RoboticMotionPlanning: SampleBasedMotionPlanning - - PowerPoint PPT Presentation

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RoboticMotionPlanning: SampleBasedMotionPlanning - - PowerPoint PPT Presentation

Jan 30, 2024 455 likes •861 views

RoboticMotionPlanning: SampleBasedMotionPlanning RoboticsInstitute16735 http://voronoi.sbp.ri.cmu.edu/~motion HowieChoset http://voronoi.sbp.ri.cmu.edu/~choset

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RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

RoboticMotionPlanning: SampleBasedMotionPlanning

RoboticsInstitute16735 http://voronoi.sbp.ri.cmu.edu/~motion HowieChoset http://voronoi.sbp.ri.cmu.edu/~choset

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SLIDE 2

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

RapidlyExploringRandomTrees(RRTs) [Kuffner,Lavalle]

TheBasicRRT singletree bidirectional multipletrees(forests) RRTs withDifferentialConstraints nonholonomic kinodynamic systems closedchains

'% '%

  • %

%

  • %

% JKK JKK % %

  • LL

LL L2 L2

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SLIDE 3

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

HighDimensionalPlanningasof1999

$%&%&!& '% ()*+&(),+ &!&-. ())+ /&'%&% ())+ /0&! (1)+2& 3&2&/ ()4+ &!&5 ()6+ 78&9&())+ !" # !" :

  • Greedy,cantake

alongtimebut goodwhenyou candiveintothe solution Spreadsoutlike uniformitybut needlotsof sampletocover space

TENSION

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SLIDE 4

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

RapidlyExploringRandomTree

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SLIDE 5

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

PathPlanningwithRRTs (RapidlyExploringRandomTrees)

/MK!NO::3<=H +,-+ & >;$ >:-N'OL'-#K@<=+ 3-N<.= F 3-N<.=

  • D$J

D$J!7 !7 &KL: &KL:( (CCB CCB

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SLIDE 6

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

PathPlanningwithRRTs (SomeDetails)

/MK!NO::3<=H +,-+ & >;$ >:-N'OL'-#K@<=+ 3-N<.= F 3-N<.=

  • STEP_LENGTH:Howfartosample

1. Samplejustatendpoint 2. Sampleallalong 3. SmallStep Extendreturns 1. Trapped,cantmakeit 2. Extended,stepstowardnode 3. Reached,connectstonode STEP_SIZE 1. NotSTEP_LENGTH 2. Smallstepsalongway 3. Binarysearch

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SLIDE 7

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

RRTvs.ExhaustiveSearch

  • Discrete
  • Continuous

A*maytryalledges Probabilisticallysubsample alledges Continuumofchoices Probabilisticallysubsample alledges

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SLIDE 8

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

NaïveRandomTree

Startwithmiddle Samplenearthis node Thenpickanodeat randomintree Samplenearit EndupStayingin middle

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SLIDE 9

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

RRTsand BiastowardlargeVoronoiregions

"IIII

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SLIDE 10

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

Biases

  • Biastowardlargerspaces
  • Biastowardgoal

– Whengeneratingarandomsample,withsomeprobabilitypickthe goalinsteadofarandomnodewhenexpanding – Thisintroducesanotherparameter – James’ experienceisthat510%istherightchoice – Ifyoudothis100%,thenthisisaRPP

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SLIDE 11

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

RRTvs.RPP

goal

Greedy getsyou stuckhere

RRT’s willpullawayandbetter approximatecosttogo

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SLIDE 12

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

GrowtwoRRTs towardseachother

  • %
  • D$&

D$&!7 !7 KL: KL:P PCCB CCB

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SLIDE 13

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %

::3L

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SLIDE 14

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %

;='5

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SLIDE 15

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %
  • 4=-5
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RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %
  • Q=LRS
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SLIDE 17

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %
  • E=35
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SLIDE 18

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %
  • *=K&.
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SLIDE 19

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %
  • *=K&.
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SLIDE 20

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %
  • *=K&.
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SLIDE 21

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %
  • ,=
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SLIDE 22

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • %

6=:

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SLIDE 23

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

BasicRRTConnect

::3OL'--L3<.%=H +,-+#+,%-+ & >;$ >:-N'OL'-#K@<=+ <3-N<.=>3= <3-N<#.=>:= : 3<.#=+ <.#=+ :#+ F

Insteadofswitching,useTa assmallertree.ThishelpedJamesalot

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SLIDE 24

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

  • qnear
  • ′

= ′

  • %
  • =

& <

== & < <

  • T
  • ′

=

Isthisthebest?

Mixingpositionandvelocity,actuallymixingposition,rotation andvelocityishard

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SLIDE 25

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

So,whatdotheydo?

  • Usenearestneighboranyway
  • Aslongasheuristicisnotbad,ithelps

(youhavealreadygivenupcompletenessandoptimality,sowhattheheck?)

  • Nearestneighborcalculationsbegintodominatethecollision

avoidance(Jamessays50,000nodes)

  • RememberKDtrees
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SLIDE 26

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

ArticulatedRobot

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SLIDE 27

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

HighlyArticulatedRobot

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SLIDE 28

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

Hovercraftwith2Thusters

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SLIDE 29

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

OutofThisWorldDemo

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SLIDE 30

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

Leftturnonlyforwardcar

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SLIDE 31

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

Analysis

.

  • THEOREM: convergesto inprobability
  • :TheRRTvertexdistributionatiteration/
  • :Thedistributionusedforgeneratingsamples
  • KEYIDEA:AstheRRTreachesallof%,theprobabilitythat-

immediatelybecomesanewvertexapproachesone.

%%/ %%/

  • 3

3 .5 .5

0 1 )

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SLIDE 32

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

OpenProblems

OpenProblems

  • Rateofconvergence
  • Optimalsamplingstrategy?

OpenIssues

  • MetricSensitivity
  • NearestneighborEfficiency
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SLIDE 33

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

ApplicationsofRRTs

: :

  • '

' <= <= %<= %<= %% %%

  • ::3.

::3. <3:K :U= <3:K :U=

  • ::3

::3

  • ::3

::3

  • ::3

::3

  • ::3

::3

  • ::3

::3

  • ::3

::3

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SLIDE 34

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

DiffusionLimitedAggregation

  • Oftenusedtomodelnaturalphysicalprocesses(e.g.snow

accumulation,rust,etc.)

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SLIDE 35

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

ExploringInfiniteSpace

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SLIDE 36

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

PolarSampling

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SLIDE 37

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

RRTSummary

Advantages

  • Singleparameter
  • Balancebetweengreedysearchandexploration
  • Convergestosamplingdistributioninthelimit
  • Simpleandeasytoimplement

Disadvantages

  • Metricsensitivity
  • Nearestneighborefficiency
  • Unknownrateofconvergence
  • “longtail” incomputationtimedistribution
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SLIDE 38

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

LinkstoFurtherReading

  • SteveLaValle’s onlinebook:

“PlanningAlgorithms” #234$ http://planning.cs.uiuc.edu/

  • TheRRTpage:

http://msl.cs.uiuc.edu/rrt/

  • MotionPlanningBenchmarks

ParasolGroup,TexasA&M

http://parasol.tamu.edu/groups/amatogroup/benchmarks/mp/

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SLIDE 39

RI16735,HowieChosetwithslidesfromNancyAmato,Sujay Bhattacharjee,G.D.Hager,S.LaValle,andalotfromJamesKuffner

PRT(Prob.RoadmapofTrees)

  • Basicidea:

– Generateasetoftreesintheconfigurationspace – Mergethetreesbyfindingnodesthatcanbeconnected

  • Algorithm

– pickseveralrandomnodes – GeneratetreesT1,T2 ....Tn (ESTorRRT) – Mergetrees

  • generatearepresentativesupernode
  • UsingPRSideastopickaneighborhoodoftrees
  • isnowthetreemergealgorithm

– Forplanning

  • generatetreesfrominitialandgoalnodestowardsclosestsupernodes
  • trytomergewith“roadmap” ofconnectedtrees
  • NotethatPRSandtreebasedalgorithmsarespecialcases