Table Of Content

Guoyuan Li Houxiang Zhang Jianwei Zhang Bio-Inspired Locomotion Control of Limbless Robots Bio-Inspired Locomotion Control of Limbless Robots · · Guoyuan Li Houxiang Zhang Jianwei Zhang Bio-Inspired Locomotion Control of Limbless Robots GuoyuanLi HouxiangZhang DepartmentofOceanOperationsandCivil DepartmentofOceanOperationsandCivil Engineering,FacultyofEngineering Engineering,FacultyofEngineering NorwegianUniversityofScience NorwegianUniversityofScience andTechnology andTechnology Ålesund,Norway Ålesund,Norway JianweiZhang DepartmentInformatics,Faculty ofMathematics,InformaticsandNatural Science UniversityofHamburg Hamburg,Germany ISBN 978-981-19-8383-2 ISBN 978-981-19-8384-9 (eBook) https://doi.org/10.1007/978-981-19-8384-9 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SingaporePteLtd.2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Contents 1 Introduction ................................................... 1 1.1 LimblessLocomotioninNature .............................. 1 1.2 LimblessLocomotioninRobots .............................. 3 1.3 ScopeandGoals ........................................... 6 References ..................................................... 7 2 OverviewofLimblessRobots .................................... 9 2.1 StateoftheArt ............................................. 9 2.1.1 ActiveCordMechanism .............................. 9 2.1.2 CMU’sSnakeRobots ................................. 11 2.1.3 AmphiBot .......................................... 12 2.1.4 OmniTread .......................................... 13 2.1.5 Others .............................................. 14 2.2 HowLimblessRobotsMove ................................. 14 2.2.1 LateralUndulationwithPassiveWheels ................. 15 2.2.2 Self-propulsionwithActiveWheels .................... 15 2.2.3 Self-propulsionwithActiveTreads ..................... 16 2.2.4 PureBodyUndulation ................................ 17 2.2.5 RectilinearwithBodyExpansionandContraction ........ 18 2.3 LimblessLocomotionControl ................................ 19 2.3.1 GaitControlTable ................................... 20 2.3.2 AnalyticalMethod ................................... 21 2.3.3 Sine-BasedMethod .................................. 22 2.3.4 CPG-BasedMethod .................................. 24 2.4 Summary .................................................. 26 References ..................................................... 26 3 SinusoidalGenerator—AnAttempttoLimblessLocomotion ....... 31 3.1 Analysis and Design of Asymmetric Oscillation forCaterpillar-LikeLocomotion .............................. 31 3.1.1 InspirationfromCaterpillars ........................... 32 3.1.2 Caterpillar-LikeLocomotionAnalysis .................. 34 v vi Contents 3.1.3 DesignofAsymmetricOscillator ....................... 42 3.1.4 SimulationandExperiments ........................... 45 3.1.5 Caterpillar-LikeLocomotionSummary .................. 51 3.2 DevelopmentofaVision-BasedTargetExplorationSystem forSnake-LikeRobots ...................................... 51 3.2.1 Snake-LikeRobotSystemOverview .................... 52 3.2.2 Vision-BasedNavigation .............................. 56 3.2.3 Experiments ......................................... 60 3.2.4 SummaryoftheTargetExplorationSystem .............. 65 References ..................................................... 66 4 DesignofaLampreySpinalGenerator ........................... 69 4.1 CPGOverview ............................................. 69 4.1.1 Ijspeert’sModel ..................................... 70 4.1.2 Matsuoka’sModel ................................... 71 4.1.3 Ekeberg’sModel ..................................... 73 4.1.4 Herrero-Carrón’sModel .............................. 74 4.1.5 Comparison ......................................... 76 4.2 DesignGoals .............................................. 77 4.3 SingleOscillatorDesign ..................................... 79 4.4 ChainedInhibitoryCPGCircuit .............................. 84 4.4.1 CPGCircuitConstruction ............................. 84 4.4.2 ParametersAdjustment ............................... 87 4.5 CyclicInhibitoryCPGCircuit ................................ 94 4.5.1 SynchronizationActivity .............................. 96 4.5.2 MaintenanceActivity ................................. 99 4.6 Summary .................................................. 100 References ..................................................... 100 5 DesignofLimblessLocomotion .................................. 103 5.1 Introduction ............................................... 103 5.2 3DGaitImplementation ..................................... 104 5.2.1 SidewindingGait .................................... 104 5.2.2 RollingGait ......................................... 109 5.2.3 TurningGait ........................................ 113 5.2.4 FlappingGait ........................................ 118 5.2.5 DesignedGaitsSummary ............................. 121 5.3 On-SiteExperiment ......................................... 122 5.4 Summary .................................................. 123 References ..................................................... 124 6 DesignofSensoryReflexMechanism ............................. 125 6.1 Introduction ............................................... 125 6.2 SensoryReflexMechanism .................................. 127 6.2.1 ReflexArc .......................................... 127 6.2.2 SensoryNeuronIntegration ............................ 129 Contents vii 6.2.3 ResponseBehaviors .................................. 131 6.3 BallHittingExperiment ..................................... 132 6.3.1 Simulation .......................................... 133 6.3.2 On-SiteExperiment .................................. 136 6.4 CorridorPassingExperiment ................................. 137 6.4.1 Simulation .......................................... 138 6.4.2 On-SiteExperiment .................................. 140 6.5 Summary .................................................. 142 References ..................................................... 143 7 DevelopmentofAdaptiveLocomotionBasedonaFeedback CoupledCPGModel ........................................... 145 7.1 Introduction ............................................... 145 7.2 AdaptiveControlSystem .................................... 149 7.2.1 RobotConstruction ................................... 149 7.2.2 ControlArchitecture .................................. 150 7.3 SensorProcessor ........................................... 152 7.4 ReactionMaker ............................................ 153 7.5 ParameterModulator ........................................ 156 7.6 MotionOptimization ........................................ 158 7.7 SimulationandExperiment .................................. 160 7.7.1 Simulation .......................................... 160 7.7.2 On-SiteExperiment .................................. 163 7.8 Summary .................................................. 166 References ..................................................... 169 8 Conclusions .................................................... 171 List of Figures Fig.1.1 Thefullyfunctionalintegrationofthelimblessrobots ......... 7 Fig.2.1 TheACMfamilyinHirose-FukushimaRoboticslab .......... 10 Fig.2.2 Gait control table for the caterpillar gait. Adopted andmodifiedfrom(Yimetal.2001) ....................... 20 Fig.2.3 Serpenoidcurve.Adoptedandmodifiedfrom(Hirose andYamada2009) ...................................... 21 Fig.2.4 Sinusoidal generators. Adopted and modified from(Gonzalez-Gomezetal.2007) ....................... 23 Fig.2.5 Limitcyclebehavior.Adoptedandmodifiedfrom(Crespi etal.2005) ............................................ 25 Fig.3.1 Caterpillar locomotion. Adopted and modified from(Brackenbury1999) ................................ 33 Fig.3.2 Morphologicalmappingfromthecaterpillartothemodular robottotheskeletonmodel .............................. 34 Fig.3.3 Discrete body shape analysis. a Two types of body shapeinthehalfwaveaswellastheiranglevariation overdiscretetime;banexampleofhalfwavegeneration andpropagationwithrespecttodiscretetimesequence ........ 35 Fig.3.4 Hypothesisofcontinuousanglevariationintheswingphase ... 35 Fig.3.5 Continuous body shape analysis. a Joint analysis; b verticaldisplacementanalysis;andccollisionanalysis ........ 37 Fig.3.6 Theverticaldisplacementwithrespecttotheamplitude andthephasedifference ................................. 41 Fig.3.7 Horizontal displacement analysis. a The body arcs withrespecttoaseriesofphasedifferences;bhorizontal displacementperstepcyclewithrespecttotheamplitude andthephasedifference ................................. 42 Fig.3.8 Thesine-basedcontrolarchitecture ........................ 42 Fig.3.9 Thedetailedoscillatormodel ............................. 43 Fig.3.10 Thedetailedoscillatormodel ............................. 45 Fig.3.11 Simulationofcaterpillar-likelocomotioninonestepcycle ..... 46 ix x ListofFigures Fig.3.12 Body shape variation with respect to the amplitude andthephasedifference ................................. 47 Fig.3.13 Onsiteexperiment ...................................... 47 Fig.3.14 Thehorizontaldisplacementcomparison.aRealcaterpillar data.Adoptedfrom(Casey1991);bon-siteexperimental data .................................................. 48 Fig.3.15 Velocityinthex-planeanddisplacementinthey-plane versustime.a DataforA3ofrealcaterpillar.Adopted from (van Griethuijsen and Trimmer 2009); b data formodule4oftherobot ................................ 49 Fig.3.16 Measured data, a the step length (cid:2)λ; b the energy consumption;cefficiencyofcaterpillar-likelocomotion ....... 50 Fig.3.17 Mechanicaldesignof aheadpart,bupperpart,cbottom part,anddassemblyforthesnake-likerobot ................ 53 Fig.3.18 Examplegaitsfor a forward,bturning,cCWrotating, anddrightsidewinding ................................. 55 Fig.3.19 Controlflowdiagram ................................... 56 Fig.3.20 Virtualsensorsonthesnake-likerobot ..................... 57 Fig.3.21 ExamplesofplanningresultsusingaRRTandbRRT* ....... 58 Fig.3.22 Gaitselectionforthesnake-likerobot ...................... 59 Fig.3.23 Deadendrecognitioninamaze ........................... 60 Fig.3.24 Experimentsetupfortargetexplorationinamaze ............ 61 Fig.3.25 Screenshotsofthepathtrackingexperiment ................. 62 Fig.3.26 Gaitchangesofthesnake-likerobotinthepathtracking experiment ............................................ 62 Fig.3.27 Screenshotsofthedeadendsearchexperiment .............. 63 Fig.3.28 Theresultsof agaitchangesofthesnake-likerobot,andb capturedimagesfromtheheadcamerainthedeadend searchexperiment ...................................... 64 Fig.4.1 Ijspeert’sCPGmodel.Adoptedfrom(IjspeertandCrespi 2007) ................................................ 70 Fig.4.2 Kimura’sextendedCPGmodel.Adoptedandmodified from(FukuokaandKimura2003) ......................... 72 Fig.4.3 Ekeberg’s CPG model. Adopted and modified from(Ekeberg1993) .................................... 73 Fig.4.4 Herrero-Carrón’s CPG model. Adopted and modified from(Herrero-Carrónetal.2011) ......................... 75 Fig.4.5 Ahierarchicalcontrolarchitecture ......................... 78 Fig.4.6 Theoscillatormodel.Thecircuitconsistsofthemotor controlcenterandtheoscillator.Theroleofthemotor control center is neuromodulation. It transfers motor commandsfromthelarge-scalelevelandadjustsrelated control parameters for desired modulation. The role oftheoscillatorisproducingrhythmicactivitythrough theinteractionbetweentheseinterneurons .................. 80 ListofFigures xi Fig.4.7 Theoutputofasingleoscillator.Theoscillatorsucceeds tooscillatebyusingthesynapticweightsinTable4.2 and the initial values in Table 4.3, with parameters τ =0.2, A=20andβ =0 .............................. 83 Fig.4.8 Theunidirectionalconnectionbetweentwooscillators and their simplification. Both the EINs in the first oscillator emit inhibitory synapses to the ipsilateral LINs in the second oscillator. The simplified version of oscillators uses the ‘L’ and the ‘R’ to represent thecorrespondinginterneuronsandconnection .............. 85 Fig.4.9 Thechainedtopologyofoscillators.Whenoscillators areunidirectional connected withthesame inhibitory synaptic weights, a phase difference between them develops.Byalteringtheweightofadditionalsynapses ofthecommandoscillator,theotheroscillatorscanbe modulated to maintain the desired phase difference. Parameters α and γ, with a range of (0, 1], are used tomodulatethephasedifference .......................... 85 Fig.4.10 The variation of phase difference between oscillators withrespecttoparametersα andγ,whereothercontrol parametersarefixedasτ = 0.4, A = 20andβ = 0.α andγ havethesamefunctionalitythatbothofthemcan shiftthephasedifferencebetweenoscillatorsmonotonously ... 86 Fig.4.11 Phasedifferencemodulationwithrespecttoparameterα, whereγ = 0.2.Thephasedifferencecanbemodulated intherangefrom45◦ to145◦ ............................. 87 Fig.4.12 Relationshipbetweentuningparametersandoscillatory characteristics of the chained inhibitory CPG circuit. a–c Show the variations of the amplitude, the period andthephasedifferencewithrespectto A,τ andα .......... 88 Fig.4.13 Decouple the influence of amplitude with α. a The variationofamplitudewithrespectto A andα.bThegain of A withrespecttothedesiredamplitudeandα.The desiredamplitudewillbemaintainedifthegainisapplied on A ................................................ 90 Fig.4.14 Decoupletheinfluenceofperiodwithα.aThevariation of period with respect to A and α. b The gain of τ with respect to the desired period and α. The desired periodwillbemaintainedifthegainisappliedonτ .......... 92 Fig.4.15 Thevariationofrelativeoffsetwithrespectto A andτ. Altering A willnotaffecttherelativeoffset.Therelative offsetisonlyaffectedbyβ inalinearfashion ............... 93