A Decentralised Coordination Algorithm for Mobile Sensors

 

School of Electronics and Computer ScienceUniversity of Southampton{rs06r2, fmdf08r, acr, nrj}@ecs.soton.ac.uk

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

LimitedCommunication

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 toneighbouring agents

Samples received fromneighbouring agents

Information processing

Model of Environment

Outgoing negotiation messages

Incomingnegotiation messages

Value of potential samples Action

Selection

Move

Samples from own sensor

SensingAgent

Rawsamples

Model

Value

Coordinate

Samples sent toneighbouring agents

Samples received fromneighbouring agents

Information processing

Model of Environment

Outgoing negotiation messages

Incomingnegotiation messages

Value of potential samples Action

Selection

Move

Samples from own sensor

SensingAgent

Rawsamples

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 toneighbouring agents

Samples received fromneighbouring agents

Information processing

Model of Environment

Outgoing negotiation messages

Incomingnegotiation messages

Value of potential samples Action

Selection

Move

Samples from own sensor

SensingAgent

Rawsamples

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 toneighbouring agents

Samples received fromneighbouring agents

Information processing

Model of Environment

Outgoing negotiation messages

Incomingnegotiation messages

Value of potential samples Action

Selection

Move

Samples from own sensor

SensingAgent

Rawsamples

Coordinate

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

)(1Y )( 12

YY )( 213YYY

1U 2U 3U

)()()(),,( 211321 321YYYYYYf YYY

)(1

1i

jjY Y

i

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

M

iYi

1

1-i

1jj)Y(maxarg

xSocial welfare:

Mobile Sensors

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

),,( 3211 pppU

),( 212 ppU

),( 323 ppU

Variable encode paths

),,( 3211 pppU

),( 212 ppU

),( 323 ppU

Variable encode paths

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

),,( 3211 pppU

),( 212 ppU

),( 323 ppU

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

DPOPOptAPOADOPT

Communication Cost

Iterative Algorithms

Best Response (BR)Distributed Stochastic

Algorithm (DSA) Fictitious Play (FP)

Max-SumAlgorithm

Optimality

The input for the Max-Sum algorithm is a graphical representation of the problem: a Factor Graph

Variable nodes Function nodes

1p

2p

3p

1U

2U

3U

Agent 1Agent 2

Agent 3

Max-Sum solves the social welfare maximisation problem by local computation and message passing

1p

2p

3p

1U

2U

3U

Variable nodes Function nodes

Agent 1Agent 2

Agent 3

Max-Sum solves the social welfare maximisation problem by local computation and message passing

jiadjk

iikiji prpq\)(

)()(

ijadjk

kjkjji

iij pqUprj \)(\p

)()p(max)(

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

1p

2p

3p

1U

2U

3U

Sensor 1Sensor 2

Sensor 3

Sensor 1

Sensor 2

Sensor 3

To use Max-Sum, we encode the mobile sensor coordination problem as a factor graph

1p

2p

3p

1U

2U

3U

Sensor 1Sensor 2

Sensor 3

Sensor 1

Sensor 2

Sensor 3

Paths to the most informativepositions

To use Max-Sum, we encode the mobile sensor coordination problem as a factor graph

1p

2p

3p

1U

2U

3U

Sensor 1Sensor 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?