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