A Decentralised Coordination Algorithm for Mobile Sensors School of Electronics and Computer Science University of Southampton {rs06r2, fmdf08r, acr, Ruben Stranders, Francesco Delle Fave, Alex Rogers, Nick Jennings

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

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)

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

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

The sensors operate in a constrained environment No centralised control

The sensors operate in a constrained environment Limited Communication

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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

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