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Decentralized prioritized planning in large multirobot teams. Prasanna Velagapudi Paul Scerri Katia Sycara Carnegie Mellon University, Robotics Institute. Motivation. Disaster response, Convoy planning 100s of robots coordinating to plan P lanning is offline
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Decentralized prioritized planning in large multirobot teams Prasanna Velagapudi Paul Scerri Katia Sycara Carnegie Mellon University, Robotics Institute IROS 2010
Motivation • Disaster response, Convoy planning • 100s of robots coordinating to plan • Planning isoffline • Computing is distributed across robots IROS 2010
Multiagent Path Planning Start Goal IROS 2010
Large-Scale Path Planning IROS 2010
Large-Scale Path Planning IROS 2010
Large-Scale Path Planning IROS 2010
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]
Prioritized Planning • Assign priorities to agents based on path length [Erdman, et al 1987; van den Berg, et al 2005] IROS 2010
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
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
Distributed Prioritized Planning Parallelizable & Equivalent IROS 2010
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
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
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
Can we send even less? • Choose num_paths_sent = k* sqrt(n) IROS 2010
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
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
Same near-optimal solutions as PP Varying Team Size Varying Density IROS 2010
Fewer sequential iterations (Iteration limit = 20) Varying Team Size Varying Density IROS 2010
Sparse DPP fails to converge (Complete, Reduced DPP always converged) Varying Team Size Varying Density IROS 2010
Reduced DPP reduces communication Varying Team Size Varying Density Complete Communication IROS 2010
DPP takes… longer? Varying Team Size Varying Density IROS 2010
Distribution of Planning Times IROS 2010
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
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
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
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