Investigation of an Articulated Spine in a Quadruped Robotic System

161 Pages·2011·6.36 MB·English

Investigation of an Articulated Spine in
a Quadruped Robotic System
by
Brooke M. Haueisen
A dissertationsubmittedinpartial fulfillment
oftherequirementsforthedegreeof
DoctorofPhilosophy
(Mechanical Engineering)
in TheUniversityofMichigan
2011
DoctoralCommittee:
ProfessorGregory M.Hulbert,Chair
ProfessorJessy W.Grizzle
ProfessorArthurD. Kuo
AssistantResearch Scientist JonathanE.Luntz
Ihavenotfailed. I’vejustfound10,000ways thatwon’twork.
-ThomasEdison
(cid:13)c BrookeM.Haueisen
AllRightsReserved
2011
Tomy favoriteengineer-my father
ii
Acknowledgments
Many, many thanks are wished to everyone who has assisted with the formulation and
executionofthisresearch. Yourhelp wasimmenselyappreciated.
Special thanks are extended to my committee for all of their support, as well as all of
the additional faculty that have helped along the way, especially Prof. Kokkolaras for his
assistance with the optimization. Prof. Assanis, Prof. Awtar, Prof. Brei, Dr. Filipi, Dr.
Garikipati, Prof. Gillespie, Prof. Hart, Prof. Koditschek, Prof. Kota, Prof. Saitou, Dr.
Skerlos, Prof. Stein, Cynthia Quann-White, Matt Navarre and Bob Coury are thanked for
alloftheirsupportandwords ofencouragement.
To my family, for always being there wheneverI needed them. Dad, Mom, Dr. Anton,
Eddie, Caitlin, Grandma Wil and George, Grandpa Chuck and Margaret, Grandpa Joe and
Grandma Marge, Aunt Mary, Uncle Mark, Aunt Andrea, Uncle Mark, Uncle Chris, Aunt
Gretchen, Uncle Roger, Aunt Adriane, Uncle Mike, Aunt Barb, Jamie, Shawn, Bobby,
Lauren, Steven, Stephanie, Diane, Kristen, Nick, Cynthia, David, Uncle Joe, Fr. Vaughn,
AuntKimandUncleHenry. Withoutmyfamily,Iwouldnothavebeenassuccessfulinmy
scholasticendeavors. Iloveallofyouandthankyouforthecontinuedsupportthroughmy
manyupsand downs.
Andlast,butdefinitelynotleast,Iwanttothankallofmyfriends. Withoutyoursupport
(and libation sharing), I couldn’t have made it through this long process. I want to espe-
cially extend thanks to Gina, Chris, Tyler, Rebecca, Chris, Rosanna, Howard, Tami, Mike,
Bill, Brenda, Mike, Dmitri, Anya, Mike, Derek, Carlos, Yasmina, Serge, Stewart, Alicia,
Aris, Nickoleta, Bruno, Rob, Jason, Dave, Kate, Mike, Brian, Colleen, Anupam, Rachel,
Ryan, Sarah, Russell, Braden, Brian, Dave, Paul, Jerry, Doug, Peter, Steve, Dave, Greg,
Jim, Connie, Chad, Jesse, Shiva, Harish, Eric, Geunsoo, Hao Pan, Jake, Sung-ick and so
many others that I’m sure should be listed. Please know that I am eternally grateful to all
ofyou.
iii
Preface
The idea to study the articulation in the spine started from a series of passive dynamic
experiments with a Tinkertoy walker and a robotic mule prototype. Through various iter-
ations, this idea blossomed into the document before you. It has been a long journey, but
well worth the many hills and valleys passed over and through along the way. With the
burgeoning research in the area of cheetah mobility and robotics, perhaps this work will
provideadditionalencouragementfor improvementsinfuturesystems.
iv
Table of Contents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
ListofAppendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Goals inBrief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 LiteratureReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 A Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Wheels, TracksorLegs? . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2.1 Configurations . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.3 Advantagesofan ArticulatedSpine . . . . . . . . . . . . . . . . . 11
2.1.3.1 Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.3.2 Robustnessand Mobility . . . . . . . . . . . . . . . . . 12
2.1.3.3 PowerandEnergy Requirements . . . . . . . . . . . . . 15
2.1.4 PriorArt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.4.1 Non-articulatingQuadruped Robots . . . . . . . . . . . . 17
2.1.4.2 ArticulatingQuadruped Robots . . . . . . . . . . . . . . 17
2.2 ExistingModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Gaiting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
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Chapter 3 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.1 Gaiting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.2 ImpulsiveTransitions . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.3 VirtualLeg Simplification . . . . . . . . . . . . . . . . . . . . . . 37
3.1.4 EquationsofMotion . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.5 Rigid Mode: Descriptionand Verification . . . . . . . . . . . . . . 39
3.1.6 ArticulatedModel: Descriptionand Verification . . . . . . . . . . . 41
3.1.7 Footcontact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.7.1 No-slipConstraint . . . . . . . . . . . . . . . . . . . . . 44
3.1.7.2 CompressiveFootForceand FrictionConstraint . . . . . 45
3.1.7.3 Foot/AnkleTorque . . . . . . . . . . . . . . . . . . . . . 45
3.1.7.4 FootVelocityMinimization . . . . . . . . . . . . . . . . 45
3.1.8 ImpulsiveTransitionBounds . . . . . . . . . . . . . . . . . . . . . 46
3.1.8.1 Forcebounds . . . . . . . . . . . . . . . . . . . . . . . 46
3.1.8.2 Mid-flightImpulse . . . . . . . . . . . . . . . . . . . . . 47
3.1.9 ActiveTorques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.1 Fixed Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.2 SimulatedAnnealing . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.3 Seed and InitialConditions . . . . . . . . . . . . . . . . . . . . . . 50
3.2.4 CyclicGait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.5 OptimizationBounds . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.6 ObjectiveFunction . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.6.1 GaitSelection . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.6.2 GaitOptimization . . . . . . . . . . . . . . . . . . . . . 53
3.2.7 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Chapter 4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1 Results: Rigid Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1.1 Cost ofTransport . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1.2 TotalWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.3 MaximumImpulsiveForces . . . . . . . . . . . . . . . . . . . . . 59
4.1.4 MaximumImpulsiveTorques . . . . . . . . . . . . . . . . . . . . 60
4.1.5 ImpulsiveTorquesby Joint . . . . . . . . . . . . . . . . . . . . . . 62
4.1.6 Reconfiguration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1.7 Gait TimeHistory . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1.8 Fractional Energy Plots . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1.9 Potentialand KineticEnergies . . . . . . . . . . . . . . . . . . . . 67
4.1.10 KineticEnergy in Detail . . . . . . . . . . . . . . . . . . . . . . . 68
4.1.11 Best Cost ofTransport . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Results: ArticulatedModel . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2.1 Cost ofTransport . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2.2 TotalWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.3 MaximumImpulsiveForces . . . . . . . . . . . . . . . . . . . . . 75
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4.2.4 MaximumImpulsiveTorques . . . . . . . . . . . . . . . . . . . . 76
4.2.5 ImpulsiveTorquesby Joint . . . . . . . . . . . . . . . . . . . . . . 77
4.2.6 Gait TimeHistory . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2.7 Fractional Energy Plots . . . . . . . . . . . . . . . . . . . . . . . . 80
4.2.8 Potentialand KineticEnergy . . . . . . . . . . . . . . . . . . . . . 82
4.2.9 KineticEnergy in Detail . . . . . . . . . . . . . . . . . . . . . . . 83
4.2.10 ActiveTorques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.11 Best Cost ofTransport . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3 ComparisonoftheRigidand ArticulatedSystems . . . . . . . . . . . . . . 91
4.3.1 Best Cost ofTransport . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3.2 ModelRobustness . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3.3 Gait Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.3.4 Potentialand KineticEnergies . . . . . . . . . . . . . . . . . . . . 95
4.3.5 Final Recommendation . . . . . . . . . . . . . . . . . . . . . . . . 98
Chapter 5 Conclusions and Future Research . . . . . . . . . . . . . . . . . . . 100
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.1.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 FutureResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.2.1 VirtualLeg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.2.2 ActiveTorques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2.3 CompliantMechanisms . . . . . . . . . . . . . . . . . . . . . . . 105
5.2.4 StabilityCharacterization and ControllerDevelopment . . . . . . . 106
5.2.5 AnthropomorphicVariation . . . . . . . . . . . . . . . . . . . . . 106
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
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List of Tables
Table
2.1 Max Speeds ofQuadrupedModels . . . . . . . . . . . . . . . . . . . . . . 32
3.1 Rigid modelparameters from(39) . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Rigid modeltestcaseinitialconditions . . . . . . . . . . . . . . . . . . . . 41
3.3 Articulatedmodelparameters . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Articulatedmodeltest caseinitialconditions . . . . . . . . . . . . . . . . . 43
B.1 ModelParameters for theRigid Model . . . . . . . . . . . . . . . . . . . . 110
B.2 ModelParameters for theArticulatedModel . . . . . . . . . . . . . . . . . 118
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