Self‐Organising Sensors for Wide Area Surveillance using the Max‐Sum Algorithm Alex Rogers and Nick Jennings School of Electronics and Computer Science.

Self Organising Sensors for ‐Wide Area Surveillance using the

Max Sum Algorithm‐ 

Alex Rogers and Nick JenningsSchool of Electronics and Computer Science

University of [email protected]

Alessandro FarinelliDepartment of Computer Science

University of VeronaVerona, Italy

[email protected]

Overview

• Self-Organisation– Landscape of Decentralised Coordination

Algorithms• Local Message Passing Algorithms

– Max-sum algorithm– Graph Colouring

• Wide Area Surveillance Scenario• Future Work

Self-Organisation

Sensors

Self-Organisation

Agents

• Multiple conflicting goals and objectives• Discrete set of possible actions

Self-Organisation

Agents

• Multiple conflicting goals and objectives• Discrete set of possible actions• Some locality of interaction

Self-Organisation

Agents

Maximise Social Welfare:• Multiple conflicting goals and objectives• Discrete set of possible actions• Some locality of interaction

Self-Organisation

Agents

Central point of controlDecentralised self-organisation through local computation and message passing.• Speed of convergence, guarantees of optimality,

communication overhead, computability

No direct communication Solution scales poorly Central point of failure Who is the centre?

Landscape of Algorithms

Complete Algorithms

DPOPOptAPOADOPT

Communication Cost

Optimality

Iterative Algorithms

Best Response (BR)Distributed Stochastic

Algorithm (DSA) Fictitious Play (FP)

Message Passing

Algorithms

Sum-ProductAlgorithm

Max-Sum Algorithm

Variable nodes

Function nodes

Factor Graph

A simple transformation:

allows us to use the same algorithms to maximise social welfare:

Find approximate solutions to global optimisation through local computation and message passing:

Graph Colouring

Agentfunction / utility

variable / state

Graph Colouring Problem Equivalent Factor Graph

Graph Colouring

Equivalent Factor GraphUtility Function

Graph Colouring

Graph Colouring

Optimality

Communication Cost

Robustness to Message Loss

Wide Area Surveillance Scenario

Dense deployment of sensors to detect pedestrian and vehicle activity within an urban environment.

Unattended Ground Sensor

Energy Constrained Sensors

Maximise event detection whilst using energy constrained sensors:– Use sense/sleep duty cycles

to maximise network lifetime of maintain energy neutral operation.

– Coordinate sensors with overlapping sensing fields.

time

duty cycle

time

duty cycle

Self-Organising Sensor Network

Energy-Aware Sensor Networks

Future Work• Continuous action spaces

– Max-sum calculations are not limited to discrete action space

– Can we perform the standard max-sum operators on continuous functions in a computationally efficient manner?

• Bounded Solutions– Max-sum is optimal on tree and limited

proofs of convergence exist for cyclic graphs– Can we construct a tree from the original

cyclic graph and calculate an lower bound on the solution quality?