1. A Probabilistic Approach to Collaborative Multi-robot Localization Dieter Fox, Wolfram Burgard, Hannes Kruppa, Sebastin Thrun Presented by Rajkumar Parthasarathy and Sulen Thomas

2. Overview  Introduction  Markov Localization  Monte Carlo Localization  Experimental results  Simulation Experiments  Conclusions and future work

3. Localization o A Fundamental problem of mobile robotics ! o D ivided into two sub-tasks Global Position Estimation Global Position Estimation Ability to determine the robot’s position in an a priori or a given frame of reference. Ability to determine the robot’s position in an a priori or a given frame of reference. Local Position Tracking Local Position Tracking Ability to keep track of the robot over time after global position estimation. Ability to keep track of the robot over time after global position estimation.

4. Collaborative Multi-Robot Localization ? o Combines sensor information from different robotic platforms. o Particularly striking for heterogeneous robot teams.

5. A Collaborative effort achieves: A Collaborative effort achieves: o Higher levels of accuracy. o Faster localization. o Improved performance with lesser data. o Remarkable reduction in equipment costs.

6. Approaches Based on the representation of state space, o Kalman filter-based techniques o Topological Markov Localization o Grid-based Markov localization o Multi-robot Markov Localization o Monte Carlo Localization method

7. D a t a Let N - > number of robots, d n - > data collected by a robot n d n - > data collected by a robot n Three types of d n : Three types of d n : o Odometric measurement (a) – change in relative position o Environmental measurement (o) – position of the robot relative to the environment o Detections (r) – information about the presence of other robots

8. M a r k o v L o c a l i z a t i o n o Concept – to compute a probability distribution over all possible locations in a particular environment o Addresses the problem of state estimation from sensor data o Can be used to solve the localization problem in both the single and multi- robot scenarios

9. S i n g l e R o b o t L o c a l i z a t i o n o 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  Bel n (t) (L) where L -> three dimensional random variable of the form (x, y, θ) o o Now the belief can be initialized by a uniform distribution (L) = P ( L n (t) | d n (t) ) Bel n (t) (L) = P ( L n (t) | d n (t) ) where d n (t) -> denotes the data collected by the nth robot at a time t

10. S i n g l e R o b o t L o c a l i z a t i o n o Case 1 : if d n (t) is an environment measurement o The Markov assumption for a robot at a location l is given by The Markov assumption for a robot at a location l is given by α P( o n )|L n = l) Bel n (L = l) α P( o n )|L n = l) Bel n (L = l) where α => normalizer that does not depend on the robot location where α => normalizer that does not depend on the robot location P (o n )|L n = l) => the environment perception model. P (o n )|L n = l) => the environment perception model.

11. S i n g l e R o b o t L o c a l i z a t i o n o Case 2 : if d n (t) is an odometric measurement (a) The Markov assumption for a robot at a location (l) can be given by The Markov assumption for a robot at a location (l) can be given by ∫ P ( l |an, l' ) Be l n (l') dl‘ ∫ P ( l |an, l' ) Be l n (l') dl‘ where l => original location of robot and l’ => new location moved to P ( l | a n, l’) => motion model of the robot n

12. M u l t i - R o b o t L o c a l i z a t i o n o Case 3 : if d n (t) is a detection (r) The Markov assumption when a robot n is detected by another robot m can be given by The Markov assumption when a robot n is detected by another robot m can be given by Bel n (l)  Be l n (l) ∫ P(L n = l | L m = l', r m ) Be l m (l')dl' Bel n (l)  Be l n (l) ∫ P(L n = l | L m = l', r m ) Be l m (l')dl' where r m => the detection variable d n (t) where r m => the detection variable d n (t)

13. L o c a l i z a t i o n A l g o r i t h m

14. R u l e s o This approach does not take into consideration negative sights o One robot cannot detect a robot more than once until it has move a pre defined distance

15. 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

16. Monte Carlo Localization (SIR) o Version of Markov Localization o Sampling based approach to approximate probability distributions. o Ability to represent arbitrary distributions o Computationally very efficient.

17. Monte Carlo Localization o Represent the posterior beliefs Bel n (l) by a set of N weighted, random samples or particles S. S = { S i | i= 1 … N } S = { S i | i= 1 … N } o A sample set constitutes a discrete approximation of probability distribution. S i = S i = where l i = denotes robot position, where l i = denotes robot position, p i ≥ 0 is the numerical weighting factor. p i ≥ 0 is the numerical weighting factor. for Consistency, ∑ n=1..N pi = 1. for Consistency, ∑ n=1..N pi = 1.

18. Robot Motion o Basically, MCL generates N samples initially. o For each robot motion ∆ do: o Sampling : Generate from each sample in S t-1, a new sample according to motion model. l i ← l i + ∆ ' l i ← l i + ∆ ' o The new sample’s l is generated by generating a single random sample from P( l | l ‘, a) where a is action observed. P( l | l ‘, a) where a is action observed. o The p value of this sample is N -1.

19. Sampling based approximation of a position

20. 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) p  α P ( s|l) where s is the sensor measurement, α is the normalization constant. where s is the sensor measurement, α is the normalization constant. o Re-sampling : Draw N samples from sample set S t according to their likelihood.

21. Global Localization of Rhino - Sonar

22. Adaptive Sample Set Sizes o Number of samples vary drastically to requirement. o Global localization requires more samples than Position tracking. o MCL determines sample size on-the-fly. o Incorporates p(l) and P(l |s), the before and after sensing belief to determine sample sets.

23. Global Localization – Adaptive Particle Filters

24. MCL Properties o Based on Particle filters or Sampling/Importance Re-sampling. o Reduces Computational Overhead. o The quality of solution increases over time. o Sampling is done only when necessary or in proportion to likelihood. o Achieves significantly more accurate results than Markov Localization.

25. Marion and Robin

26. Multi-Robot MCL - Idea

27. Robot Detection o Camera Image of robot Robin passing Marion as seen from Marion. o Laser Scan of Marion showing Robin’s position in an angular fashion.

28. Multi-Robot MCL o The extension of MCL to collaborative multi- robot localization is not straightforward. o Factorial representation of Beliefs are used. L = L 1 × L 2 × L 3 × … × L N L = L 1 × L 2 × L 3 × … × L N where each robot maintains its local sample set. where each robot maintains its local sample set. o Need for a synchronization interface arises.

29. Probabilistic Detection Model o Sample sets across different robotic platforms are synchronized in accordance to incremental update equation. Bel n (l) ← Bel n (l) ∫ P (L n =l |Lm= l ' ) Bel m (l ' ) dl ‘ Bel n (l) ← Bel n (l) ∫ P (L n =l |Lm= l ' ) Bel m (l ' ) dl ‘ o Bel n (l) and Bel m (l ) are drawn randomly. o Need to transform sample sets to density trees which grows recursively. o Density values are multiplied with every individual sample of the detected robot.

31. Multi Robot Localization Map of the environment with the sample set, An equal distribution of uncertainty initially. Map of the environment with the sample set, An equal distribution of uncertainty initially. Approximation done using density trees. More the samples finer the tree. Approximation done using density trees. More the samples finer the tree.

37. Multi-Robot MCL – Example Run

38. S i m u l a t i o n s Simulations were done with two test cases Case 1 : Homogenous robots task : Global localization – ultrasound sensors task : Global localization – ultrasound sensors

39. S i m u l a t i o n s o Case 2 : Heterogeneous robots Task : Global localization – sonar sensors and laser range finders collaborative approach to localization efficient Task : Global localization – sonar sensors and laser range finders collaborative approach to localization efficient

40. R e l a t e d W o r k o Most of the research is in the area of single robot localization. o Majority based on the positive tracking phenomenon o Mostly help to solve the odometric errors in multi-robots

41. A d v a n t a g e s o Global localization - knowledge of initial position not required - knowledge of initial position not required - robust and can recover from localization failures - robust and can recover from localization failures o Authors approach - more universally applicable - more universally applicable - uses raw sensor data to achieve greater accuracy - uses raw sensor data to achieve greater accuracy

42. C h a l l e n g e s o Only positive detections considered o Proper identification of robots needed to reduce complexity o Approach of active localization to be applied o Reduction of the false detection percentage o Integration when confident of position

43. C o n c l u s i o n o Statistical method for collaborative multi-robot localization. o Implementation of the Markov, MCL and Detection based schemes o Experiments using real and simulated robots to prove efficiency

44. Thank You.