decentralised coordination of mobile sensors
DESCRIPTION
Decentralised Coordination of Mobile Sensors. Ruben Stranders , Alessandro Farinelli , Francesco Delle Fave , Alex Rogers, Nick Jennings. School of Electronics and Computer Science University of Southampton [email protected]. - PowerPoint PPT PresentationTRANSCRIPT
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
This presentation focuses on coordinating mobile sensors for information gathering tasks
Sensor Architecture
Decentralised Control using Max-Sum
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
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
PE P+
The aim of the sensors is to collectively maximise the value of the observations they take
As a result, the predictive variance is minimised
SF
16
This presentation focuses on coordinating mobile sensors for information gathering tasks
Sensor Architecture
Decentralised Control using Max-Sum
Model
Value
Coordinate
Problem Formulation
17
This presentation focuses on coordinating mobile sensors for information gathering tasks
Sensor Architecture
Decentralised Control using Max-Sum
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
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
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
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
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
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 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!
This presentation focuses on coordinating mobile sensors for information gathering tasks
Sensor Architecture
Decentralised Control using Max-Sum
Model
Value
Coordinate
Problem Formulation
This presentation focuses on coordinating mobile sensors for information gathering tasks
Sensor Architecture
Decentralised Control using Max-Sum
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
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
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
From function j to variable i
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
From function j to variable i
Bottleneck!
ijadjk
kjkjjiiij xqUxrj \)(\
)()(max)( xx
Therefore, we developed two general pruning techniques that speed up Max-Sum
Goal: Make as small as possible
ijadjk
kjkjjiiij xqUxrj \)(\
)()(max)( xx
Therefore, we developed two general pruning techniques that speed up Max-Sum
Goal: Make as small as possible
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
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]
The first pruning technique prunes individual actions by identifying dominated actions
↑ [2, 2]↓ [1, 1]
↑ [5, 6]↓ [0, 1]
↑ [1, 2]↓ [3, 4]
2. Bounds are summed
↑ [8, 10]↓ [4, 7]
The first pruning technique prunes individual actions by identifying dominated actions
2. Bounds are summed
↑ [8, 10]↓ [4, 7]
↓ [4, 7]↑ [8, 10]
The first pruning technique prunes individual actions by identifying dominated actions
3. Dominated actions are pruned
[8, 10][4, 7]
X
ijadjk
kjkjjiiij xqUxrj \)(\
)()(max)( xx
We developed two general pruning techniques that speed up Max-Sum
Goal: Make as small as possible
1. Try to prune the action spaces of individual sensors
2. Try to prune joint actions
ix
ij \x✔
ijadjk
kjkjjiiij xqUxrj \)(\
)()(max)( xx
Sensor 1 Sensor 2 Sensor 3
The second pruning technique reduces the joint action space because exhaustive enumeration is too costly
Sensor 1 Sensor 2 Sensor 3
ijadjk
kjkjjiiij xqUxrj \)(\
)()(max)( xx
The second pruning technique reduces the joint action space because exhaustive enumeration is too costly
132 \)(},{
11 )()(max)(xjadjk
kjkjjxx
j xqUxr x
132 \)(},{
11 )()(max)(xjadjk
kjkjjxx
j xqUxr x
Sensor 1 Sensor 2 Sensor 3
The second pruning technique reduces the joint action space because exhaustive enumeration is too costly
),,(max)( 32},{
132
xxUr jxx
j
The second pruning technique reduces the joint action space because exhaustive enumeration is too costly
),,(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
The second pruning technique prunes the joint action space using Branch and Bound
[7, 13][0, 4] [2, 6]XXSensor 1
Sensor 2
Sensor 3
The second pruning technique prunes the joint action space using Branch and Bound
The second pruning technique prunes the joint action space using Branch and Bound
9 10 7 8
[7, 13][0, 4] [2, 6]XXSensor 1
Sensor 2
Sensor 3
The second pruning technique prunes the joint action space using Branch and Bound
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?