arcs presentation 2008
DESCRIPTION
Was used at the ARCS\'08 conference held at Orlando, FL.TRANSCRIPT
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An Anytime Winner Determination Algorithm
forTime-Extended Multi-Robot Task
Allocation
Dr. Fang Tang & Spondon SahaIntelligent Robotics Lab
California State Polytechnic University Pomona, CA
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Outline
Introduction ASyMTRe-D Combinatorial Auctions
Simultaneous Task Allocation (STA)Performance MetricsFuture WorkConclusionReferencesQ&A
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: ASyMTRe-D
Automated Synthesis of Multi-robot Task solutions through software Reconfiguration.
ASyMTRe determines: a coalition of robots. from a heterogeneous group of robots. to carry out a given multi-robot task.
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: ASyMTRe-D
Heterogeneous group of robots??? Robots with different functional capabilities.
Multi-robot task??? A task that cannot be carried out by a single robot. Requires a “strongly cooperative” solution.
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: ASyMTRe-D
ASyMTRe Centralized algorithm. Runs on a central server. Aware of the number of robots and their individual capabilities.
ASyMTRe-D Distributed ASyMTRe designed using the Contract Net Protocol. Runs locally on each robot. Uses a group negotiation process to determine coalitions.
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: ASyMTRe-D
R1
R4 R3
R2R5Task A
Idle Robots
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: ASyMTRe-D
ASyMTRe-D takes into account: Task-Specific cost. Robot-inherent cost.
Determines a suitable mapping between: Task. Robots.
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: ASyMTRe-D
Problem: Can handle only one task at a time. Each round results in idle robots.
Desired behavior: Need to reduce instances of idle robots. Make idle robots work on other tasks (if any).
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: Combinatorial Auctions
Sequential Auctions.
Parallel Auctions.
Combinatorial Auctions.
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: Combinatorial Auctions
Item 1 Item 4Item 3Item 2 Item 5
Auctioneer
[1,2] [1,3,5] [3,5] [1, 4]
???
???
,[2,5]
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: Combinatorial Auctions
Complexity: A NP-complete problem. Similar to the Partitioning problem → NPC.
Dynamic Programming: Long execution time. Explores the entire solution space. Scales to only a small number of bids.
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: Combinatorial Auctions
Solution: An Anytime tree algorithm. Explores only the relevant solution space. Polynomial in the number of bids submitted.
Intelligent Robotics Lab, Cal Poly Pomona
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Introduction: Combinatorial Auctions
Bids:123451,21,3,51,42,53,5
Root
1,2
3,5 3
4 4
5
1,3,5
4
2
1,4
2,5 2
3 3,5 3
5
1
2,5 2
3 3,5 3
44 4
5
Intelligent Robotics Lab, Cal Poly Pomona
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Quick Review
ASyMTRe-D Drawbacks: Accepts tasks sequentially. Order of task execution determine total execution time. Idle robots are waste of resources.
Need: A task scheduler. Least robot idle-time → maximum utilization of resources.
Inspiration for STA: Combinatorial Auctions.
Intelligent Robotics Lab, Cal Poly Pomona
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Simultaneous Task Allocation (STA)
Task1 Task 2 Task 3
{R1,R2, $3}
R2
R3R1
{R2,R3, $4}
{R3, $5}
{R1,R2, $4}
{R2, $1}
{R3, $3}
{R1,R3, $4}
{R2,R3, $4}
Intelligent Robotics Lab, Cal Poly Pomona
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Simultaneous Task Allocation (STA)
`
Task Bids
1
{R1, R2, $3}
{R2, R3, $4}
{R3, $5}
2
{R1, R2, $4}
{R2, $1}
{R3, $3}
3
{R1, R3, $4}
{R2, R3, $4}
Root
R1, R2
R2, R3
R3
3 4 5 0
R3
6 3 4R1, R2
9
R2
6 5R1, R2
4R2
1R3
3 0
R2, R3
4R1, R3
4R1, R3
5
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Intelligent Robotics Lab, Cal Poly Pomona
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Simultaneous Task Allocation (STA)
Will always return a partial answer if terminated early.
Each path is a set of disjoint coalitions → Partition.
All possible partitions of robots are considered.
Run time complexity depends on: Number of bids submitted. Number of tasks considered.
Intelligent Robotics Lab, Cal Poly Pomona
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Simultaneous Task Allocation (STA)
Task B
Task C
……
Task N
STA Algorithm
Task D
Task E Task F
Task A
Intelligent Robotics Lab, Cal Poly Pomona
ASyMTRe-D equipped…
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Performance (STA)
Test Environment: Dell Inspiron 6400. 1.73 GHz Pentium Dual Core Processors. 2 GB of RAM. Python.
Objective: To measure the execution time of the algorithm For increasing bids. For increasing task sizes.
Intelligent Robotics Lab, Cal Poly Pomona
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Performance (STA)
Random Distribution: Bids accepted → 10 - 100 Task Sizes → 5, 10, 15, 20 Robots → 10 Maximum allowed coalition size → 9
Uniform Distribution: Bids accepted → 10 - 50 Task Sizes → 5, 10, 15, 20 Robots → 10 Maximum allowed coalition size → 3
Intelligent Robotics Lab, Cal Poly Pomona
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Performance (STA)
Random Distribution
Intelligent Robotics Lab, Cal Poly Pomona
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Performance (STA)
Uniform Distribution
Intelligent Robotics Lab, Cal Poly Pomona
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Performance (STA)
Problems: Execution time is exceedingly long. The entire tree is generated irrespective.
Need: Faster execution time. Generate only relevant parts of tree.
Intelligent Robotics Lab, Cal Poly Pomona
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Future Work (STA)
Use heuristics to generate only relevant portions of tree. Iterative Deepening A* (IDA*)
Optimize the current version of the algorithm.
Demonstrate the complete approach using ASyMTRe-D.
Intelligent Robotics Lab, Cal Poly Pomona
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Conclusion (STA)
Multiple tasks are being considered. All possible mapping of tasks to coalitions. No restriction on coalition size.
Reduced overall execution time. STA (Higher level). ASyMTRe-D (Lower level).
An Anytime Algorithm!!
Intelligent Robotics Lab, Cal Poly Pomona
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References Sandholm, T. 1999. Algorithm for Optimal Winner Determination in Combinatorial Auctions,
International Joint Conference on Artificial Intelligence (July). Stockholm, Sweden, 542-547.
Parker, L.E., Tang, F., 2005. ASyMTRe: Automated Synthesis of Multi-Robot Task Solutions through Software Reconfiguration. In Proceedings of IEEE International Conference on Robotics and Automation (April).
Tang, F., Parker, L. E. , 2005. Distributed Multi-Robot Coalitions through ASyMTRe-D. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (August).
Parker, L.E. and Tang, F., 2006. Building Multirobot Coalitions through Automated Task Solution Synthesis. In Proceedings of the IEEE v. 94 No. 7 (July). 1289-1305.
Parker, L.E., Tang, F., 2007. A Complete Methodology for Generating Multi-Robot Task Solutions using ASyMTRe-D and Market-Based Task Allocation. To Appear in the IEEE International Conference on Robotics and Automation (April).
Wikipedia. http://www.wikipedia.org/
Intelligent Robotics Lab, Cal Poly Pomona
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Questions??Intelligent Robotics Lab, Cal Poly Pomona