1. Autonomous Robot Navigation Panos Trahanias e-mail: trahania@csd.uoc.gr ΗΥ475 Fall 2007

2. Panos Trahanias: Autonomous Robot Navigation Mobile Robots - Examples The Mars rover Sojourner The museum tour-guide Minerva The RHex Hexapod The museum tour-guide Lefkos

3. Panos Trahanias: Autonomous Robot Navigation Typical Mobile Robot Setup Interaction Processing Power Motors Sensors Stereo vision Sonars Bump sensors Infrared sensors Laser scanner Bump sensors Sonars Odometry Communications

4. Panos Trahanias: Autonomous Robot Navigation Scope of the Course Mobile Robots – How to move and achieve motion target goals in (indoor) environments Hence Localization (where am I?) Mapping, simultaneous localization and mapping – SLAM (what is my workspace?) Path planning (how to get there?) Obstacle avoidance (… get there safely…)

5. Panos Trahanias: Autonomous Robot Navigation Given An environment representation - Map C G Knowledge of current position C  A path has to be planned and tracked that will take the robot from C to G Target position G Autonomous Navigation- Research Directions

6. Panos Trahanias: Autonomous Robot Navigation During execution (run- time) Objects / Obstacles O may block the robot C G The planned path is no- longer valid The obstacle needs to be avoided and the path may need to be re- planned O X Autonomous Navigation- Research Directions

7. Panos Trahanias: Autonomous Robot Navigation Navigation Issues Important questions (Levitt et al ’91) Important navigation issues Where am I Where are other places relative to me Where are other places relative to me How do I get to other places from here How do I get to other places from here Robot localization Map building Path/motion planning

8. Panos Trahanias: Autonomous Robot Navigation Navigation Issues – Underlying HW Interaction Processing Power Motors Sensors Stereo vision Sonars Bump sensors Infrared sensors Laser scanner Bump sensors Sonars Odometry Communications Laser Scanner

9. Panos Trahanias: Autonomous Robot Navigation Range Sensor Model Laser Rangefinder Model range and angle errors.

10. Panos Trahanias: Autonomous Robot Navigation Need for Modeling Extremely Complex Dynamical System Need for Appropriate Modeling Robot Environment+

11. Panos Trahanias: Autonomous Robot Navigation Markov Assumption State depends only on previous state and observations Static world assumption Hidden Markov Model (HMM) Bayesian estimation: Attempt to construct the posterior distribution of the state given all measurements

12. Panos Trahanias: Autonomous Robot Navigation A Dynamic System Most commonly - Available: Initial State Observations System (motion) Model Measurement (observation) Model

13. Panos Trahanias: Autonomous Robot Navigation Inference - Learning Localization (inference task) Compute the probability that the robot is at pose z at time t given all observations up to time t (forward recursions only) Map building (learning task) Determine the map m that maximizes the probability of the observation sequence.

14. Panos Trahanias: Autonomous Robot Navigation Belief State Discrete representation –Grid (Dynamic)(Dynamic) Markov localization (Burgard98) –SamplesMonte Carlo localization (Fox99) Continuous representation –Gaussian distributionsKalman filters (Kalman60) How is the prior distribution represented? How is the posterior distribution calculated?

15. Panos Trahanias: Autonomous Robot Navigation Example: State Representations for Robot Localization Grid Based approaches (Markov localization) Particle Filters (Monte Carlo localization) Kalman Tracking Discrete RepresentationsContinuous Representations

16. Panos Trahanias: Autonomous Robot Navigation LOCALIZATION

17. Panos Trahanias: Autonomous Robot Navigation Markov Assumption Localization: determine the likelihood of robot’s state Given a sequence of observations Determine the probability

18. Panos Trahanias: Autonomous Robot Navigation Markov Assumption In practice: too difficult to determine the joint effect of all observations up to time K. Common assumption: hidden states obey the Markov assumption (static world assumption), so as we can factor as

19. Panos Trahanias: Autonomous Robot Navigation Markov Assumption

20. Panos Trahanias: Autonomous Robot Navigation Markov Assumption All information about past history is represented in Different approaches in this representation lead to different treatments of the problem. Integrate over all possible states

21. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering Probabilistic estimation Simultaneously maintain estimates for both the state x and error covariance matrix P Equivalent to say: output of a Kalman filter is a Gaussian PDF (other methods can handle more general distributions)

22. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering Crude localization method: integrate robot velocity commands Problem: info continuously lost, no new info added. Solution: add info from exterioreceptive sensors.

23. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering Sensor measurements add new info – PDF in sensor space. Localization knowledge (prior to sensor measurement) is a PDF in state space. Probabilistic Estimation: merge the 2 PDFs Two step process: prediction update

24. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering Simple observer update

25. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering Prediction Update

26. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering Observing with probability distributions

27. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering Prediction Update where

28. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering

29. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering

30. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering

31. Panos Trahanias: Autonomous Robot Navigation Kalman Filtering

32. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods

33. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Discrete Approximations

34. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Discrete Approximations

35. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Discrete Approximations Results

36. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Discrete Approximations Results

37. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Particle Filters

38. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Particle Filters/Resampling

39. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Particle Filters Motion Model

40. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Particle Filters State Belief

41. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Particle Filters Global Localization

42. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Particle Filters Global Localization - Results

43. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Sensor Models Typical Sonar Scan

44. Panos Trahanias: Autonomous Robot Navigation Bayesian Methods – Sensor Models Histograms

45. Panos Trahanias: Autonomous Robot Navigation PATH PLANNING

46. Panos Trahanias: Autonomous Robot Navigation Bug Algorithms Bug1

47. Panos Trahanias: Autonomous Robot Navigation Bug Algorithms Bug1

48. Panos Trahanias: Autonomous Robot Navigation Bug Algorithms Bug2

49. Panos Trahanias: Autonomous Robot Navigation Bug Algorithms Bug2

50. Panos Trahanias: Autonomous Robot Navigation Bug Algorithms Bug2

51. Panos Trahanias: Autonomous Robot Navigation POTENTIAL FUNCTIONS

52. Panos Trahanias: Autonomous Robot Navigation Potential Field Attractive – Repulsive Forces

53. Panos Trahanias: Autonomous Robot Navigation Potential Field Potential Function

54. Panos Trahanias: Autonomous Robot Navigation Potential Field Attractive Potential

55. Panos Trahanias: Autonomous Robot Navigation Potential Field Repulsive Potential

56. Panos Trahanias: Autonomous Robot Navigation Potential Field BrushFire Algorithm

57. Panos Trahanias: Autonomous Robot Navigation Potential Field Local Minima Problem

58. Panos Trahanias: Autonomous Robot Navigation Potential Field Wavefront Planner

59. Panos Trahanias: Autonomous Robot Navigation Navigation Functions

60. Panos Trahanias: Autonomous Robot Navigation Navigation Functions

61. Panos Trahanias: Autonomous Robot Navigation Value Iteration Value Iteration Algorithm Dynamic programming (fast) Creates potential field (run only once per target) Initialization rule Update rule

62. Panos Trahanias: Autonomous Robot Navigation Value Iteration - Results

63. Panos Trahanias: Autonomous Robot Navigation OBSTACLE AVOIDANCE

64. Panos Trahanias: Autonomous Robot Navigation Certainty Grid Representation

65. Panos Trahanias: Autonomous Robot Navigation VFF – Virtual Force Field

66. Panos Trahanias: Autonomous Robot Navigation VFF – Virtual Force Field

67. Panos Trahanias: Autonomous Robot Navigation Polar Histogram

68. Panos Trahanias: Autonomous Robot Navigation Polar Histogram

69. Panos Trahanias: Autonomous Robot Navigation Motion Candidate Directions

70. Panos Trahanias: Autonomous Robot Navigation Traveling Alongside an Obstacle

71. Panos Trahanias: Autonomous Robot Navigation Steering Reference

72. Panos Trahanias: Autonomous Robot Navigation VFH – Example Course

73. Panos Trahanias: Autonomous Robot Navigation CONFIGURATION SPACE

74. Panos Trahanias: Autonomous Robot Navigation Two-link Manipulator - Workspace

75. Panos Trahanias: Autonomous Robot Navigation Two-link Manipulator – Configuration Space

76. Panos Trahanias: Autonomous Robot Navigation Obstacles – Configuration Space

77. Panos Trahanias: Autonomous Robot Navigation Obstacles – Configuration Space

78. Panos Trahanias: Autonomous Robot Navigation Obstacles – Configuration Space

79. Panos Trahanias: Autonomous Robot Navigation Obstacles – Configuration Space

80. Panos Trahanias: Autonomous Robot Navigation Workspace – Configuration Space

81. Panos Trahanias: Autonomous Robot Navigation Workspace – Configuration Space

82. Panos Trahanias: Autonomous Robot Navigation Workspace – Configuration Space

83. Panos Trahanias: Autonomous Robot Navigation Planar Parallel Mechanism