Robotics

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2 Νοε 2013 (πριν από 4 χρόνια και 6 μέρες)

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Robotics
Chapter25
Chapter251
Outline
Robots,Eectors,andSensors
LocalizationandMapping
MotionPlanning
MotorControl
Chapter252
MobileRobots
Chapter253
Manipulators
R
R
R
P
R
R
Congurationofrobotspeciedby6numbers
)6
degreesoffreedom
(DOF)
6istheminimumnumberrequiredtopositionend-eectorarbitrarily.
Fordynamicalsystems,addvelocityforeachDOF.
Chapter254
Non-holonomicrobots
θ?
(x, y)
AcarhasmoreDOF(3)thancontrols(2),sois
non-holonomic
;
cannotgenerallytransitionbetweentwoinnitesimallyclosecongurations
Chapter255
Sensors
Rangenders
:sonar(land,underwater),laserrangender,radar(aircraft),
tactilesensors,GPS
Imagingsensors
:cameras(visual,infrared)
Proprioceptivesensors
:shaftdecoders(joints,wheels),inertialsensors,
forcesensors,torquesensors
Chapter256
Localization|WhereAmI?
Computecurrentlocationandorientation(
pose
)givenobservations:
Xt+1
Xt
At−2
At−1
At
Zt−1
Xt−1
Zt
Zt+1
Chapter257
Localizationcontd.
xi, yi
vt Δt
t Δt
t+1
xt+1
h(xt)
xt
θt
θ
ω
Z1
Z2
Z3
Z4
AssumeGaussiannoiseinmotionprediction,sensorrangemeasurements
Chapter258
Localizationcontd.
Canuseparticlelteringtoproduceapproximatepositionestimate
Robot position
Robot position
Robot position
Chapter259
Localizationcontd.
Canalsouse
extendedKalmanlter
forsimplecases:
robot
landmark
Assumesthatlandmarksareidentiable|otherwise,posteriorismultimodal
Chapter2510
Mapping
Localization:givenmapandobservedlandmarks,updateposedistribution
Mapping:givenposeandobservedlandmarks,updatemapdistribution
SLAM:givenobservedlandmarks,updateposeandmapdistribution
ProbabilisticformulationofSLAM:
addlandmarklocationsL1
;:::;Lk
tothestatevector,
proceedasforlocalization
Chapter2511
Mappingcontd.
Chapter2512
3DMappingexample
Chapter2513
MotionPlanning
Idea:planin
congurationspace
denedbytherobot'sDOFs
conf-3
conf-1
conf-2
conf-3
conf-2
conf-1
w
w
elb
shou
SolutionisapointtrajectoryinfreeC-space
Chapter2514
Congurationspaceplanning
Basicproblem:1d
states!Convertto
nite
statespace.
Celldecomposition
:
divideupspaceintosimple
cells
,
eachofwhichcanbetraversed\easily"(e.g.,convex)
Skeletonization
:
identifynitenumberofeasilyconnectedpoints/lines
thatformagraphsuchthatanytwopointsareconnected
byapathonthegraph
Chapter2515
Celldecompositionexample
start
goal
start
goal
Problem:maybenopathinpurefreespacecells
Solution:recursivedecompositionofmixed(free+obstacle)cells
Chapter2516
Skeletonization:Voronoidiagram
Voronoidiagram:locusofpointsequidistantfromobstacles
Problem:doesn'tscalewelltohigherdimensions
Chapter2517
Skeletonization:ProbabilisticRoadmap
AprobabilisticroadmapisgeneratedbygeneratingrandompointsinC-space
andkeepingthoseinfreespace;creategraphbyjoiningpairsbystraightlines
Problem:needtogenerateenoughpointstoensurethateverystart/goal
pairisconnectedthroughthegraph
Chapter2518
Motorcontrol
Canviewthemotorcontrolproblemasasearchproblem
inthe
dynamic
ratherthan
kinematic
statespace:
{statespacedenedbyx1
;x2
;:::;_x1
;_x2;:::
{continuous,high-dimensional(Sarcoshumanoid:162dimensions)
Deterministiccontrol:manyproblemsareexactlysolvable
esp.iflinear,low-dimensional,exactlyknown,observable
Simple
regulatorycontrol
lawsareeectiveforspeciedmotions
Stochastic
optimalcontrol
:veryfewproblemsexactlysolvable
)approximate/adaptivemethods
Chapter2519
Biologicalmotorcontrol
Motorcontrolsystemsarecharacterizedbymassiveredundancy
Innitelymanytrajectoriesachieveanygiventask
E.g.,3-linkarmmovinginplanethrowingatatarget
simple12-parametercontroller,onedegreeoffreedomattarget
11-dimensionalcontinuousspaceofoptimalcontrollers
Idea:ifthearmisnoisy,only\one"optimalpolicyminimizeserrorattarget
I.e.,noise-tolerancemightexplainactualmotorbehaviour
Harris&Wolpert(Nature,1998):signal-dependentnoise
explainseyesaccadevelocityproleperfectly
Chapter2520
Setup
Supposeacontrollerhas\intended"controlparameters0
whicharecorruptedbynoise,givingdrawnfromP
0
Output(e.g.,distancefromtarget)y=F();
Simplelearningalgorithm:Stochasticgradient
MinimizeE
[y
2]bygradientdescent:
r0
E
[y
2]=r0
Z
P0
()F()2
d
=
Z
r0
P0
()
P0
()
F()2
P0
()d
=E
[
r0
P0
()
P0
()
y2]
Givensamples(j
;yj
),j=1;:::;N,wehave
^
r0
E
[y
2]=
1
N
N
X
j=1
r0
P0
(j
)
P0
(j
)
y
2
j
ForGaussiannoisewithcovariance,i.e.,P
0
()=N(0
;),weobtain
^
r0
E
[y
2]=
1
N
N
X
j=1
1
(j
0
)y2
j
Chapter2522
Whatthealgorithmisdoing
x
x
x
x
x
x
x
x
x
x
xx
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Chapter2523
Resultsfor2{Dcontroller
4
5
6
7
8
9
10
0.2
0.4
0.6
0.8
1
1.2
Velocity v
Angle phi
Chapter2524
Resultsfor2{Dcontroller
4.51
4.52
4.53
4.54
4.55
4.56
4.57
4.58
4.59
4.6
4.61
0.6
0.61
0.62
0.63
0.64
0.65
Velocity v
Angle phi
Chapter2525
Resultsfor2{Dcontroller
0.0055
0.006
0.0065
0.007
0.0075
0.008
0.0085
0.009
0.0095
0
2000
4000
6000
8000
10000
E(y^2)
Step
Chapter2526
Summary
Therubberhitstheroad
Mobilerobotsandmanipulators
Degreesoffreedomtodenerobotconguration
Localizationandmappingasprobabilisticinferenceproblems
(requiregoodsensorandmotionmodels)
Motionplanningincongurationspace
requiressomemethodfornitization
Chapter2527