1. P ARTICLE F ILTER L OCALIZATION Mohammad Shahab Ahmad Salam AlRefai

2. O UTLINE References Introduction Bayesian Filtering Particle Filters Monte-Carlo Localization Visually… The Use of Negative information Localization Architecture in GT What Next? 2

3. R EFERENCES Sebastian Thrun, Dieter Fox, Wolfram Burgard. “Monte Carlo Localization With Mixture Proposal Distribution”. Wolfram Burgard. “Recursive Bayes Filtering”, PPT file Jan Hoffmann, Michael Spranger, Daniel Gohring, and Matthias Jungel. “Making Use of What you Don’t See: Negative Information in Markov Localization. Dieter Fox, Jeffrey Hightower, Lin Liao, and Dirk Schulz 3

4. I NTRODUCTION 4

5. M OTIVATION Where am I? ? 5

6. L OCALIZATION P ROBLEM “Using sensory information to locate the robot in its environment is the most fundamental problem to providing a mobile robot with autonomous capabilities.” [Cox ’91] Given Map of the environment: Soccer Field Sequence of percepts & actions: Camera Frames, Odometry, etc Wanted Estimate of the robot’s state (pose): 6

7. P ROBABILISTIC S TATE E STIMATION Advantages Can accommodate inaccurate models Can accommodate imperfect sensors Robust in real-world applications Best known approach to many hard robotics problems Disadvantages Computationally demanding False assumptions Approximate! 7

8. B AYESIAN F ILTER 8

9. B AYESIAN F ILTERS Bayes’ Rule with background knowledge Total Probability 9

10. B AYESIAN F ILTERS Let x(t) be pose of robot at time instant t o(t) be robot observation (sensor information) a(t) be robot action (odometry ) The Idea in Bayesian Filtering is to find Probability Density (distribution) of the Belief 10

11. B AYESIAN F ILTERS So, by Bayes Rule Markov Assumption : Past & Future data are independent if current state known 11

12. B AYESIAN F ILTERS Denominator is not a function of x(t), then it is replaced with normalization constant With Law of Total Probability for rightmost term in numerator; and further simplifications We get the Recursive Equation 12

13. B AYESIAN F ILTERS So we need for any Bayesian Estimation problem: 1. Initial Belief distribution, 2. Next State Probabilities, 3. Observation Likelihood, 13

14. P ARTICLE F ILTER 14

15. P ARTICLE F ILTER The Belief is modeled as the discrete distribution as m is the number of particles hypothetical state estimates weights reflecting a “confidence” in how well is the particle 15

16. P ARTICLE F ILTER Estimation of non-Gaussian, nonlinear processes It is also called: Monte Carlo filter, Survival of the fittest, Condensation, Bootstrap filter, 16

17. M ONTE -C ARLO L OCALIZATION Framework Observation Model Motion Model Previous Belief 17

18. M ONTE -C ARLO L OCALIZATION 18

19. M ONTE -C ARLO L OCALIZATION Algorithm 1. Using previous samples, project ahead by generating a new samples by the motion model 2. Reweight each sample based upon the new sensor information One approach is to compute for each i 3. Normalize the weight factors for all m particles 4. Maybe resample or not! And go to step 1 The normalized weight defines the potential distribution of state 19

20. M ONTE -C ARLO L OCALIZATION Algorithm Step 2&3 for all m Step 1 for all m after Step 4 20

21. M ONTE -C ARLO L OCALIZATION State Estimation, i.e. Pose Calculation Mean particle with the highest weight find the cell (particle subset) with the highest total weight, and calculate the mean over this particle subset. GT2005 Most crucial thing about MCL is the calculation of weights Other alternatives can be imagined 21

22. M ONTE -C ARLO L OCALIZATION Advantages to using particle filters (MCL) Able to model non-linear system dynamics and sensor models No Gaussian noise model assumptions In practice, performs well in the presence of large amounts of noise and assumption violations (e.g. Markov assumption, weighting model…) Simple implementation Disadvantages Higher computational complexity Computational complexity increases exponentially compared with increases in state dimension In some applications, the filter is more likely to diverge with more accurate measurements!!!! 22

23. … V ISUALLY 23

24. 24

25. O NE – D IMENSIONAL ILLUSTRATION OF B AYES F ILTER 25

26. O NE – D IMENSIONAL ILLUSTRATION OF B AYES F ILTER 26

27. O NE – D IMENSIONAL ILLUSTRATION OF B AYES F ILTER 27

28. O NE – D IMENSIONAL ILLUSTRATION OF B AYES F ILTER 28

29. O NE – D IMENSIONAL ILLUSTRATION OF B AYES F ILTER 29

30. A PPLYING P ARTICLE F ILTERS TO L OCATION E STIMATION 30

31. A PPLYING P ARTICLE F ILTERS TO L OCATION E STIMATION 31

32. A PPLYING P ARTICLE F ILTERS TO L OCATION E STIMATION 32

33. A PPLYING P ARTICLE F ILTERS TO L OCATION E STIMATION 33

34. A PPLYING P ARTICLE F ILTERS TO L OCATION E STIMATION 34

35. N EGATIVE I NFORMATION 35

36. M AKING U SE OF N EGATIVE I NFORMATION 36

37. M AKING U SE OF N EGATIVE I NFORMATION 37

38. M AKING U SE OF N EGATIVE I NFORMATION 38

39. M AKING U SE OF N EGATIVE I NFORMATION 39

40. M ATHEMATICAL M ODELING t : Time l: Landmark z: Observation u: action s: State *: negative information r: sensing range o: possible occlusion 40

41. A LGORITHM if (landmark l detected) then else end if 41

42. E XPERIMENTS Particle Distribution 100 Particles (MCL) 2000 Particles to get better representation. Not Using negative Information VS using negative information. Entropy H (information theoretical quality measure of the positon estimate. 42

43. R ESULTS 43

44. R ESULTS 44

45. R ESULTS 45

46. G ERMAN T EAM L OCALIZATION ARCHITECTURE 46

47. G ERMAN T EAM S ELF -L OCALIZATION C LASSES 47

48. C OGNITION 48

49. W HAT N EXT ? Monte Carlo is bad for accurate sensors??! There are different types of localization techniques: Kalman, Multihypothesis tracking, Grid, Topology, in addition to particle… What is the difference between them? And which one is better? All These issues will be discussed with a lot more in our next presentation (next week) Inshallah. 49

50. F UTURE 50

51. G UIDENCE 51

52. H OLDING OUR B AGS 52

53. M EDICINE 53

54. D ANCING … 54

55. U NDERSTAND AND F EAL 55

56. P LAY W ITH 56

57. O R M AYBE … 57

58. Q UESTIONS 58