distributed dynamic task allocation for sensor management · 6 april 19, 2019 a4h field day liang...

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Liang Sun, PhDAutonomous Systems Laboratory (ASL)

Department of Mechanical and Aerospace EngineeringNew Mexico State University, Las Cruces, NM

[email protected]

Distributed Dynamic Task Allocation for Sensor Management

mailto:[email protected]

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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019

Motivation

Ø Mobile Sensor Management for Target TrackingØ Intelligent, Surveillance, and Reconnaissance (ISR)

Ø Search and rescue

Ø Wildlife management

Ø Space Exploration

Ø Disaster analysis

Picture credit: Sun et al., 2015

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Problem StatementAssumptions:• # vehicles < # targets• Mobile targets w/ unknown planned trajectories• Limited sensing range and field of view• Decoupled sensor orientation and vehicle motion (by using gimbals)Goal:• Minimize the overall uncertainty of target states

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Framework

Sensors Signal Processing

Sensor Orientation

Sensor Action

Vehicle Path Planning

Vehicle Action

Ø SensorsØ IMU, RGB/IR cameras, RADAR, LiDAR, etc.

Ø Signal Processing (Sensor Exploitation)Ø ATR: Target detection, identification, and characterization

Ø Sensor Orientation and Vehicle Path PlanningØ Distributed Task Allocation (Hungarian-Based Approaches)Ø Optimization (Model Predictive Control (MPC))

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Framework


Sensor Orientation

Sensor Action


Vehicle Action




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Sensors and Signal Processing

Sensor States(e.g., orientations,

slew rate)

Estimation Algorithm

Vehicle States (e.g., Pos, velocity,

attitude)

Sensor Measurements (e.g., images)

Global Target Coordinates

Signal (image) Processing

Local (Pixel) Target Coordinates

Vision-Based Geo-Localization

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Framework


Sensor Orientation

Sensor Action


Vehicle Action




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Sensor Orientation

Ø Target AssignmentØ Distributed Multi-Task Allocation

Ø Gimbal-Pose Candidate Generation Ø Dynamic Weighted Graph Ø Check for Field-of-View Constraint

Ø Model Predictive Control (MPC)

Global Target

CoordinatesTarget

Assignment

Gimbal-Pose

Candidate Generation

MPC Sensor Orientation

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Sensor Orientation




Global Target

CoordinatesTarget

Assignment

Gimbal-Pose



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Literature Review

Ø Centralized ApproachesØ Bertsekas et al. (1987): Auction AlgorithmØ Kuhn (1955): Hungarian Algorithm

Ø Turra (2004) and Tanner (2007): UAS applications. Ø Ji et al., (2006): Robots.

Ø Munkres (1957): Munkres AlgorithmØ Jonker and Volgenant (1987): Jonker-Volgenant AlgorithmØ Annamalai (2016): matchings in bipartite hypergraphs

Ø Distributed ApproachesØ Auction Algorithms

Ø Choi et al., (2009): Single-task allocation: Consensus-Based Auction Algorithm (CBAA)Ø Brunet et al. (2008) & Choi et al. (2009): multi-task allocation: Consensus-Based

Bundle Algorithm (CBBA)Ø Buckman (2018): CBBA with Partial Replanning

Ø Distributed Hungarian methodsØ Giordani et al. (2010) and Chopra et al. (2017): single-task allocation, bipartite graphs

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Ø Auction vs Hungarian Ø Centralized Single-Task Allocation

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Auction Vs Hungarian

1. Auction Approaches:ü Agents compete for tasks through a bidding process.

ü Agent with the highest bid wins the assignment.

ü Central auctioneer used to elect the winner.

2. Hungarian Approaches:ü It is a procedure for solving an assignment problem.

ü It uses a cost matrix containing all the data.

ü Optimal solution is obtained by a cost minimizationprocess.

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Auction AlgorithmAlgorithm 2.1: Auction Algorithm

Initialization:

Form the reward matrix ! such that:

"#$ =1

'()*(#) − ).($)/2 + (2*(#) − 2.($)/

2

where # denotes the agent and $ stands for the target.

Form the price vector 3 such that:

4$ = 0

Procedure: For Step ..

For Agent #

if ∑ 7#$ (.) = 0$ then, i.e., 7#$ is the assignment matrix.

8# = "9:;"7$ <"#$ − 4$ = if ∑ 7#8# (.) > 0# then

?# = "#8# − 48# @# = ;"7$≠8# <"#$ − 4$ = 48# = 48# + ?# − @# end if

7#8# (.) = 1

end if End Procedure

Auction Conflict Resolution

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Auction Algorithm (cont’d)

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Hungarian AlgorithmAlgorithm 2.2: Hungarian Algorithm

Initialization:

• Form the cost matrix ! such that:

"#$ = &'()(#) − (-($).2 + '1)(#) − 1-($).

2

where # denotes the UAV and $ stands for the Target.

• Define the smallest entry in each row and column where 2# is the smallest entry

in row # and 3$ is the smallest entry column $. Step 1: Subtract the smallest entry in each row from all the entries of its row.

"#̅$ = "#$ − 2#

Step 2: Subtract the smallest entry in each column from all the entries of its column.

"#̅$ = "#̅$ − 3$

Procedure:

Step 3: Draw lines through appropriate rows and columns so that all the zero entries

of the cost matrix are covered and the minimum number, 5, of such lines is used.

Step 4: Test for optimality:

if 5 = 6) then

An optimal assignment of zeros is possible and the assignment is obtained as

follows:

7#8# = 1, i.e., 8# = argmin$ '"#̅$ .

end if

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Algorithm 2.2: Hungarian Algorithm

Initialization:

• Form the cost matrix ! such that:

"#$ = &'()(#) − (-($).2 + '1)(#) − 1-($).

2

where # denotes the UAV and $ stands for the Target.

• Define the smallest entry in each row and column where 2# is the smallest entry

in row # and 3$ is the smallest entry column $. Step 1: Subtract the smallest entry in each row from all the entries of its row.

"#̅$ = "#$ − 2#

Step 2: Subtract the smallest entry in each column from all the entries of its column.

"#̅$ = "#̅$ − 3$

Procedure:

Step 3: Draw lines through appropriate rows and columns so that all the zero entries

of the cost matrix are covered and the minimum number, 5, of such lines is used.

Step 4: Test for optimality:

if 5 = 6) then

An optimal assignment of zeros is possible and the assignment is obtained as

follows:

7#8# = 1, i.e., 8# = argmin$ '"#̅$ .

end if

Hungarian Algorithm (cont’d)

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Ø Draw lines through appropriate rows and columns so that all the zero entries of the cost matrix are covered and the minimum number, !, of such lines is used.

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Auction vs Hungarian

0 10 20 30 40 500

10

20

30

40

50

60

70

NumberofUAVsinthegroupAveragecomputationaltime(sec)

AuctionHungrian

Table 2.1 The average computational time for the

different UAV groups.

GroupNumber of

Agents

Average computational time

Auction Hungarian

#1 2 0.33605 0.3369

#2 4 0.34195 0.3427

#3 8 0.36189 0.37092

#4 12 0.473236 0.38200

#5 16 0.85227 0.38677

#6 24 2.57046 0.41101

#7 32 8.1303 0.41902

#8 50 71.013 0.43035

Time Efficiency:

Computational Complexity (Narayanan et al., 2000):Auction: 8"# + 20" memory locationsHungarian: 8"# + 12" memory locations

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Decentralized Task Allocation Algorithm

Ø Consensus Based Auction Algorithm (CBAA)

q Single task allocation algorithm: #Agent = #Tasks

q Iterating between 2 phases

ü Phase 1: Auction Algorithm (greedy selection of tasks)

ü Phase 2: Consensus Algorithm (conflict resolving)

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Consensus Based Auction Algorithm (CBAA)

Ø Auction

Ø Consensus

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Ø Motivation:

Ø The (centralized) Hungarian algorithm outperforms the auction

algorithm.

Ø Question:

Ø How the Hungarian approach can be used in a decentralized

manner?

Decentralized Hungarian-Based Algorithm

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Assumptions

ü Each agent knows where all tasks are.ü Initially, the total number of participating agents is

known but the locations are unknown.ü Each agent performs TA individually based on

the collected the information.ü When communicating, information exchange

among agents.ü When the global information is identical at each

agent, a final assignment is obtained.

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Ø Fully Connected Network

Ø Loosely Connected Network

Communication Network Topology

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q InitializationAlgorithm 3.2: Decentralized Hungarian Based Algorithm (DHBA)

Initialization:

For Agent !, form a cost matrix "! such that:

if # = ! then

%#& = '()*(#) − ).(&)/2 + (2*(#) − 2.(&)/

2

else

%#& = ∞

end if where & stands for the Target.


1. Phase 1: Apply Hungarian Algorithm (Algorithm 2) and get assignment for Agent i.

2. Phase 2: Update "! Procedure: For Agent !:

Connect with neighbor 4 and receive "4

Update "! such that:

if (%!& /4 ≠ ∞ then (%!& /! = (%!& /4 end if

End Procedure

- Return to Phase 1.

End Procedure

q Agents scan its local area and locate neighbors and targets.q Each agent forms its own G and C matrices.

Distributed Hungarian-Based Algorithm

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DHBA (cont’d)

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q 2-Phase Process

Algorithm 3.2: Decentralized Hungarian Based Algorithm (DHBA)

Initialization:

For Agent !, form a cost matrix "! such that:

if # = ! then

%#& = '()*(#) − ).(&)/2 + (2*(#) − 2.(&)/

2

else

%#& = ∞

end if where & stands for the Target.


1. Phase 1: Apply Hungarian Algorithm (Algorithm 2) and get assignment for Agent i.

2. Phase 2: Update "! Procedure: For Agent !:

Connect with neighbor 4 and receive "4

Update "! such that:

if (%!& /4 ≠ ∞ then (%!& /! = (%!& /4 end if

End Procedure

- Return to Phase 1.

End Procedure

q The DHBA algorithmiterates between two mainphases.

q In phase 1, the centralizedHungarian algorithm isapplied in each iteration.

q In phase 2, each agentconnects with itsneighbors to exchangetheir cost matrices.

q Each agent update its owncost matrix.

DHBA (cont’d)

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Comparison of CBAA and DHBA

Loosely Connected Network

Scalability

0 1 2 3 4 50246810

l2

#ofSteps

0 1 2 3 4 50

5

10

15

l2

#ofSteps

0 1 2 3 4 5 60

10

20

30

l2

#ofSteps

0 1 2 3 4 5 60

20

40

60

80

l2

#ofSteps

0 1 2 3 4 5 6 70

20

40

60

80

l2

#ofSteps

0 1 2 3 4 5 6 7 80

30

60

90

120

l2

#ofSteps

CBAADHBA

CBAADHBA

CBAADHBA

CBAADHBA

CBAADHBA

CBAADHBA

OptimalityEfficiency

Ismail, S. and Sun, L., "Decentralized Hungarian-Based Approach for Fast and Scalable Task Allocation", IEEE International Conference on Unmanned Aircraft Systems, Miami, Florida, USA, June 2017, pp. 23-28.

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Distributed Multi-Task Allocation

Ø Consensus-Based Bundle Algorithm (Brunet, 2008)Ø Phase I: Bundle Building

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Distributed Multi-Task Allocation

Ø Consensus-Based Bundle Algorithm (Brunet, 2008):Ø Phase II: Consensus

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Distributed Hungarian-Based ApproachesØ Clustering-Based Hungarian Algorithm

(CBHA)Ø Clustering: Group targets into the #agent

clustersØ Run HAØ Path Planning

Ø Recursive Hungarian Algorithm (RHA)Ø Introduce Pseudo TasksØ Recursively run HA until all tasks are

assignedØ No need for path planning nor clustering

Ø Duplication Hungarian Algorithm (DHA)Ø Introduce both Pseudo Tasks and

Pseudo AgentsØ Run HAØ Path planning Ø No need for clustering

2 1 4 3

5 6 8 3

x x x x

x x x x

2 1 4 3

5 6 8 3

2 1 4 3

5 6 8 3

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Future directions

Ø Data driven approachesØ Retasking frequency vs look-ahead time

horizon

Ø Formulation of costØ Uncertainty quantificationØ Converging speed vs network connectivityØ Conflict evaluation in a dynamic context

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Sensor Orientation




Global Target

CoordinatesTarget

Assignment

Gimbal-Pose



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Gimbal-Pose Candidate Generation • Dynamic Weighted Graph (DWG) with quantified uncertainty

Farmani, N., Sun, L., and Pack, D., IEEE Transactions on Aerospace and Electronic Systems, 2017

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Check for Field-of-View Constraint

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Sensor Orientation



Ø Model Predictive Control (MPC) for Planning

Global Target

CoordinatesTarget

Assignment

Gimbal-Pose



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Model Predictive Control for PlanningØ Sensor Orientation Planning

Ø Vehicle Path Planning

Farmani, N., Sun, L., and Pack, D., IEEE Transactions on Aerospace and Electronic Systems, 2017

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Videos3D simulation: 2 UAVs Tracking 3 Mobile Ground Targets

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Videos 2D simulation w/ prob. maps: 4 UAV cooperatively tracking 7 mobile targets

Sun, L., Baek, S., and Pack, D., "Distributed Probabilistic Search and Tracking of Agile Mobile Ground Targets Using a Network of Unmanned Aerial Vehicles", Human Behavior Understanding in Networked Sensing, Springer International Publishing, 2014.

FeatureMap

Prob.Map

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Videos

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Thank you!

distributed dynamic task allocation for sensor management · 6 april 19, 2019 a4h field day liang...

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