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
2. AGENDA Complex Routing Problem (CRP) Our algorithm: SAGL Experimental evaluation: SAGL vs others
3. AGENDA Complex Routing Problem (CRP) Our algorithm: SAGL Experimental evaluation: SAGL vs others
4. MOTIVATION Search-and-rescue: li ing heavy debris (source: https://www.fema.gov/media- library/assets/images/100223 )
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)
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
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
8. AGENDA Complex Routing Problem (CRP) Our algorithm: SAGL Experimental evaluation: SAGL vs others
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.
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.
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
12. WHICH ROBOTS SHOULD VISIT WHICH TASKS 1. Spanning tree construction Provides a base for task assignments 2. Task assignment
13. CONSTRUCT THE SPANNING TREE Provides a base for task assignments: inspired by 2-approximation TSP
14. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
15. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
16. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
17. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
18. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
19. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
20. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
21. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
22. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
23. CONSTRUCT THE SPANNING TREE T 2 T 1 R 1 R 2
24. ASSIGN TASKS TO ROBOTS According to the distances on the spanning tree.
25. WHAT VISITATION ORDER SHOULD THE ROBOTS USE 1. Global visitation order determination for complex tasks Prevent deadlocks 2. Local visitation order determination
26. DEADLOCKS A B X Y A B Robot A waits at X forever. Robot B waits at Y forever.
27. GLOBAL VISITATION ORDER OF COMPLEX TASKS Prevent deadlocks
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
29. AGENDA Complex Routing Problem (CRP) Our algorithm: SAGL Experimental evaluation: SAGL vs others
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
31. OFFICE MAP image source: [Koenig et al. '07]
32. Percentage of instances solved by ARF within 2 minutes. SAGL solved each of them within one second. COMPARED WITH ARF: EFFICIENCY
33. COMPARED WITH ARF: MAKESPAN
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
35. SAGL VS BASELINE: MAKESPAN VS NUMBER OF TASKS
36. SAGL VS BASELINE: MAKESPAN VS MAXIMUM COMPLEXITY LEVELS
37. FUTURE WORK Heterogenous robots Distributed version Flexible complexity levels (task accomplishment time depends on number of robots)
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