1. A Decentralised Coordination Algorithm for Mobile Sensors School of Electronics and Computer Science University of Southampton {rs06r2, fmdf08r, acr, nrj}@ecs.soton.ac.uk Ruben Stranders, 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. 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) (previous work)

4. We focus on two well known information gathering domains: (1) Pursuit Evasion

5. We focus on two well known information gathering domains: (2) Patrolling

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

7. The sensors operate in a constrained environment Limited Communication

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

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

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

11. 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?

12. 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

13. 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

14. 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

15. 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

16. We value a set of observations by measuring how much they reduce the probability of detecting the target High probability Low probability High value: - target might be there Low value: -Target is probably somewhere else

17. 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

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

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

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

21. Coordinating over all paths is infeasible: it results in a combinatorial explosion for increasing path length

22. 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!

23. 23 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

24. 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

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

26. 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

27. 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

28. 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

29. 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

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

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

32. In conclusion, we show that our algorithm is effective for a broad range of information gathering problems 1. Decentralised 2. General 3. Effective

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

34. In conclusion, we show that our algorithm is effective for a broad range of information gathering problems 1. Decentralised 2. General 3. Effective QUESTIONS?