IROS 2010
Decentralized prioritized planning in large multirobot teams
Prasanna VelagapudiPaul Scerri
Katia Sycara
Carnegie Mellon University, Robotics Institute
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Motivation
• Disaster response, Convoy planning
• 100s of robots coordinating to plan
• Planning is offline• Computing is
distributed across robots
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Multiagent Path Planning
Start
Goal
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Large-Scale Path Planning
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Large-Scale Path Planning
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Large-Scale Path Planning
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]
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Prioritized Planning
• Assign priorities to agents based on path length
[Erdman, et al 1987; van den Berg, et al 2005]
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Prioritized Planning
• Plan from highest priority to lowest priority• Use previous agents as dynamic obstacles
[Erdman, et al 1987; van den Berg, et al 2005]
Effective, but requiresn sequential planning steps
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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
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Distributed Prioritized Planning
Parallelizable& Equivalent
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Distributed Prioritized Planning
• At each robot:1. Compute initial path2. Determine local priority3. Broadcast path to team4. Listen for other teammates paths5. If a higher priority path is received, add as an obstacle in
space-time6. Compute new collision-free path7. Go to step 3.
Equivalent, but n2 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(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
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Can we send even less?
• Choose num_paths_sent = k * sqrt(n)
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Sparse DPP
• Goal: reduce # of messages even more than RDPP O(n*sqrt(n))1. Each robot sends path to k*sqrt(n) random neighbors2. 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
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*
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Same near-optimal solutions as PP
Varying Team Size Varying Density
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Fewer sequential iterations (Iteration limit = 20)
Varying Team Size Varying Density
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Sparse DPP fails to converge (Complete, Reduced DPP always converged)
Varying Team Size Varying Density
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Reduced DPP reduces communication
Varying Team Size Varying Density
Complete Communication
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DPP takes… longer?
Varying Team Size Varying Density
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Distribution of Planning Times
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• Prioritized Planning
• DPP
Replanning for the Worst Agent
ABCD
ABCD
Longest planning agents might replan multiple times
Individual agent planning times varied by >2 orders of magnitude
Potential solution:Incremental Planning
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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
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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
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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