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VISHNU R . DESARAJU AND JONATHAN P . HOW

DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

ICRA 2011

AUTONOMOUS ROBOTS 2012

PRESENTED BY: RAJ DASGUPTA

Decentralized Path Planning for Multi-Agent Teams in Complex Environments using Rapidly-exploring Random Trees

Overview

� Path planning in multi-robot (agent) system

� Sampling-based planner

� New algorithm called DMA-RRT proposed

� Includes coordination strategy based on token ring passing between robots

� Extension to basic algorithm called Cooperative DMA-RRT allows agents to update each other’s plans

� Verified experimentally through simulations and on iRobot Create platform

2/4/2013CMANTIC Lab Reading Group: Raj Dasgupta

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Problem Addressed

� Plan a collision free path for multiple agents

� Constraints

� Complex environment

� Agents (called a team) should not collide with each other

� Static or linear paths cannot be used - requires paths to be dynamically updated

� Centralized planning cannot be used


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Related Work: Robot Path Planning

� Dynamic path planning using constraint solvers scale poorly in number of constraints

� Mixed Integer Linear Programming (MILP)

� Model Predictive Control (MPC)

� Potential field based planning – works for simple environments only

� Sampling-based methods

� Probabilistic Roadmap Planners (PRM)

� Rapidly-exploring Random Trees (RRT)

� Extension called closed loop RRT (CL-RRT) used as basis of work


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Related Work: Robot Coordination

� Agents must reach consensus on updated path before moving (Scerri et al.)� Synchronization of plans causes delay

� Agents reserve regions of map that they will move into and must reach consensus about changes to those regions (Purvin et al.)� Asynchronous planning allowed, but some tradeoff due to working with large areas instead of paths

� Reachability-based collision avoidance considers non-cooperating agents (worst case scenario)

� Decentralized MPC (Trodden and Richards): Agents allowed to update plans sequentially in pre-determined order - solves synchronization issues; fixed order makes it inefficient


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CL-RRT Algorithm


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� Generates a set of feasible paths � Satisfying current path constraints

� Selects least cost path from set

� Not guaranteed to be optimal

� Fast (faster than comparable path planner RRT*)

� Verified successfully on robots in DARPA Grand Challenge 2007

� Three phases� Tree expansion

� Execution loop

� Lazy check for feasibility

CL-RRT Algorithm


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Multi-agent CL-RRT

� Naïve approach: Every agent plans its path subject to constraints imposed by other agents� Problem: Inefficiency

� A1 calculates its plan and sends to A2 as set of constraints

� A2 starts calculating its plan using A1’s constraints

� A1 updates its plan and corresponding set of constraints

� A2 finishes plan with old set of A1’s constraints; sees A1 has new constraints; replans…

� More complicated and inefficient with more agents

� CL-RRT can fail (cause collisions) when used by multiple agents with inter-dependent path constraints plan simultaneously

� Needs coordination protocol


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Coordination Protocol: Merit-based Token Passing

� Basis: (Trodden and Richards, ACC 2006)� Sequential order imposed among agents � In each iteration only one agent can update its plan

� Merit-based Token Passing� Remove sequential order by introducing a token� Agent that has token can update its plan� Each agent without token calculates metric called Potential Path Improvement (PPI) � PPI = difference in cost between best path in RRT and current path

� Broadcasts PPI to all other agents� In next round token goes to agent with highest PPI from last round; ties broken at random

� Advantages: � Agent that benefits most from re-planning is given next chance to replan� Agents that can quickly find path to goal get token first without waiting in a sequential order


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Decentralized Multi-Agent (DMA) RRT


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DMA-RRT: Path Constraint Satisfaction

Main idea: DMA-RRT does not introduce any new path conflicts; proven by induction


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DMA-RRT: Merit-based token passing


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DMA-RRT vs. Cooperative DMA-RRT


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Cooperative DMA-RRT Algorithm: 1


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Cooperative DMA-RRT Algorithm: 2


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Experimental Results

� Simulations:

� Each agent simulated on 1 desktop (2.13 GHz, 1 GB RAM)

� 10 desktops connected by LAN

� Two wheel skid steer robot model

� Path cost=Travel time along path

� Physical robot experiments

� iRobot Create

� Pure pursuit controller used to determine robot velocity


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Simulation Results: Open Map, 10 Agents

� No obstacle environment with 10 goals (waypoints)

� Agents cycle through goals for 10 mins (results avg. over 12 trials)

� Fig. 2(b) shows agent 1’s view of other agents trajectories (obstacles) with round robin sched.

� Legends:� Blue circle/red arrow : agent 1� Yellow circle/blue arrow: other agents� Magenta dots: waypoints for agent 1’s path

� Red: current position of other agent� Green: future position (+10 sec.) other agent

� Red-green: time parameterized obstacles presented by other agents’ paths

Round-robin scheduling: 12.5 goals/agent in 10 mins.Merit-based scheduling: 15.1 goals /agent in 10 minsImprovement because agent that finds a shorter (better) path to goal does not have to wait for all other agents to finish their turn before it gets token and can replan2/4/2013CMANTIC Lab Reading Group: Raj Dasgupta

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Simulation Results: Open Map – Replan Times

� Round-robin gives regular replan start times (uniformly spaced dots in Fig. 3 (a))

� Merit-based gives task-driven replan start times (non-uniformly spaced dots in Fig. 3 (b))


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Experiment 2: 4 agents with obstacles

� Sim. Time: 10 mins� Round robin: 11.9 goals/agent (in 10 mins)

� Merit-based: 11.9 goals/agent (in 10 mins)� Too few agents, little delay in getting token – same wait time as round robin

� Cooperative: � Stop nodes every 4 sec. along trajectory

� 13.0 goals/agent� Emergency stops at or near openings of narrow passage between obstacles – helps agents replan

� Cooperation strategy prevents other agents from blocking path found by an agent through narrow passages


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Experiment 3: Open map, physical robots


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Experiment 4: Emergency Stop with Cooperative DMA-RRT


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Experiment 3: Collision Avoidance

� 5 min run on open map� Minimum inter-agent separation allowed = 0.3 m� Satisfied by both algorithms as per Tables I and II

� Implies both algorithms achieve collision avoidance


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Conclusion

� Main contribution: Merit-based token passing integrated with CL-RRT planner

� Future work

� Communication (range) constraints

� Dynamic obstacles

� Larger simulations/experiments


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decentralized path planning for multi-agent teams in ... filevishnu r. desarajuand jonathan p. how...

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