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Liang Sun, PhDAutonomous Systems Laboratory (ASL)
Department of Mechanical and Aerospace EngineeringNew Mexico State University, Las Cruces, NM
Distributed Dynamic Task Allocation for Sensor Management
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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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Ø Auction vs Hungarian Ø Centralized Single-Task Allocation
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Auction Algorithm (cont’d)
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Hungarian Algorithm (cont’d)
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Hungarian Algorithm (cont’d)
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Consensus Based Auction Algorithm (CBAA)
Ø Auction
Ø Consensus
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Ø Fully Connected Network
Ø Loosely Connected Network
Communication Network Topology
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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.
Procedure: For Step ..
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
DHBA (cont’d)
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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.
Procedure: For Step ..
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Distributed Multi-Task Allocation
Ø Consensus-Based Bundle Algorithm (Brunet, 2008)Ø Phase I: Bundle Building
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Distributed Multi-Task Allocation
Ø Consensus-Based Bundle Algorithm (Brunet, 2008):Ø Phase II: Consensus
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Check for Field-of-View Constraint
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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) for Planning
Global Target
CoordinatesTarget
Assignment
Gimbal-Pose
Candidate Generation
MPC Sensor Orientation
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Videos3D simulation: 2 UAVs Tracking 3 Mobile Ground Targets
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
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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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Videos
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A4H Field Day Liang Sun, MAE, NMSUApril 19, 2019
Thank you!