1. Decentralised Coordination of Mobile Sensors School of Electronics and Computer Science University of Southampton rs2@ecs.soton.ac.uk Ruben Stranders, Alessandro Farinelli, Francesco Delle Fave, Alex Rogers, Nick Jennings

2. 2 This presentation focuses on coordinating mobile sensors for information gathering tasks Sensor Architecture Decentralised Control using Max-Sum Model Value Coordinate Problem Formulation

3. 3 This presentation focuses on coordinating mobile sensors for information gathering tasks Sensor Architecture Decentralised Control using Max-Sum Model Value Coordinate Problem Formulation

4. Mobile sensor platforms are becoming the de facto means of establishing situational awareness “3D” Dull Dirty Dangerous Know what is happening Predict what will happen and understand the impact on the mission

5. Currently, there is a strong trend toward making these platforms fully autonomous and cooperative “Auto target engage by 2049…” (My focus was on less nightmarish scenarios….) Individual remote controlled vehicles Teams of autonomous vehicles

6. The key challenge is to coordinate a team of sensors to gather information about some features of an environment Sensors Feature: moving target spatial phenomena (e.g. temperature)

7. We focus on three well known information gathering domains: (1) Pursuit Evasion PE

8. We focus on three well known information gathering domains: (2) Patrolling P

9. We focus on three well known information gathering domains: (3) Monitoring Spatial Fields SF

10. The sensors operate in a constrained environment No centralised control

11. The sensors operate in a constrained environment Limited Communication

12. The aim of the sensors is to collectively maximise the value of the observations they take Paths leading to areas already explored - Low value

13. The aim of the sensors is to collectively maximise the value of the observations they take Paths leading to unexplored areas - High value

14. The aim of the sensors is to collectively maximise the value of the observations they take As a result, the target is detected faster PEP +

15. The aim of the sensors is to collectively maximise the value of the observations they take As a result, the predictive variance is minimised SF

16. 16 This presentation focuses on coordinating mobile sensors for information gathering tasks Sensor Architecture Decentralised Control using Max-Sum Model Value Coordinate Problem Formulation

17. 17 This presentation focuses on coordinating mobile sensors for information gathering tasks Sensor Architecture Decentralised Control using Max-Sum Model Value Coordinate Problem Formulation

18. To solve this coordination problem, we had to address three challenges 1.How to model the problem? 2.How to value potential samples? 3.How to coordinate to gather samples of highest value?

19. The three central challenges are clearly reflected in the architecture of our sensing agents Samples sent to neighbouring agents Samples received from neighbouring agents Information processing Model of Environment Outgoing negotiation messages Incoming negotiation messages Value of potential samples Action Selection Move Samples from own sensor Sensing Agent Raw samples Model Value Coordinate

20. Samples sent to neighbouring agents Samples received from neighbouring agents Information processing Model of Environment Outgoing negotiation messages Incoming negotiation messages Value of potential samples Action Selection Move Samples from own sensor Sensing Agent Raw samples Model

21. Each sensor builds its own belief map containing all the information gathered about the target Map of the probability distribution over the target’s position The map is dynamically updated by fusing the new observation gathered PEP +

22. The sensors model the spatial fields using Gaussian Processes Weak Strong Spatial Correlations SF

23. The sensors model the spatial fields using Gaussian Processes Weak Strong Temporal Correlations SF

24. Samples sent to neighbouring agents Samples received from neighbouring agents Information processing Model of Environment Outgoing negotiation messages Incoming negotiation messages Value of potential samples Action Selection Move Samples from own sensor Sensing Agent Raw samples Value

25. The value of a set of observations is equal to the probability of detecting the target High probability Low probability High value: - target might be there Low value: -Target is probably somewhere else PEP +

26. The value of a sample is based on how much it reduces uncertainty Prediction Confidence Interval Collected Sample High entropy High value: - Strong uncertainty reduction Low entropy Low value: - Small uncertainty reduction SF

27. The sensor agents coordinate using the Max-Sum algorithm Samples sent to neighbouring agents Samples received from neighbouring agents Information processing Model of Environment Outgoing negotiation messages Incoming negotiation messages Value of potential samples Action Selection Move Samples from own sensor Sensing Agent Raw samples Coordinate

28. To decompose the utility function we use the concept of incremental utility value

29. The key problem is to maximise the social welfare of the team of sensors in a decentralised way Social welfare: Mobile Sensors

30. The key problem is to maximise the social welfare of the team of sensors in a decentralised way Variable encode paths

31. Variable encode paths of finite length Coordinating over all paths is infeasible: it results in a combinatorial explosion for increasing path length Thus, we apply receding horizon control

32. Clusters Our solution: we cluster the neighborhood of each sensor (now each variable represent a path to the Center of each cluster) Most informative is chosen!

33. This presentation focuses on coordinating mobile sensors for information gathering tasks Sensor Architecture Decentralised Control using Max-Sum Model Value Coordinate Problem Formulation

34. This presentation focuses on coordinating mobile sensors for information gathering tasks Sensor Architecture Decentralised Control using Max-Sum Model Value Coordinate Problem Formulation

35. 35 We can now use Max-Sum to solve the social welfare maximisation problem Complete Algorithms DPOP OptAPO ADOPT Communication Cost Iterative Algorithms Best Response (BR) Distributed Stochastic Algorithm (DSA) Fictitious Play (FP) Max-Sum Algorithm Optimality

36. The input for the Max-Sum algorithm is a graphical representation of the problem: a Factor Graph Variable nodes Function nodes Agent 1 Agent 2 Agent 3

37. Max-Sum solves the social welfare maximisation problem by local computation and message passing Variable nodes Function nodes Agent 1 Agent 2 Agent 3

38. Max-Sum solves the social welfare maximisation problem by local computation and message passing From variable i to function j From function j to variable i

39. In acyclic factor graphs, the messages converge to the marginal utility functions A B

40. A B In such cases, maximising the marginal utility functions is equivalent to maximising the global objective function Max-Sum is optimal on acyclic factor graphs

41. To use Max-Sum, we encode the mobile sensor coordination problem as a factor graph Sensor 1 Sensor 2 Sensor 3 Sensor 1 Sensor 2 Sensor 3

42. To use Max-Sum, we encode the mobile sensor coordination problem as a factor graph Sensor 1 Sensor 2 Sensor 3 Sensor 1 Sensor 2 Sensor 3 Paths to the most informative positions

43. To use Max-Sum, we encode the mobile sensor coordination problem as a factor graph Sensor 1 Sensor 2 Sensor 3 Sensor 1 Sensor 2 Sensor 3 Local Utility Functions Measure value of observations along paths

44. Unfortunately, the straightforward application of Max-Sum is too computationally expensive From variable i to function j From function j to variable i

45. Unfortunately, the straightforward application of Max-Sum is too computationally expensive From variable i to function j From function j to variable i Bottleneck!

46. Therefore, we developed two general pruning techniques that speed up Max-Sum Goal: Make as small as possible

47. Therefore, we developed two general pruning techniques that speed up Max-Sum Goal: Make as small as possible 1.Try to prune the action spaces of individual sensors 2.Try to prune joint actions

48. The first pruning technique prunes individual actions by identifying dominated actions

49. 1. Neighbours send bounds ↑ [2, 2] ↓ [1, 1] ↑ [5, 6] ↓ [0, 1] ↑ [1, 2] ↓ [3, 4]

50. The first pruning technique prunes individual actions by identifying dominated actions ↑ [2, 2] ↓ [1, 1] ↑ [5, 6] ↓ [0, 1] ↑ [1, 2] ↓ [3, 4] 2. Bounds are summed ↑ [8, 10] ↓ [4, 7]

51. The first pruning technique prunes individual actions by identifying dominated actions 2. Bounds are summed ↑ [8, 10] ↓ [4, 7]

52. ↑ [8, 10] The first pruning technique prunes individual actions by identifying dominated actions 3. Dominated actions are pruned [8, 10] [4, 7]

53. We developed two general pruning techniques that speed up Max-Sum Goal: Make as small as possible 1.Try to prune the action spaces of individual sensors 2.Try to prune joint actions

54. Sensor 1Sensor 2Sensor 3 The second pruning technique reduces the joint action space because exhaustive enumeration is too costly

55. Sensor 1Sensor 2Sensor 3 The second pruning technique reduces the joint action space because exhaustive enumeration is too costly

56. Sensor 1Sensor 2Sensor 3 The second pruning technique reduces the joint action space because exhaustive enumeration is too costly

58. The second pruning technique prunes the joint action space using Branch and Bound Sensor 1 Sensor 2 Sensor 3

59. [7, 13][0, 4][2, 6] Sensor 1 Sensor 2 Sensor 3 The second pruning technique prunes the joint action space using Branch and Bound

60. [7, 13][0, 4][2, 6] Sensor 1 Sensor 2 Sensor 3 The second pruning technique prunes the joint action space using Branch and Bound

61. 91078 [7, 13][0, 4][2, 6] Sensor 1 Sensor 2 Sensor 3

62. The second pruning technique prunes the joint action space using Branch and Bound 91078 [7, 13][0, 4][2, 6] Sensor 1 Sensor 2 Sensor 3

63. The two pruning techniques combined prune 95% of the action space with 6 neighbouring sensors Number of neighbouring sensors % of joint actions pruned

64. Our Algorithm outperforms state-of-the-art approaches by up to 52% for Pursuit Evasion PE

65. Our Algorithm outperforms state-of-the-art approaches by up to 44% for Patrolling P

66. Avg. Root Mean Squared Error Our Algorithm reduces Root Mean Squared Error of predictions up to 50% compared to Greedy SF

67. In conclusion, our algorithm is effective for a broad range of information gathering problems 1. Decentralised + robust 2. General 3. Effective and efficient

68. For future work, we intend to extend our approach to compute solutions with a guaranteed approximation ratio for any planning horizon

69. In conclusion, our algorithm is effective for a broad range of information gathering problems 1. Decentralised 2. General 3. Effective and efficient QUESTIONS?