A Probabilistic A Probabilistic Approach to Approach to

Collaborative Multi-Collaborative Multi-robot Localizationrobot Localization

Dieter Fox, Wolfram Burgard, Dieter Fox, Wolfram Burgard, Hannes Kruppa, Sebastin ThrunHannes Kruppa, Sebastin Thrun

Presented byPresented byRajkumar Parthasarathy and Sulen ThomasRajkumar Parthasarathy and Sulen Thomas

OverviewOverview

IntroductionIntroduction Markov LocalizationMarkov Localization Monte Carlo LocalizationMonte Carlo Localization Experimental resultsExperimental results Simulation ExperimentsSimulation Experiments Conclusions and future workConclusions and future work

LocalizationLocalization

o A Fundamental problem of mobile A Fundamental problem of mobile robotics !robotics !

o DDivided into two sub-tasksivided into two sub-tasks

Global Position EstimationGlobal Position Estimation

Ability to determine the robot’s Ability to determine the robot’s position in an position in an a priori a priori or a given or a given frame of reference.frame of reference.

Local Position TrackingLocal Position Tracking

Ability to keep track of the robot over Ability to keep track of the robot over time after global position estimation.time after global position estimation.

Collaborative Multi-Robot Collaborative Multi-Robot Localization ?Localization ?

o Combines sensor information from Combines sensor information from different robotic platforms.different robotic platforms.

o Particularly striking for Particularly striking for heterogeneous robot teams.heterogeneous robot teams.

A Collaborative effort A Collaborative effort achievesachieves::

o Higher levels of accuracy.Higher levels of accuracy.o Faster localization.Faster localization.o Improved performance with lesser Improved performance with lesser

data.data.o Remarkable reduction in equipment Remarkable reduction in equipment

costs.costs.

Approaches Approaches

Based on the representation of state Based on the representation of state spacespace, , o Kalman filter-based techniquesKalman filter-based techniqueso Topological Markov LocalizationTopological Markov Localizationo Grid-based Markov localization Grid-based Markov localization o Multi-robot Markov LocalizationMulti-robot Markov Localizationo Monte Carlo Localization methodMonte Carlo Localization method

D a t aD a t aLet Let NN - > number of robots , - > number of robots ,

ddnn - > data collected by a robot - > data collected by a robot nn

Three types of Three types of ddnn : : o Odometric measurement (a)Odometric measurement (a) – change in – change in

relative positionrelative position

o Environmental measurement (o)Environmental measurement (o) – position of – position of the robot relative to the environment the robot relative to the environment

o Detections (r)Detections (r) – information about the – information about the

presence of other robotspresence of other robots

M a r k o v L o c a l i z a t i o nM a r k o v L o c a l i z a t i o n

o Concept Concept – to compute a – to compute a probability distribution probability distribution over all possible over all possible locations in a locations in a particular environmentparticular environment

o Addresses the problem Addresses the problem of of state estimationstate estimation from sensor datafrom sensor data

o Can be used to solve Can be used to solve the localization the localization problem in both the problem in both the single and multi-robot single and multi-robot scenariosscenarios

S i n g l e R o b o t L o c a l i z a t i S i n g l e R o b o t L o c a l i z a t i o no n

o Key idea Key idea – each robot is said to maintain a ‘ – each robot is said to maintain a ‘ Belief Belief ’ about its position. ’ about its position.

The belief of the nth robot at a time t is given by belief Beln

(t) (L)

where L -> three dimensional random variable of the

form (x, y, θ)

o Now the belief can be initialized by a uniform distribution

Beln(t)(L) = P ( L(L) = P ( Lnn(t) | d(t) | dnn(t) )(t) )

where dn(t) -> denotes the data collected by the nth robot at a time t

S i n g l e R o b o t L o c a l i z S i n g l e R o b o t L o c a l i z a t i o na t i o n

o Case 1Case 1 : : if if ddnn(t)(t) is an is an

environment measurement environment measurement o o

The Markov assumption for a The Markov assumption for a robot at a location robot at a location ll is given is given by by

α P( oα P( onn)|L)|Lnn= l) Bel= l) Beln n (L = l)(L = l)

where where αα => normalizer that => normalizer that does not depend on the robot does not depend on the robot location location

P (oP (onn)|L)|Lnn= l)= l) => the => the environment perception environment perception model.model.

S i n g l e R o b o t L o c a l i z S i n g l e R o b o t L o c a l i z a t i o na t i o n

o Case 2Case 2 : : if if ddnn(t)(t) is an is an

odometric measurement (a)odometric measurement (a) The Markov assumption for The Markov assumption for

a robot at a location (l) can a robot at a location (l) can be given bybe given by

∫ ∫ P ( l |an, l' ) Be lP ( l |an, l' ) Be lnn (l') dl‘ (l') dl‘

where l => original location of robot

and l’ => new location moved to

P ( l | an, l’) => motion model of the robot n

M u l t i - R o b o t L o c a l i z a t M u l t i - R o b o t L o c a l i z a t i o ni o n

o Case 3Case 3 : : if dif dnn(t)(t) is a detection (r) is a detection (r)

The Markov assumption when a robot n is The Markov assumption when a robot n is detected by another robot m can be given bydetected by another robot m can be given by

BelBelnn(l) (l) Be l Be lnn(l) ∫ P(L(l) ∫ P(Lnn= l | L= l | Lmm= l', r= l', rmm) Be ) Be llmm(l')dl'(l')dl'

where rwhere rm m => the detection variable d=> the detection variable dnn(t)(t)

L o c a l i z a t i o n A l g o r i t h L o c a l i z a t i o n A l g o r i t h mm

R u l e sR u l e s

o This approach does not take into This approach does not take into consideration negative sightsconsideration negative sights

o One robot cannot detect a robot more than One robot cannot detect a robot more than once until it has move a pre defined distanceonce until it has move a pre defined distance

Monte Carlo LocalizationMonte Carlo Localization

Alternatively known asAlternatively known as o Bootstrap filterBootstrap filtero Monte Carlo filterMonte Carlo filtero Condensation AlgorithmCondensation Algorithmo Survival of the fittest algorithmSurvival of the fittest algorithm

Generically grouped togetherGenerically grouped together asas particle filtersparticle filters

Monte Carlo Localization (SIR)Monte Carlo Localization (SIR)

o Version of Markov LocalizationVersion of Markov Localizationo Sampling based approach to Sampling based approach to

approximate probability approximate probability distributions.distributions.

o Ability to represent arbitrary Ability to represent arbitrary distributionsdistributions

o Computationally very efficient.Computationally very efficient.

Monte Carlo LocalizationMonte Carlo Localizationo Represent the posterior beliefs Represent the posterior beliefs BelBelnn(l) (l) by a set by a set

of of NN weighted, random samplesweighted, random samples or or particles Sparticles S..

S = { SS = { Sii| i= | i= 1 … 1 … N }N }o A sample set constitutes a discrete A sample set constitutes a discrete

approximation of probability distribution.approximation of probability distribution.

SSii = <l = <lii , p , pii > >

wherewhere l lii = <x = <xii, y, yi i , θ, θ > > denotes robot denotes robot position,position,

ppii ≥ ≥ 0 0 is the numerical weighting factor.is the numerical weighting factor.

ffor Consistency,or Consistency, ∑ ∑n=1..N n=1..N pi = pi = 11..

Robot MotionRobot Motiono Basically, MCL generates Basically, MCL generates NN samples initially. samples initially.o For each For each robot motion ∆robot motion ∆ do: do:

o SamplingSampling : Generate from each sample : Generate from each sample in in SSt-1,t-1, a new sample according to a new sample according to motion model. motion model.

lli i ← ← l lii + + ∆∆''

o The new sample’s The new sample’s ll is generated by is generated by generating a single random sample generating a single random sample fromfrom

P( l | lP( l | l ‘ ‘ , a) , a) wherewhere a a is action is action observed.observed.

o The The pp value of this sample is value of this sample is NN-1.-1.

Sampling based approximation of Sampling based approximation of a positiona position

Sensor ReadingsSensor Readings

For each For each Observation Observation SS do: do:o Importance SamplingImportance Sampling : Re-weighting : Re-weighting

each sample in the sample set with each sample in the sample set with likelihood.likelihood.

p p α α P ( s|l)P ( s|l)

where where ss is the sensor measurement, is the sensor measurement, αα is the is the normalization constant.normalization constant.

o Re-samplingRe-sampling : Draw : Draw NN samples from samples from samplesample set set SStt according to their according to their likelihood. likelihood.

Global Localization of Global Localization of RhinoRhino - - SonarSonar

Adaptive Sample Set SizesAdaptive Sample Set Sizes

o Number of samples vary drastically to Number of samples vary drastically to requirement.requirement.

o Global localization requires more Global localization requires more samples than Position tracking.samples than Position tracking.

o MCL determines sample size on-the-MCL determines sample size on-the-fly.fly.

o Incorporates Incorporates p(l)p(l) and and P(l |s),P(l |s), the the beforebefore and and afterafter sensing belief to sensing belief to determine sample sets.determine sample sets.

Global Localization – Adaptive Global Localization – Adaptive Particle FiltersParticle Filters

MCL PropertiesMCL Properties

o Based on Based on Particle filters Particle filters oror Sampling/Importance Re-samplingSampling/Importance Re-sampling..

o Reduces Computational Overhead.Reduces Computational Overhead.o The quality of solution increases over The quality of solution increases over

time.time.o Sampling is done only when necessary Sampling is done only when necessary

or in proportion to or in proportion to likelihoodlikelihood..o Achieves significantly more accurate Achieves significantly more accurate

results than Markov Localization.results than Markov Localization.

Marion and RobinMarion and Robin

Multi-Robot MCL - IdeaMulti-Robot MCL - Idea

Robot DetectionRobot Detection

o Camera Image of Camera Image of robot robot Robin Robin passing Marion as passing Marion as seen from seen from Marion.Marion.

o Laser Scan of Laser Scan of MarionMarion showing showing Robin’sRobin’s position in position in an angular an angular fashion.fashion.

Multi-Robot MCLMulti-Robot MCLo The extension of MCL to collaborative multi-The extension of MCL to collaborative multi-

robot localization is robot localization is not not straightforward.straightforward.o Factorial representation of Factorial representation of Beliefs Beliefs are used.are used.

L = LL = L11× L× L22 × L × L33 × … × L × … × LNN

where each robot maintains its where each robot maintains its local sample local sample set.set.

o Need for a synchronization interface arises.Need for a synchronization interface arises.

Probabilistic Detection ModelProbabilistic Detection Model

o Sample sets across different robotic Sample sets across different robotic platforms are synchronized in accordance platforms are synchronized in accordance to incremental update equation.to incremental update equation.

BelBelnn(l) (l) ← ← BelBelnn(l) (l) ∫∫ P (L P (Lnn=l |Lm= l =l |Lm= l '' ) ) BelBelmm(l (l '') ) dl dl ‘‘

o BelBelnn(l) (l) and and BelBelmm(l ) (l ) are drawn randomly.are drawn randomly.o Need to transform sample sets to Need to transform sample sets to density density

trees trees which grows recursively.which grows recursively.o Density values are multiplied with every Density values are multiplied with every

individual sample individual sample <<l, p> l, p> of the detected of the detected robot.robot.

Multi Robot LocalizationMulti Robot Localization Map of the Map of the

environment with environment with the sample set, An the sample set, An equal distribution of equal distribution of uncertainty uncertainty initiallyinitially..

Approximation done Approximation done using using density trees. density trees. More the samples More the samples finer the tree.finer the tree.

Multi-Robot MCL – Example RunMulti-Robot MCL – Example Run

S i m u l a t i o n sS i m u l a t i o n s

Simulations were done with Simulations were done with two test casestwo test cases

Case 1Case 1 : : Homogenous robotsHomogenous robots

task : Global localization – ultrasound task : Global localization – ultrasound

sensorssensors

S i m u l a t i o n sS i m u l a t i o n s

o Case 2Case 2 : : Heterogeneous robotsHeterogeneous robots

TaskTask : Global localization – sonar sensors : Global localization – sonar sensors and laser range finders collaborative and laser range finders collaborative approach to localization efficientapproach to localization efficient

R e l a t e d W o r kR e l a t e d W o r k

o Most of the research is in the area of single Most of the research is in the area of single robot localization.robot localization.

o Majority based on the positive tracking Majority based on the positive tracking phenomenonphenomenon

o Mostly help to solve the odometric errors in Mostly help to solve the odometric errors in multi-robots multi-robots

A d v a n t a g e sA d v a n t a g e s

o Global localizationGlobal localization

- - knowledge of initial position not requiredknowledge of initial position not required

- robust and can recover from localization - robust and can recover from localization failuresfailures

o Authors approachAuthors approach

- - more universally applicablemore universally applicable

- uses raw sensor data to achieve greater - uses raw sensor data to achieve greater accuracyaccuracy

C h a l l e n g e sC h a l l e n g e s

o Only positive detections consideredOnly positive detections considered

o Proper identification of robots needed to Proper identification of robots needed to reduce complexityreduce complexity

o Approach of active localization to be appliedApproach of active localization to be applied

o Reduction of the false detection percentageReduction of the false detection percentage

o Integration when confident of positionIntegration when confident of position

C o n c l u s i o nC o n c l u s i o n

o Statistical method for collaborative multi-Statistical method for collaborative multi-robot localization.robot localization.

o Implementation of the Markov, MCL and Implementation of the Markov, MCL and Detection based schemesDetection based schemes

o Experiments using real and simulated Experiments using real and simulated robots to prove efficiencyrobots to prove efficiency

Thank You.Thank You.