Decentralized prioritized planning in large multirobot teams

1. Decentralized prioritized planning in large multirobot teams Prasanna Velagapudi Paul Scerri Katia Sycara Carnegie Mellon University, Robotics Institute IROS 2010

2. Motivation • Disaster response, Convoy planning • 100s of robots coordinating to plan • Planning isoffline • Computing is distributed across robots IROS 2010

3. Multiagent Path Planning Start Goal IROS 2010

4. Large-Scale Path Planning IROS 2010

5. Large-Scale Path Planning IROS 2010

6. Large-Scale Path Planning IROS 2010

7. Multiagent Path Planning • Many, many approaches: offline fewer robots • Take a simple, decoupled approach, prioritized planning • [Erdman 1987], [van den Berg 2005] • Try parallelization + scale up, see what happens • Large teams, fast convergence, low communication • Similar to some reactive/online approaches • [Chun 1999], [Clark 2003], [Chiddawar 2009]

8. Prioritized Planning • Assign priorities to agents based on path length [Erdman, et al 1987; van den Berg, et al 2005] IROS 2010

9. Prioritized Planning • Plan from highest priority to lowest priority • Use previous agents as dynamic obstacles Effective, but requires n sequential planning steps [Erdman, et al 1987; van den Berg, et al 2005] IROS 2010

10. Can we do better? • Each agent has local computing anyway • Let agents try to plan instead of doing nothing • Maybe we’ll need to re-plan • If we don’t re-plan, we have saved time • Hypothesis: Agents only actually collide with few other agents, so sequential iterations << n IROS 2010

11. Distributed Prioritized Planning Parallelizable & Equivalent IROS 2010

12. Distributed Prioritized Planning • At each robot: • Compute initial path • Determine local priority • Broadcast path to team • Listen for other teammates paths • If a higher priority path is received, add as an obstacle in space-time • Compute new collision-free path • Go to step 3. Equivalent, but n2 messages! IROS 2010

13. Reduced DPP • DPP requires broadcasting messages to every teammate every time agents replan • Reduce this with two assumptions • If you didn’t hear from someone, they didn’t change their plan • If someone is higher priority, they don’t care what you do, so don’t send them anything Better, but still O(n2) messages

14. Can we send even less? • Birthday Paradox • If everybody in a room compares birthdays, chances of two people having the same birthday grows quickly as number of people grows • Collision communications • If everybody in the team compares a few other agents’ paths, the chance of detecting a collision between anybody grows quickly as number of paths compared increases • Each agent is doing a small O(n2) check IROS 2010

15. Can we send even less? • Choose num_paths_sent = k* sqrt(n) IROS 2010

16. Sparse DPP • Goal: reduce # of messages even more than RDPP O(n*sqrt(n)) • Each robot sends path to k*sqrt(n) random neighbors • Each robot checks for conflicts between every combination of paths it receives, then notifies conflicting robots • Lower priority robots in the collision re-plan IROS 2010

17. Experimental Results • Scaling Dataset • # robots varied: {40, 60, 80, 120, 160, 240} • Density of map constant: 8 cells per robot • Density Dataset • # robots constant: 240 • Density of map varied: {32, 24, 16, 12, 8} cells per robot • Cellular automata to generate 15 random maps • Maps solved with centralized prioritized planning • DPP variants capped at 20 iterations • Local planner: A* IROS 2010

18. Same near-optimal solutions as PP Varying Team Size Varying Density IROS 2010

19. Fewer sequential iterations (Iteration limit = 20) Varying Team Size Varying Density IROS 2010

20. Sparse DPP fails to converge (Complete, Reduced DPP always converged) Varying Team Size Varying Density IROS 2010

21. Reduced DPP reduces communication Varying Team Size Varying Density Complete Communication IROS 2010

22. DPP takes… longer? Varying Team Size Varying Density IROS 2010

23. Distribution of Planning Times IROS 2010

24. Replanning for the Worst Agent • Prioritized Planning • DPP Longest planning agents might replan multiple times A A B B C C Individual agent planning times varied by >2 orders of magnitude D D Potential solution: Incremental Planning IROS 2010

25. Summary of Results • DPP gets same quality solutions as centralized • Reduced DPPis efficient • Many fewer sequential steps, messages • Longer wall-clock time (due to uneven planning times) • Sparse DPP does surprisingly poorly overall • Detecting collisions alone(reactive) leads to slower convergence, more re-planning • Better to exchange relevant paths (proactive) • In Reduced DPP, agents preemptively discover conflicts before collisions occur IROS 2010

26. Conclusions • DPP shows promise for larger problems with distributed computing • Far fewer sequential planning iterations • Incremental planning should reduce execution time • However, there are some caveats • Sensitive to collision detection • If distribution of planning times varies, can be slow IROS 2010

27. Future Work • Generalizing framework for distributed planning through iterative message exchange • Asynchronous collision-detection, re-planning • Reducing necessary communication • Planning under uncertainty • Scaling to larger team sizes IROS 2010