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 is offline Computing is distributed across robots IROS 20102

Multiagent Path Planning 3IROS 2010 Start Goal

Large-Scale Path Planning 4IROS 2010

Large-Scale Path Planning 5IROS 2010

Large-Scale Path Planning 6IROS 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 IROS [Erdman, et al 1987; van den Berg, et al 2005]

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

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

Distributed Prioritized Planning 11IROS 2010 Parallelizable & Equivalent Parallelizable & Equivalent

Distributed Prioritized Planning At each robot: 1. Compute initial path 2. Determine local priority 3. Broadcast path to team 4. Listen for other teammates paths 5. If a higher priority path is received, add as an obstacle in space-time 6. Compute new collision-free path 7. Go to step 3. IROS Equivalent, but n 2 messages!

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(n 2 ) 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(n 2 ) check IROS

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

Sparse DPP Goal: reduce # of messages even more than RDPP  O(n*sqrt(n)) 1. Each robot sends path to k*sqrt(n) random neighbors 2. Each robot checks for conflicts between every combination of paths it receives, then notifies conflicting robots 3. Lower priority robots in the collision re-plan IROS

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

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

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

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

Reduced DPP reduces communication Varying Team Size Varying Density IROS Complete Communication

DPP takes… longer? Varying Team Size Varying Density IROS

Distribution of Planning Times IROS

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

Summary of Results DPP gets same quality solutions as centralized Reduced DPP is 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

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

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 27IROS 2010