Decentralised Coordination of Mobile Sensors

Decentralised Coordination of Mobile Sensors

School of Electronics and Computer ScienceUniversity of [email protected]

Ruben Stranders, Alessandro Farinelli, 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

3


Sensor Architecture


Model

Value

Coordinate

Problem Formulation

Mobile sensor platforms are becoming the de facto means of establishing situational awareness

“3D”Dull

DirtyDangerous

Know what is happening

Predict what will happen

and understand the impact on the mission

Currently, there is a strong trend toward making these platforms fully autonomous and cooperative

“Auto target engage by 2049…”

(My focus was on less nightmarish scenarios….)

Individual remote controlled vehicles

Teams of autonomous vehicles

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)

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

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

We focus on three well known information gathering domains: (3) Monitoring Spatial Fields SF

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


Paths leading to unexplored areas- High value


As a result, the target is detected faster

PE P+


As a result, the predictive variance is minimised

SF

16


Sensor Architecture


Model

Value

Coordinate

Problem Formulation

17


Sensor Architecture


Model

Value

Coordinate

Problem Formulation

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








Selection

Move


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

PE P+

The sensors model the spatial fields using Gaussian Processes

Weak Strong

Spatial Correlations SF

The sensors model the spatial fields using Gaussian Processes

Weak Strong

Temporal Correlations SF








Selection

Move


SensingAgent

Rawsamples

Value

The value of a set of observations is equal to the probability of detecting the target

High probability

Low probability

High value: - target might be there

Low value:- Target is probably

somewhere else

PE P+

The value of a sample is based on how much it reduces uncertainty

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

PredictionConfidence IntervalCollected Sample

High entropyHigh value: - Strong uncertainty reduction

Low entropyLow value: - Small uncertainty reduction

SF

The sensor agents coordinate using the Max-Sum algorithm








Selection

Move


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 of finite length

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

Thus, we apply receding horizon control

),,( 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!


Sensor Architecture


Model

Value

Coordinate

Problem Formulation


Sensor Architecture


Model

Value

Coordinate

Problem Formulation

35

We can now use Max-Sum to solve the social welfare maximisation problem

Complete Algorithms

DPOPOptAPOADOPT

Communication Cost

Iterative AlgorithmsBest 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

kjkjjiiij pqUprj \)(\p

)()p(max)(

From variable i to function j

From function j to variable i

In acyclic factor graphs, the messages converge to the marginal utility functions

)( iij pr A B

)( iji pq

)p(max)(B\p j

kkiiij Upr

j

)p(max)(A\p j

kkiiij Upq

j

In acyclic factor graphs, the messages converge to the marginal utility functions

)( iij pr A B

)( iji pq

In such cases, maximising the marginal utility functions is equivalent to maximising the global objective function

Max-Sum is optimal on acyclic factor graphs

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


1p

2p

3p

1U

2U

3U

Sensor 1Sensor 2

Sensor 3

Sensor 1

Sensor 2

Sensor 3

Paths to the most informativepositions


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

ijadjk

kjkjjiiij xqUxrj \)(\

)()(max)( xx

Unfortunately, the straightforward application of Max-Sum is too computationally expensive

jiadjk

iikiji xrxq\)(

)()(From variable i to function j


ijadjk


)()(max)( xx

Unfortunately, the straightforward application of Max-Sum is too computationally expensive

jiadjk

iikiji xrxq\)(

)()(From variable i to function j


Bottleneck!

ijadjk


)()(max)( xx

Therefore, we developed two general pruning techniques that speed up Max-Sum

Goal: Make as small as possible

ijadjk


)()(max)( xx

Therefore, we developed two general pruning techniques that speed up Max-Sum


1. Try to prune the action spaces of individual sensors

2. Try to prune joint actions

ix

ij \x

The first pruning technique prunes individual actions by identifying dominated actions


1. Neighbours send bounds

↑ [2, 2]↓ [1, 1]

↑ [5, 6]↓ [0, 1]

↑ [1, 2]↓ [3, 4]


↑ [2, 2]↓ [1, 1]

↑ [5, 6]↓ [0, 1]

↑ [1, 2]↓ [3, 4]

2. Bounds are summed

↑ [8, 10]↓ [4, 7]


2. Bounds are summed

↑ [8, 10]↓ [4, 7]

↓ [4, 7]↑ [8, 10]


3. Dominated actions are pruned

[8, 10][4, 7]

X

ijadjk


)()(max)( xx

We developed two general pruning techniques that speed up Max-Sum


1. Try to prune the action spaces of individual sensors

2. Try to prune joint actions

ix

ij \x✔

ijadjk


)()(max)( xx

Sensor 1 Sensor 2 Sensor 3

The second pruning technique reduces the joint action space because exhaustive enumeration is too costly


ijadjk


)()(max)( xx


132 \)(},{

11 )()(max)(xjadjk

kjkjjxx

j xqUxr x

132 \)(},{

11 )()(max)(xjadjk

kjkjjxx

j xqUxr x



),,(max)( 32},{

132

xxUr jxx

j


),,(max)( 32},{

132

xxUr jxx

j

),,,(),,,(max jj UU

),,,(),,,( jj UU...),,,(),,,( jj UU

The second pruning technique prunes the joint action space using Branch and Bound

Sensor 1

Sensor 2

Sensor 3

[7, 13][0, 4] [2, 6]

Sensor 1

Sensor 2

Sensor 3


[7, 13][0, 4] [2, 6]XXSensor 1

Sensor 2

Sensor 3



9 10 7 8

[7, 13][0, 4] [2, 6]XXSensor 1

Sensor 2

Sensor 3


9 10 7 8

[7, 13][0, 4] [2, 6]XX

X X XO

Sensor 1

Sensor 2

Sensor 3

The two pruning techniques combined prune 95% of the action space with 6 neighbouring sensors

2 2.5 3 3.5 4 4.5 5 5.5 60

25

50

75

100

Number of neighbouring sensors

% o

f joi

nt a

ction

s pru

ned

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

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

Avg.

Roo

t Mea

n Sq

uare

d Er

ror

Our Algorithm reduces Root Mean Squared Error of predictions up to 50% compared to Greedy

Our Al-gorithm

Greedy Random Fixed0.0

0.2

0.4

0.6

0.8

1.0

SF

In conclusion, our algorithm is effective for a broad range of information gathering problems

1. Decentralised + robust

2. General

3. Effective and efficient

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

In conclusion, our algorithm is effective for a broad range of information gathering problems

1. Decentralised

2. General

3. Effective and efficient

QUESTIONS?

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Decentralised Coordination of Mobile Sensors