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
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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)
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!
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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
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