechanism at the front andone parallelogram bogie on each side. The rear wheel is directly con-nected to the body structure. No differential is required.

WMRInformation on this rover is also sparse. The suspension of the wheeledmobile robot (WMR) proposed by (Woo et al., 2006) consists of a fourbar linkage with a limited pin joint. The design and optimization pro-cesses are described in broad detail, the evaluation of the prototype,however, is limited to a pass/fail table. Left and right suspension areidentical and linked by a differential.

Four wheel vehicleVehicles with more than three wheels need a suspension to keep contactwith the ground on all wheels. The three rovers, Nomad (Apostolopou-los, 2001), Dune-Explorer (Ishigami et al., 2007), and K11 (Lachatet al., 2006), are examples of possible four wheel congurations. Asshown above, the 2D model of these vehicles is the same as the model of a car which means that the suspension does not act in the longitudinaldirection and does not increase obstacle climbing capabilities. However,all three rovers have a passive suspension system which enables them tomove safely on rough terrain. While Nomad and Dune-Explorer havedifferentials between the left and right suspension, K11 has a passivelinkage between front and rear axle.

3.3 Rover breadboardFor the validation of the simulation results, a modular hardware system wasdeveloped that allows for easy reconguration of the suspension type. All fourrovers, namely CRAB, RB, RCL-E, and ExoMars (3-Bogie), are depicted inFig. 3.4on at ground and during step climbing.

3.3.1 Mechanics

The mechanics were designed in a modular way in order to keep the number of parts and the technical complexity low. By exchanging the suspension parts,


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Mobility Evaluation of Wheeled All Terrain Robots Metrics and Application