Optimal Multirobot Path Planning on Graphs: Complete Algorithms and Effective Heuristics

We study optimal multirobot path planning on graphs (MPP) over four minimization objectives: the makespan (last arrival time), the maximum (single-robot traveled) distance, the total arrival time, and the total distance. Having established previously that these objectives are distinct and NP-hard to...

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Bibliographic Details
Published in:IEEE transactions on robotics Vol. 32; no. 5; pp. 1163 - 1177
Main Authors: Jingjin Yu, LaValle, Steven M.
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Collision avoidance
Games
Heuristic
Heuristic algorithms
Linear programming
Path planning
Robot kinematics
Robots
ISSN:1552-3098, 1941-0468
Online Access:Get full text
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Summary:We study optimal multirobot path planning on graphs (MPP) over four minimization objectives: the makespan (last arrival time), the maximum (single-robot traveled) distance, the total arrival time, and the total distance. Having established previously that these objectives are distinct and NP-hard to optimize, in this paper, we focus on efficient algorithmic solutions for solving these optimal MPP problems. Toward this goal, we first establish a one-to-one solution mapping between MPP and a special type of multiflow network. Based on this equivalence and integer linear programming (ILP), we design novel and complete algorithms for optimizing over each of the four objectives. In particular, our exact algorithm for computing optimal makespan solutions is a first that is capable of solving extremely challenging problems with robot-vertex ratios as high as 100%. Then, we further improve the computational performance of these exact algorithms through the introduction of principled heuristics, at the expense of slight optimality loss. The combination of ILP model based algorithms and the heuristics proves to be highly effective, allowing the computation of 1.x-optimal solutions for problems containing hundreds of robots, densely populated in the environment, often in just seconds.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2016.2593448