A brief intro to robots Spring 2018yiannisr/790/2018/Lectures/01-Robot.pdf · A brief intro to...
Transcript of A brief intro to robots Spring 2018yiannisr/790/2018/Lectures/01-Robot.pdf · A brief intro to...
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Ioannis Rekleitis
AbriefintrotorobotsSpring2018
Presentation: Marios Xanthidis
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RobotSensors
• Sensorsaredevicesthatcansenseandmeasurephysicalpropertiesoftheenvironment,• e.g.temperature,luminance,resistancetotouch,weight,size,etc.
• Thekeyphenomenonistransduction• Transduction(engineering)isaprocessthatconvertsonetypeofenergytoanother
• Theydeliverlow-levelinformationabouttheenvironmenttherobotisworkingin.– Returnanincompletedescriptionoftheworld.
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RobotSensors
• Thisinformationisnoisy(imprecise).• Cannotbemodelledcompletely:– Reading=f(env)wherefisthemodelofthesensor– Findingtheinverse:
• illposedproblem(solutionnotuniquelydeEined)• collapsingofdimensionalityleadstoambiguity
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Typesofsensor
• GeneralclassiEication:– activeversuspassive• Active:emitenergyinenvironment– Morerobust,lessefEicient
• Passive:passivelyreceiveenergyfromenv.– Lessintrusive,butdependsonenv.e.g.lightforcamera
• Example:stereovisionversusrangeEinder.– contactversusnon-contact
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Sensors
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• ProprioceptiveSensors(monitorstateofrobot)– IMU(accels&gyros)– Wheelencoders– Dopplerradar…
• ExteroceptiveSensors(monitorenvironment)– Cameras(single,stereo,omni,FLIR…)
– Laserscanner– MWradar– Sonar– Tactile…
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TypesofsensorSpeciEicexamples– tactile– close-rangeproximity– angularposition– infrared– Sonar– laser(varioustypes)– radar– compasses,gyroscopes– Force– GPS– vision
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AngularPosi6on:RotaryEncoder• Potentiometer– UsedintheServoontheboebots
• OpticalDisks(Relative)– Countingtheslots– Directionbyhavingparsofemitters/receiversoutofphase:Quadraturedecoding
– Canspinveryfast:500kHz
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Whatisanactuator?
• Deviceformovingorcontrollingasystem.
• “RobotMuscles”
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HydraulicActuators
• Pros:– Powerful– Fast– Stiff
• Cons– Messy– Maintenance– ExternalPump
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Pneuma6cActuators
• Pros:– Powerful– Cheap
• Cons– Soft/Compliant– ExternalCompressor
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ShapeMemoryAlloyActuators
• WorksbywarmingandcoolingNitinolwires.
• Pros:– Light– Powerful
• Cons:– Slow(cooling)
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ElectricActuators
• Pros– Betterpositionprecision– Wellunderstood– Noseparatepowersource– Cheap
• Cons– Heavy– Weaker/slowerthanhydraulics– Coolingissue
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DCmotortorqueτ
I∝τ
torque=τcurrent =I
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VehicleLocomo6on
• Objective:convertdesiretomoveAàBintoanactualmotion:
– Howtoarrangeactuators(mechanicaldesign)
– actuatoroutputßàIncrementalmotion:Forwardkinematicsandinversekinematics
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VehicleLocomo6on
• ForwardKinematics:– (actuatorsactions)àpose
• InverseKinematics(inverse-K):– poseà(actuatorsactions)
},,{ pose θyx=
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WheeledVehicles
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Differen6aldrive
Basicdesign:• 2circularwheels• inEinitelythin• samediameter• mountedalongacommonaxis• vehiclebodyisirrelevant(intheory).
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Idealizeddifferen6aldrive
w1 w2
axle
w2w1
axle
top view
side view
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Differen6alDriveIntui6on
• Drivestraightahead?
• Turninplace?
• (thesearequestionsofkinematics)
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Differen6alDriveObserva6on
• Vehiclerotationcanbedescribedrelativetoanaxisrunningthoughthetwowheels.
Instantaneous Center of Curvature
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ForwardKinema6csofDifferen6alDrive• Wheelrotationbyangleφ1,φ2• DistanceofwheelmotionDi=φir
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WalkingRobots:RHex:TripodGait
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• Presentedactuatorsandsensors,e.g.:– Electricalmotor– Angularpositionencoder
• Howtogetthebestprecision/performance?
Actuators+Sensors
Electric Motor
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Potentiometer Optical Encoder
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Open-loop
Power Amplifier
Electric Motor
Computer
Volta
ge
Angular Velocity
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• Goal:moveadifferentialdriverobot– spinmotorsatagivenangularvelocity
• How:applyaEixedvoltagetoit,– andneverchecktoseeifitisrotatingproperly…
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• Let’smeasuretheactualangularvelocities.• Compensateforchangesinloadbyfeedingbacksomeinformation.
Closingtheloop
Power Amplifier
Electric Motor
Computer
Vol
tage
AngularVelocity
PositionEncoder
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ComponentsofFeedbackSystems
• PowerampliEication– Neuralsignalpower(µW)vs.musclepoweroutput(tensofW)– Meansitisanactivesystem,asopposedtopassive.
• Actuator• Feedback– measurement(sensor)
• Errorsignal• Controller
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EffectofControllerFunc6ons
• ProportionalAction– SimplestControllerFunction
• IntegralAction– Eliminatessteady-stateerror– Cancauseoscillations
• DerivativeAction(“ratecontrol”)– Effectiveintransientperiods– Providesfasterresponse(highersensitivity)– Neverusedalone
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LineFollowing
• Considera2Drobotwithpose(x,y,θ)followingaline.Therobotismovingwithconstantspeedv,andwecontroltheangularvelocityω (turnrate).
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d
φ
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Calcula6ngtheerror
• Considertwoerrormeasures,– d– φ
• Theorientationerrorisusedtoestimatewhenweareheadingtoomuchinthewrongdirection–
• Thedistanceerroriswhatwefeedtoourcontroller.
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bounded is 90 if ωφ °<
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P-Controller
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0 20 40 60 80 100 120 140 160 180 200
0
20
40
60
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Casaded control kp=1 ki=0 kd=0
0 50 100 150-10
0
10
Time (s)Rot
atio
n C
omm
and
(deg
/s)
Gain too low
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P-Controller
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0 20 40 60 80 100 120 140 160 180 200
0
20
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Casaded control kp=4 ki=0 kd=0
0 100 200 300 400 500 600-50
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Time (s)Rot
atio
n C
omm
and
(deg
/s)
Gain high
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P-Controller
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0 20 40 60 80 100 120 140 160 180 200
0
20
40
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Casaded control kp=10 ki=0 kd=0
0 100 200 300 400 500 600-100
-50
0
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Time (s)Rot
atio
n C
omm
and
(deg
/s)
Gain too high
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Pd-Controller
• Weareusingalsothederivativeoftheerror:– tocalculatetheturnrateω:
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dtdde tt 1−−
=!
ekdk dtp !⋅+⋅=ω
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Pd-Controller
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0 20 40 60 80 100 120 140 160 180 2000
20
40
60
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Casaded control kp=4 ki=0 kd=4
0 50 100 150 200 250 300 350 400-100
0
100
Time (s)Rot
atio
n C
omm
and
(deg
/s)
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Pd-Controller
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0 20 40 60 80 100 120 140 160 180 2000
20
40
60
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Casaded control kp=4 ki=0 kd=10
0 50 100 150 200 250 300 350-100
-50
0
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Time (s)Rot
atio
n C
omm
and
(deg
/s)
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Pd-Controller
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0 20 40 60 80 100 120 140 160 180 2000
20
40
60
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Casaded control kp=4 ki=0 kd=20
0 50 100 150 200 250 300 350-100
-50
0
50
Time (s)Rot
atio
n C
omm
and
(deg
/s)
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Pd-Controller
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0 20 40 60 80 100 120 140 160 180 200
0
20
40
60
80
Casaded control kp=20 ki=0 kd=50
0 50 100 150 200 250 300 350-100
0
100
Time (s)Rot
atio
n C
omm
and
(deg
/s)
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Posi6onRepresenta6on
• Positionrepresentationis:
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X
Y
Z
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
=
z
y
xA
ppp
PPA
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Orienta6onRepresenta6ons
• Describestherotationofonecoordinatesystemwithrespecttoanother
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XA
YA
ZA
XB
YB
ZB
A
B
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Rota6onMatrix• WritetheunitvectorsofBinthecoordinatesystemofA.
• RotationMatrix:
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XA
YA
ZA
A
AXB
AYB
AZB
B [ ]
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⋅⋅⋅
⋅⋅⋅
⋅⋅⋅
=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
==
ABABAB
ABABAB
ABABAB
BA
BA
BAA
B
ZZZYZXYZYYYXXZXYXX
rrrrrrrrr
ZYXR
ˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆ
ˆˆˆ
333231
232221
131211
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EulerAngles
• TraditionallythethreeanglesalongtheaxisarecalledRoll,Pitch,andYaw
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X
Y
Z
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EulerAngles
• TraditionallythethreeanglesalongtheaxisarecalledRoll,Pitch,andYaw
Roll
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X
Y
Z
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EulerAngles
• TraditionallythethreeanglesalongtheaxisarecalledRoll,Pitch,andYaw
Pitch
CSCE 790 Machine Learning in Robotics 43
X
Y
Z
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EulerAngles
• TraditionallythethreeanglesalongtheaxisarecalledRoll,Pitch,andYaw
Yaw
CSCE 790 Machine Learning in Robotics 44
X
Y
Z
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Axis-AngleRepresenta6on
• Representanarbitraryrotationasacombinationofavectorandanangle
CSCE 790 Machine Learning in Robotics 45
X
Y
Z
V θ
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Quaternions• Aresimilartoaxis-anglerepresentation• Twoformulations– Classical– BasedonJPL’sstandardsW.G.Breckenridge,“Quaternions-ProposedStandardConventions,”JPL,Tech.Rep.INTEROFFICEMEMORANDUMIOM343-79-1199,1999.
• AvoidsGimballock
• Seealso:M.D.Shuster,“Asurveyofattituderepresentations,”JournaloftheAstronauticalSciences,vol.41,no.4,pp.439–517,Oct.–Dec.1993.
CSCE 790 Machine Learning in Robotics 46
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QuaternionsClassicnotation JPL-based
CSCE 790 Machine Learning in Robotics 47
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See also: N. Trawny and S. I. Roumeliotis, “Indirect Kalman Filter for 3D Attitude Estimation,” University of Minnesota, Dept. of Comp. Sci. & Eng., Tech. Rep. 2005-002, March 2005.
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ThreeMainChallengesinRobo6cs
1. WhereamI?(Localization)2. Whattheworldlookslike?(Mapping)– Together1and2formtheproblemofSimultaneousLocalizationandMapping(SLAM)
3. HowdoIgofromAtoB?(PathPlanning)– Moregeneral:WhichactionshouldIpicknext?
(Planning)
48 CSCE 790 Machine Learning in Robotics
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Robot
Reason
ActSense
49 CSCE 790 Machine Learning in Robotics
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Mo6onPlanning• TheabilitytogofromAtoB– Knownmap–Off-lineplanning– UnknownEnvironment–Onlineplanning– Static/DynamicEnvironment
CSCE 790 Machine Learning in Robotics 50
qgoalqinit
qgoal
qgoalqinit
qinit
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PathPlanning
Robot Map
World
• Topological • Metric • Feature Based • 1D,2D,2.5D,3D
• Mobile Ø Indoor/Outdoor Ø Walking/Flying/Swimming
• Manipulator • Humanoid • Abstract
• Indoor/Outdoor • 2D/2.5D/3D • Static/Dynamic • Known/Unknown • Abstract (web)
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PathPlanning:Assump6ons• KnownMap• Roadmaps(Graphrepresentations)• PolygonalRepresentation
qgoal
qinit
52 CSCE 790 Machine Learning in Robotics
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Local techniques Potential Field methods
• compute a repulsive force away from obstacles
• compute an attractive force toward the goal
let the sum of the forces control the robot
key advantages?CSCE 790 Machine Learning in Robotics 53
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Ioannis Rekleitis
Configuration Space
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Ioannis Rekleitis
Configuration Space
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Definition
A robot configuration is a specification of the positions of all robot points relative to a fixed coordinate system Usually a configuration is expressed as a “vector” of position/orientation parameters
CSCE 790 Machine Learning in Robotics 56
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What is a Path?
CSCE 790 Machine Learning in Robotics 57
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Tool: Configuration Space (C-Space C)
q1
q1
q2
q2
CSCE 790 Machine Learning in Robotics 58
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Probabilis6cRoadmapsPRMs
ThebasicideabehindPRMistotakerandomsamplesfromtheconfigura:onspaceoftherobot,tes:ngthemforwhethertheyareinthefreespace,andusealocalplannertoa>empttoconnecttheseconfigura:onstoothernearbyconfigura:ons.Thestar:ngandgoalconfigura:onsareaddedin,andagraphsearchalgorithmisappliedtotheresul:nggraphtodetermineapathbetweenthestar:ngandgoalconfigura:ons.Kavraki,L.E.;Svestka,P.;Latombe,J.-C.;Overmars,M.H.(1996),"Probabilis:croadmapsforpathplanninginhigh-dimensionalconfigura:onspaces",IEEETransac:onsonRobo:csandAutoma:on12(4):566–580.
CSCE 790 Machine Learning in Robotics 59
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Rapidly-exploringRandomTrees
• ApointPinCisrandomlychosen.• ThenearestvertexintheRRTisselected.• AnewedgeisaddedfromthisvertexinthedirectionofP,atdistanceε.
• Thefurtherthealgorithmgoes,themorespaceiscovered.
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FundamentalProblemsInRobo6cs
• HowtoGoFromAtoB?(PathPlanning)• Whatdoestheworldlookslike?(mapping)
– sensefromvariouspositions– integratemeasurementstoproducemap– assumesperfectknowledgeofposition
• WhereamIintheworld?(localization)– Sense– relatesensorreadingstoaworldmodel– computelocationrelativetomodel– assumesaperfectworldmodel
• Together,theabovetwoarecalledSLAM (SimultaneousLocalizationandMapping)
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Introduc6ontoMapping
• Whattheworldlookslike?• Knowledgerepresentation– Robotics,AI,Vision
• Whoistheend-user?– HumanorMachine
• EaseofPathPlanning• Uncertainty!
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SimultaneousLocaliza6onAndMapping
SLAMistheprocessofbuildingamapofanenvironmentwhile,atthesametime,usingthatmaptomaintainthelocationoftherobot.
• ProblemsforSLAMinlargescaleenvironments:– Controllinggrowthofuncertaintyandcomplexity– Achievingautonomousexploration
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Localiza6on
• Tracking:Knowninitialposition• GlobalLocalization:Unknowninitialposition• Re-Localization:Incorrectknownposition– (kidnappedrobotproblem)
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Uncertainty
Centraltoanyrealsystem!
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Localiza6on
Initial state detects nothing:
Moves and detects landmark:
Moves and detects nothing:
Moves and detects landmark:
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BayesianFilter
• EstimatestatexfromdataZ– Whatistheprobabilityoftherobotbeingatx?
• xcouldberobotlocation,mapinformation,locationsoftargets,etc…
• Zcouldbesensorreadingssuchasrange,actions,odometryfromencoders,etc…)
• Thisisageneralformalismthatdoesnotdependontheparticularprobabilityrepresentation
• BayesEilterrecursivelycomputestheposteriordistribution:
CSCE 790 Machine Learning in Robotics 67
)|()( TTT ZxPxBel =
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Deriva6onoftheBayesianFilter
CSCE 790 Machine Learning in Robotics 68
)|()( Ttt ZxpxBel =
),...,,,,|()( 0211 oaoaoxpxBel tttttt −−−=
),...,|(),...,|(),...,,|()(
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Estimation of the robot’s state given the data:
The robot’s data, Z, is expanded into two types: observations oi and actions ai
Invoking the Bayesian theorem
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Deriva6onoftheBayesianFilter
CSCE 790 Machine Learning in Robotics 69
),...,|(/1 01 oaop tt −=η
),...,|(),...,,|()( 0101 oaxpoaxopxBel tttttt −−=η
),...,|()|()( 01 oaxpxopxBel ttttt −=η
1011011 ),...,|(),...,,|()|()( −−−−−∫= ttttttttt dxoaxpoaxxpxopxBel η
Denominator is constant relative to xt
First-order Markov assumption shortens first term:
Expanding the last term (theorem of total probability):
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Deriva6onoftheBayesianFilter
CSCE 790 Machine Learning in Robotics 70
101111 ),...,|(),|()|()( −−−−−∫= ttttttttt dxoaxpaxxpxopxBel η
1111 )(),|()|()( −−−−∫= tttttttt dxxBelaxxpxopxBel η
First-order Markov assumption shortens middle term:
Finally, substituting the definition of Bel(xt-1):
The above is the probability distribution that must be estimated from the robot’s data
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Itera6ngtheBayesianFilter• Propagatethemotionmodel:
• Updatethesensormodel:
CSCE 790 Machine Learning in Robotics 71
∫ −−−−− = 1111 )(),|()( tttttt dxxBelxaxPxBel
)()|()( tttt xBelxoPxBel −=η
Compute the current state estimate before taking a sensor reading by integrating over all possible previous state estimates and applying the motion model
Compute the current state estimate by taking a sensor reading and multiplying by the current estimate based on the most recent motion history
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DifferentApproachesDiscreteapproaches(’95)• Topologicalrepresentation(’95)• Uncertaintyhandling(POMDPs)• occas.globallocalization,recovery• Grid-based,metricrepresentation(’96)• globallocalization,recovery
ParticleEilters(’98)• Condensation(IsardandBlake’98)• Sample-basedrepresentation• Globallocalization,recovery• Rao-BlackwellizedParticleFilter
KalmanEilters(Early-60s?)• Gaussians• approximatelylinearmodels• positiontrackingExtendedKalmanFilterInformationFilterUnscentedKalmanFilter
Multi-hypothesis(’00)• MixtureofGaussians• MultipleKalmanEilters• Globallocalization,recovery
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BayesianFilter:RequirementsforImplementa6on
• Representationforthebelieffunction• Updateequations• Motionmodel• Sensormodel• Initialbeliefstate
73 CSCE 790 Machine Learning in Robotics