Towards Uncertainty-Aware Path Planning On Road Networks Using Augmented-MDPs. Lorenzo Nardi and Cyrill Stachniss

Transcription

1 Towards Uncertainty-Aware Path Planning On Road Networks Using Augmented-MDPs Lorenzo Nardi and Cyrill Stachniss

2 Navigation under uncertainty C B C B A A 2

3 `B` is the most likely position C B C B A A 3

4 If the robot is at `A` instead C B C B A A 4

5 Safer to go up and turn at `C` C B C B A A 5

6 Safer to go up and turn at `C` C C B Objective Select actions that reduce the risk A A with large position uncertainty to make mistakes during navigation B 6

7 Planning on road networks 7

8 Planning on road networks 8

9 Markov Decision Process (MDP) 9

10 Optimal actions at intersections

11 MDP state is fully observable C B A

12 Uncertainty is ignored C B A 2

13 Uncertainty-aware planning Reduce the risk to make wrong navigation decisions Consider position uncertainty during planning General formulation as Partially Observable MDPs or POMDPs POMDPs are hard to solve for real-world applications 3

14 Augmented-MDPs (A-MDP) Efficient POMDPs approximation Augment MDP state space with position uncertainty Approximate state estimate during planning with isotropic Gaussian 4

15 Transitions between beliefs MDP A-MDP 5

16 Localizability information Estimate the localization accuracy OpenStreetMap Vysotska et al. 27 6

17 Localizability information Estimate the localization accuracy high low OpenStreetMap 7

18 EKF prediction + Localizability Estimate the belief propagation high low 8

19 EKF prediction + Localizability Estimate the belief propagation high low 9

20 Transition probability According to Bhattacharyya distance between posterior and output state high low 2

21 Augmented-MDP Transitions between beliefs Rewards minimize the travel time 2

22 Augmented-MDP Transitions between beliefs Rewards minimize the travel time Representation analogous to MDPs But larger number of states Solve using Policy Iteration 22

23 Augmented-MDP Transitions between beliefs Rewards minimize the travel time Representation analogous to MDPs But larger number of states Solve using Policy Iteration Optimal policy minimizes travel time while reducing the mistakes during navigation 23

24 Uncertainty-aware decisions C B C B A A 24

25 Uncertainty-aware decisions C B C B A A 25

26 Uncertainty-aware decisions C B C B A A 26

27 Uncertainty-aware decisions C B C B A A 27

28 Uncertainty-aware decisions C B C B A A 28

29 Uncertainty-aware decisions C B C B A A 29

30 3

31 Shortest path policy 3

32 Shortest path, Path Policy small uncertainty 32

33 Shortest path, Path Policy small uncertainty 33

34 Shortest path, Path Policy small uncertainty 34

35 Shortest path, Path Policy small uncertainty 35

36 Shortest path, Path Policy small uncertainty 36

37 Shortest Path path, Policy large uncertainty 37

38 Shortest Path path, Policy large uncertainty 38

39 Shortest Path path, Policy large uncertainty 39

40 Shortest Path path, Policy large uncertainty 4

41 Shortest Path path, Policy large uncertainty 4

42 Shortest Path path, Policy large uncertainty 42

43 Shortest Path path, Policy large uncertainty 43

44 Safest path policy 44

45 Safest path, large uncertainty 45

46 Safest Path, path, large High Uncertainty uncertainty 46

47 Safest Path, path, large High Uncertainty uncertainty 47

48 Safest Path, path, large High Uncertainty uncertainty 48

49 Safest Path, path, large High Uncertainty uncertainty 49

50 Safest Path, path, large High Uncertainty uncertainty 5

51 Safest Path, path, large High Uncertainty uncertainty 5

52 Shortest Safest path, Path small Policy uncertainty 52

53 Shortest Safest path, Path small Policy uncertainty 53

54 Shortest Safest path, Path small Policy uncertainty 54

55 Shortest Our approach, Path Policy small uncertainty 55

56 Shortest Our approach, Path Policy small uncertainty 56

57 Shortest Our approach, Path Policy small uncertainty 57

58 Our approach, large uncertainty 58

59 Safest Our approach, Path, Large High large Uncertainty uncertainty 59

60 Safest Our approach, Path, High large Uncertainty uncertainty 6

61 Safest Our approach, Path, High large Uncertainty uncertainty 6

62 Safest Our approach, Path, High large Uncertainty uncertainty 62

63 Safest Our approach, Path, High large Uncertainty uncertainty 63

64 Shorter avg. travel time than the shortest and safest path policy 64

65 Summary Planning on road networks explicitly considering position uncertainty Augmented-MDP approximates efficiently POMDP Localization prior estimates belief propagation through the network Policy trades-off safety and travel time given the current belief 65

66 Thank you for your attention 66