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Simultaneous Task Allocation for Multi-Robot systems using ASyMTRe-D

Simultaneous Task Allocation for Multi-Robot systems using ASyMTRe-D

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  • 1. A Simultaneous Task Allocation Algorithm for Multi-Robot systems using ASyMTRe-D
    Spondon Saha
    Fall 2010
    Masters Thesis Presentation
    Department of Computer Science
    Cal Poly Pomona.
  • 2. Outline
    Introduction
    ASyMTRe-D
    Combinatorial Auctions
    The Simultaneous Task Allocation (STA) algorithm
    The A* enhancement
    The IDA* enhancement
    Simulation Setup
    Performance Metrics
    Time Complexity
    Space Complexity
    Future Work
    Conclusion
    Q&A
    2
  • 3. Introduction: ASyMTRe-D
    Automated Synthesis of Multi-robot Task solutions through software Reconfiguration.
    ASyMTRe:
    determines a coalition of robots to accomplish a multi-robot task.
    uses schema theory to determine a robot coalition.
    robot teams can be heterogeneous in nature.
    3
  • 4. 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.
    4
  • 5. Introduction: ASyMTRe-D
    ASyMTRe
    Centralized algorithm.
    Has full information regarding all robots and task parameters.
    Suffers from single point of failure.
    ASyMTRe-D
    Distributed ASyMTRe.
    Runs locally on each robot.
    Uses a group negotiation process to determine coalitions.
    Uses the Contract Net Protocol (CNP) for negotiation.
    Does not have all the information for creating optimal solutions.
    5
  • 6. Introduction: ASyMTRe-D
    R1
    Multi-robot Task
    Idle Robots
    R5
    R2
    R4
    R3
    6
  • 7. Introduction: ASyMTRe-D
    ASyMTRe-D takes into account:
    Task-Specific cost.
    Robot-inherent cost.
    Determines a suitable mapping between
    Tasks.
    Robots.
    7
  • 8. 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).
    Instantaneously allocate multiple tasks to different coalitions.
    8
  • 9. Introduction: ASyMTRe-D
    Proposed approach
    9
  • 10. Introduction: Combinatorial Auctions
    Sequential Auctions.
    Parallel Auctions.
    Combinatorial Auctions.
    10
  • 11. Introduction: Combinatorial Auctions
    Auctioneer
    ???
    ???
    Item 1
    Item 4
    Item 3
    Item 2
    Item 5
    [3,5]
    [1,2]
    [1,3,5]
    [1, 4]
    ,[2,5]
    11
  • 12. Introduction: Combinatorial Auctions
    Complexity:
    A NP-Hard 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.
    12
  • 13. Introduction: Combinatorial Auctions
    Solution:
    An Anytime tree algorithm.
    Explores only the relevant solution space of submitted bids.
    Polynomial in the number of bids submitted.
    13
  • 14. Introduction: Combinatorial Auctions
    Bids:
    1
    2
    3
    4
    5
    1,2
    1,3,5
    1,4
    2,5
    3,5
    Root
    1,2
    1,3,5
    1,4
    1
    3,5
    3
    2
    2,5
    2
    2,5
    2
    4
    4
    4
    3
    3,5
    3
    3
    3,5
    3
    5
    5
    4
    4
    4
    5
    14
  • 15. Quick Review
    ASyMTRe-D Drawbacks:
    Can accomplish tasks sequentially.
    Idle robots are waste of resources.
    Need:
    A task scheduler or an instantaneous task allocation system.
    Least robot idle-time -> maximum utilization of resources.
    Inspiration for STA:
    Combinatorial Auctions.
    15
  • 16. Simultaneous Task Allocation (STA)
    {R3, $5}
    {R3, $3}
    {R2,R3, $4}
    {R2, $1}
    {R2,R3, $4}
    {R1,R2, $3}
    {R1,R2, $4}
    {R1,R3, $4}
    Task1
    Task2
    Task 3
    R1
    R2
    R3
    16
  • 17. Simultaneous Task Allocation (STA)
    `
    Root
    3
    4
    5
    0
    R1, R2
    R2, R3
    R3
    6
    9
    6
    5
    4
    1
    3
    3
    4
    0
    R3
    R1, R2
    R2
    R1, R2
    R2
    R3
    4
    4
    5
    R2, R3
    R1, R3
    R1, R3
    17
  • 18. Simultaneous Task Allocation (STA)
    Anytime property:
    Will return a suboptimal solution if terminated early.
    If given enough time, will always return an optimal solution.
    Each path is a set of disjoint coalitions -> Partition.
    All possible partitions of robots are considered.
    Only relevant solution space of submitted bids are considered.
    Run time complexity depends on:
    Number of bids submitted.
    Number of tasks considered.
    18
  • 19. Simultaneous Task Allocation (STA)
    Task B
    Task C
    ……
    Task N
    Task D
    Task E
    Task F
    Task A
    STA Algorithm
    ASyMTRe-D equipped…
























    19
  • 20. Simultaneous Task Allocation (STA)
    Problems:
    Execution time is exceedingly long.
    The entire tree is generated irrespective.
    Need:
    Faster execution time.
    Generate only relevant parts of tree.
    20
  • 21. STA – A*
    The A* variant
    Uses an admissible heuristic to generate only parts of the tree.
    Heuristic determines which path holds the highest probability of containing the winning coalitions.
    21
  • 22. STA – A*
    `
    Root
    9
    4
    20
    8
    R1, R2
    R2, R3
    R3
    14
    11
    5
    R3
    R1, R2
    R2
    R1, R2
    R2
    R3
    R2, R3
    R1, R3
    R1, R3
    22
  • 23. STA – IDA*
    The IDA* variant:
    Execution time comparable to A*
    Does not store all nodes in previous state in memory
    Less memory footprint.
    Should ace in space complexity.
    Optimal STA algorithm variant.
    23
  • 24. STA – BFS, A* and IDA*
    The BFS variant generates the entire tree
    A* variant only generates parts of the tree that holds a high probability of containing winning coalitions.
    IDA* variant does the same as A*, but consumes less memory and is as fast as A*.
    24
  • 25. Simulation Setup
    Test Environment:
    CPP’s “Garrison” and “Fluffy” servers.
    3.16 GHz Intel Xeon Octa-Core Processors.
    8 GB of RAM.
    Implementation in Python.
    Objective:
    To measure the execution time of the algorithm and its variants.
    To measure the space complexity of each of the variants and compare them.
    Parameters for testing:
    For increasing bids.
    For increasing task sizes.
    25
  • 26. Simulation Setup
    Random Distribution:
    Task Sizes -> 20, 40, 60, 80, 100
    Robots -> 10
    Coalition sizes range from -> 1 to 9
    Uniform Distribution:
    Task Sizes -> 20, 40, 60, 80, 100
    Robots -> 10
    Maximum allowed coalition size -> 3
    Bounded Distribution:
    Task Sizes -> 20, 40, 60, 80, 100
    Robots -> 10
    Coalition sizes range from -> 3 to 6
    26
  • 27. Simulation Setup
    27
  • 28. Simulation Setup
    28
  • 29. Performance (Time Complexity)
    Random Distribution (80 Tasks)
    29
  • 30. Performance (Time Complexity)
    Uniform Distribution (80 Tasks)
    30
  • 31. Performance (Time Complexity)
    Bounded Distribution (80 Tasks)
    31
  • 32. Performance (Space Complexity)
    Random Distribution (80 Tasks)
    32
  • 33. Performance (Space Complexity)
    Uniform Distribution (80 Tasks)
    33
  • 34. Performance (Space Complexity)
    Bounded Distribution (80 Tasks)
    34
  • 35. Future Work
    Demonstrate the complete approach using ASyMTRe-D.
    Treasure Hunt Mission
    Site-clearing Mission
    Create a distributed variant of the STA algorithm
    Load-balance work load
    Fault-tolerance
    Problem: Could return suboptimal solutions
    35
  • 36. Conclusion
    Multiple tasks are being considered.
    All possible mapping of tasks to coalitions.
    No restriction on coalition size.
    Instantaneous allocation of multiple tasks.
    STA (Higher level).
    ASyMTRe-D (Lower level).
    An Anytime Algorithm.
    36
  • 37. Q & A
    37