Transcript A Probabilistic Approach to Collaborative Multi

A Probabilistic Approach to
Collaborative Multi-robot
Localization
Dieter Fox, Wolfram Burgard, Hannes Kruppa,
Sebastin Thrun
Presented by
Rajkumar Parthasarathy and Sulen Thomas
Overview
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Introduction
Markov Localization
Monte Carlo Localization
Experimental results
Simulation Experiments
Conclusions and future work
Localization
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A Fundamental problem of mobile robotics !
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Divided into two sub-tasks
Global Position Estimation
Ability to determine the robot’s position in an a
priori or a given frame of reference.
Local Position Tracking
Ability to keep track of the robot over time after
global position estimation.
Collaborative Multi-Robot Localization ?
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Combines sensor information from different
robotic platforms.
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Particularly striking for heterogeneous robot
teams.
A Collaborative effort achieves:
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Higher levels of accuracy.
Faster localization.
Improved performance with lesser data.
Remarkable reduction in equipment costs.
Approaches
Based on the representation of state space,
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Kalman filter-based techniques
Topological Markov Localization
Grid-based Markov localization
Multi-robot Markov Localization
Monte Carlo Localization method
Data
Let N - > number of robots ,
dn - > data collected by a robot n
Three types of dn :
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Odometric measurement (a) – change in relative position
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Environmental measurement (o) – position of the robot
relative to the environment
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Detections (r) – information about the presence of other
robots
Markov Localization
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Concept – to compute a
probability distribution
over all possible locations
in a particular environment
Addresses the problem of
state estimation from
sensor data
Can be used to solve the
localization problem in
both the single and multirobot scenarios
Single Robot
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Localization
Key idea – each robot is said to maintain a ‘ Belief ’ 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)
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Now the belief can be initialized by a uniform distribution
Beln(t)(L) = P ( Ln(t) | dn(t) )
where dn(t) -> denotes the data collected by the nth robot
at a time t
Single Robot Localization
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Case 1 : if dn(t) is an environment
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The Markov assumption for a
robot at a location l is given by
α P( on)|Ln= l) Beln (L = l)
where α => normalizer that does
not depend on the robot location
P (on)|Ln= l) => the environment
perception model.
Single Robot Localization
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Case 2 : if dn(t) is an odometric
measurement (a)
The Markov assumption for a robot
at a location (l) can be given by
∫ P ( l |an, l' ) Be ln (l') dl‘
where l => original location of
robot
and l’ => new location moved to
P ( l | an, l’) => motion model of the
robot n
Multi-Robot Localization
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Case 3 : if dn(t) is a detection (r)
The Markov assumption when a robot n is detected by
another robot m can be given by
Beln(l)  Be ln(l) ∫ P(Ln= l | Lm= l', r m) Be lm(l')dl'
where r m => the detection variable dn(t)
Localization
Algorithm
Rules
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This approach does not take into consideration negative
sights
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One robot cannot detect a robot more than once until it has
move a pre defined distance
Monte Carlo Localization
Alternatively known as
o Bootstrap filter
o Monte Carlo filter
o Condensation Algorithm
o Survival of the fittest algorithm
Generically grouped together as particle filters
Monte Carlo Localization (SIR)
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Version of Markov Localization
Sampling based approach to approximate
probability distributions.
Ability to represent arbitrary distributions
Computationally very efficient.
Monte Carlo Localization
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Represent the posterior beliefs Beln(l) by a set of N
weighted, random samples or particles S.
S = { Si| i= 1 … N }
A sample set constitutes a discrete approximation
of probability distribution.
Si = <li , pi >
where li = <xi, yi , θ > denotes robot position,
pi ≥ 0 is the numerical weighting factor.
for Consistency, ∑n=1..N pi = 1.
Robot Motion
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Basically, MCL generates N samples initially.
For each robot motion ∆ do:
o Sampling : Generate from each sample in
St-1, a new sample according to motion
model.
li ← li + ∆'
o The new sample’s l is generated by
generating a single random sample from
P( l | l ‘ , a) where a is action observed.
o The p value of this sample is N-1.
Sampling based approximation of a position
Sensor Readings
For each Observation S do:
o Importance Sampling : Re-weighting each
sample in the sample set with likelihood.
p  α P ( s|l)
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where s is the sensor measurement,
α is the normalization constant.
Re-sampling : Draw N samples from sample
set St according to their likelihood.
Global Localization of Rhino - Sonar
Adaptive Sample Set Sizes
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Number of samples vary drastically to
requirement.
Global localization requires more samples than
Position tracking.
MCL determines sample size on-the-fly.
Incorporates p(l) and P(l |s), the before and after
sensing belief to determine sample sets.
Global Localization – Adaptive Particle Filters
MCL Properties
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Based on Particle filters or Sampling/Importance
Re-sampling.
Reduces Computational Overhead.
The quality of solution increases over time.
Sampling is done only when necessary or in
proportion to likelihood.
Achieves significantly more accurate results than
Markov Localization.
Marion and Robin
Multi-Robot MCL - Idea
Robot Detection
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Camera Image of
robot Robin passing
Marion as seen from
Marion.
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Laser Scan of Marion
showing Robin’s
position in an angular
fashion.
Multi-Robot MCL
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The extension of MCL to collaborative multirobot localization is not straightforward.
Factorial representation of Beliefs are used.
L = L1× L2 × L3 × … × LN
where each robot maintains its local sample set.
Need for a synchronization interface arises.
Probabilistic Detection Model
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Sample sets across different robotic platforms are
synchronized in accordance to incremental update
equation.
Beln(l) ← Beln(l) ∫ P (Ln=l |Lm= l ' ) Belm(l ') dl ‘
Beln(l) and Belm(l ) are drawn randomly.
Need to transform sample sets to density trees which
grows recursively.
Density values are multiplied with every individual
sample <l, p> of the detected robot.
Multi Robot Localization
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Map of the environment
with the sample set, An
equal distribution of
uncertainty initially.
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Approximation done
using density trees. More
the samples finer the
tree.
Multi-Robot MCL – Example Run
Simulations
Simulations were done with two test cases
Case 1 : Homogenous robots
task : Global localization – ultrasound sensors
Simulations
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Case 2 : Heterogeneous robots
Task : Global localization – sonar sensors and laser range
finders collaborative approach to localization efficient
Related
Work
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Most of the research is in the area of single robot
localization.
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Majority based on the positive tracking phenomenon
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Mostly help to solve the odometric errors in multi-robots
Advantages
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Global localization
- knowledge of initial position not required
- robust and can recover from localization failures
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Authors approach
- more universally applicable
- uses raw sensor data to achieve greater accuracy
Challenges
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Only positive detections considered
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Proper identification of robots needed to reduce
complexity
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Approach of active localization to be applied
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Reduction of the false detection percentage
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Integration when confident of position
Conclusion
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Statistical method for collaborative multi-robot localization.
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Implementation of the Markov, MCL and Detection based
schemes
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Experiments using real and simulated robots to prove
efficiency
Thank You.