SAGL: a new heuristic for multi-robot routing with complex tasks

The presentation slides of the paper "Hong Xu, T. K. Satish Kumar, Dylan Johnke, Nora Ayanian, and Sven Koenig. SAGL: a new heuristic for multi-robot routing with complex tasks. In the Proceedings of the 28th IEEE International Conference on Tools with Artificial Intelligence (ICTAI), 530–535. 2016. doi:10.1109/ICTAI.2016.0087."

More details: http://www.hong.me/papers/xu2016a.html
Link to the published paper: https://doi.org/10.1109/ICTAI.2016.0087

Transcript

1. SAGL: A NEW HEURISTIC FOR MULTI-
   ROBOT ROUTING WITH COMPLEX
   TASKS
   Hong Xu*, T. K. Satish Kumar*, Dylan Johnke†,
   Nora Ayanian* and Sven Koenig*
   * University of Southern Calfornia, Los Angeles, CA 90089
   † Cornell University, Ithaca, NY 14853
   ICTAI November 7, 2016
   

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2. AGENDA
   Complex Routing Problem (CRP)
   Our algorithm: SAGL
   Experimental evaluation: SAGL vs others
   

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3. AGENDA
   Complex Routing Problem (CRP)
   Our algorithm: SAGL
   Experimental evaluation: SAGL vs others
   

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4. MOTIVATION
   Search-and-rescue: li ing heavy debris
   (source: https://www.fema.gov/media-
   library/assets/images/100223 )
   

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5. COMPLEX ROUTING PROBLEM (CRP)
   Multiple homogeneous robots
   same moving speed
   same ability to accomplish tasks
   Multiple tasks in different locations
   Some tasks require more than one robots to accomplish
   Cooperative settings
   Solution: Task visitation order for each robot
   Solution evaluation: Makespan (total time required to
   accomplish all tasks)
   

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6. COMPLEX ROUTING PROBLEM EXAMPLE
   Cyan: robots
   Yellow: tasks requiring only 1 robot (simple tasks)
   Red: tasks requiring robots ( ) (complex tasks
   with a complexity level of )
   Reduces to TSP-Path if only one robot and no complex
   tasks.
   N N ≥ 2
   N
   

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7. State-of-the-art: Approach with Reaction Functions (ARF)
   [Zheng et al. '08, '11]
   Based on auction mechanism
   Produces good solution
   Does not scale
   e.g., cannot solve 20 complex tasks with a complexity
   level of 2 within 1 hour
   SAGL
   Produces decent solution
   Polynomial time complexity and scalable
   Can handle high complexity levels and a large
   number of complex tasks
   

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8. AGENDA
   Complex Routing Problem (CRP)
   Our algorithm: SAGL
   Experimental evaluation: SAGL vs others
   

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9. EMBED COMPLEX ROUTING
   PROBLEM INTO A GRAPH
   A
   B
   C
   2
   2
   3
   We embed a problem instance into
   a complete undirected edge-weighted graph
   Vertices represent task and robot initial locations.
   Edges represent distances between the locations.
   

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10. ASSUMPTIONS
    No collisions between robots.
    Distances satisfy the triangle inequality.
    Distances are symmetric.
    All robots move with unit speed.
    All tasks are accomplished immediately once all robots
    arrive—time span required for accomplishing tasks can be
    amortized into the incident edges.
    

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11. SAGL OVERVIEW
    Which robots should visit which tasks
    1. Spanning tree construction
    2. Task assignment
    What visitation order should the robots use
    3. Global visitation order determination for complex tasks
    4. Local visitation order determination
    

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12. WHICH ROBOTS SHOULD VISIT
    WHICH TASKS
    1. Spanning tree construction
    Provides a base for task assignments
    2. Task assignment
    

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13. CONSTRUCT THE SPANNING TREE
    Provides a base for task assignments:
    inspired by 2-approximation TSP
    

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14. CONSTRUCT THE SPANNING TREE
    T
    2
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15. CONSTRUCT THE SPANNING TREE
    T
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16. CONSTRUCT THE SPANNING TREE
    T
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17. CONSTRUCT THE SPANNING TREE
    T
    2
    T
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18. CONSTRUCT THE SPANNING TREE
    T
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19. CONSTRUCT THE SPANNING TREE
    T
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    2
    

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20. CONSTRUCT THE SPANNING TREE
    T
    2
    T
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21. CONSTRUCT THE SPANNING TREE
    T
    2
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22. CONSTRUCT THE SPANNING TREE
    T
    2
    T
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    R
    2
    

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23. CONSTRUCT THE SPANNING TREE
    T
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    2
    

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24. ASSIGN TASKS TO ROBOTS
    According to the distances on the spanning tree.
    

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25. WHAT VISITATION ORDER SHOULD
    THE ROBOTS USE
    1. Global visitation order determination for complex tasks
    Prevent deadlocks
    2. Local visitation order determination
    

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26. DEADLOCKS
    A B
    X Y
    A
    B
    Robot A waits at X forever.
    Robot B waits at Y forever.
    

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27. GLOBAL VISITATION ORDER OF
    COMPLEX TASKS
    Prevent deadlocks
    

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28. LOCAL VISITATION ORDER
    A
    B
    C
    2
    2
    3
    A
    B
    C
    Path-constrained TSP [Bachrach et al. '05]:
    Consistent with the global visitation order
    

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29. AGENDA
    Complex Routing Problem (CRP)
    Our algorithm: SAGL
    Experimental evaluation: SAGL vs others
    

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30. EXPERIMENT SET 1
    Compared with Approach with Reaction Functions (ARF)
    [Zheng et al. '08, '11]
    Map: 51x51 grid office environment
    200 CRP instances with random vertices for
    10 robots
    80 simple tasks
    various numbers of complex tasks with a complexity
    level of 2
    

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31. OFFICE MAP
    image source: [Koenig et al. '07]
    

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32. Percentage of instances solved by ARF within 2 minutes.
    SAGL solved each of them within one second.
    COMPARED WITH ARF: EFFICIENCY
    

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33. COMPARED WITH ARF: MAKESPAN
    

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34. EXPERIMENT SET 2
    Large instances
    ARF cannot solve large instances
    Compared with a baseline algorithm
    No spanning tree
    Random global visitation order
    No use of path-constrained TSP
    Map: obstacle free 300x300 continuous square
    15 CRP instances for random
    5, 8 or 10 robots
    100, 500 or 1000 tasks
    max complexity levels of 2, 3 or 4
    

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35. SAGL VS BASELINE: MAKESPAN VS NUMBER OF TASKS
    

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36. SAGL VS BASELINE: MAKESPAN VS MAXIMUM COMPLEXITY
    LEVELS
    

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37. FUTURE WORK
    Heterogenous robots
    Distributed version
    Flexible complexity levels (task accomplishment time
    depends on number of robots)
    

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38. CONCLUSION
    SAGL is
    A polynomial time solver for the Complex Routing
    Problem
    Four steps:
    1. Spanning tree construction
    2. Task assignment
    3. Global visitation order determination for complex
    tasks
    4. Local visitation order determination
    More scalable than ARF
    decent solution quality
    

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