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Fast algorithms for optimal multi-robot path planning are sought after in real-world applications. Known methods, however, generally do not simultaneously guar- antee good solution optimality and good (e.g., polynomial) running time. In this work, we develop a first low-polynomial running time algorithm, called SplitAndGroup (SaG), that solves the multi-robot path planning problem on grids and grid-like environments, and produces constant factor makespan optimal solutions on average over all problem in- stances. That is, SaG is an average case O(1)-approximation algorithm and computes solutions with sub-linear makespan. SaG is capable of handling cases when the density of robots is extremely high - in a graph-theoretic setting, the al- gorithm supports cases where all vertices of the underly- ing graph are occupied. SaG attains its desirable proper- ties through a careful combination of a novel divide-and- conquer technique, which we denote as global decoupling, and network flow based methods for routing the robots. Solutions from SaG, in a weaker sense, are also a constant factor approximation on total distance optimality.
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SEAR: A Polynomial-Time Multi-Robot Path Planning Algorithm with Expected Constant-Factor Optimality Guarantee
We study the labeled multi-robot path planning problem in continuous 2D and 3D domains in the absence of obstacles where robots must not collide with each other. For an arbitrary number of robots in arbitrary initial and goal arrangements, we derive a polynomial time, complete algorithm that produces solutions with constant-factor optimality guarantees on both makespan and distance optimality, in expectation, under the assumption that the robot labels are uniformly randomly distributed. Our algorithm only requires a small constant-factor expansion of the initial and goal configuration footprints for solving the problem, i.e., the problem can be solved in a fairly small bounded region. Beside theoretical guarantees, we present a thorough computational evaluation of the proposed solution. In addition to the baseline implementation, adapting an effective (but non-polynomial time) routing subroutine, we also provide a highly efficient implementation that quickly computes near-optimal solutions. Hardware experiments on the microMVP platform composed of non-holonomic robots confirms the practical applicability of our algorithmic pipeline.
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- Award ID(s):
- 1734419
- PAR ID:
- 10071651
- Date Published:
- Journal Name:
- 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Fast algorithms for optimal multi-robot path planning are sought after in both research and real-world applications. Known methods, however, generally do not simultaneously guarantee good solution optimality and fast run time for difficult instances. In this work, we develop a low-polynomial running time algorithm, called SplitAndGroup, that solves the multi-robot path planning problem on grids and grid-like environments, and produces constant factor time- and distance-optimal solutions, in expectation. In particular, SplitAndGroup computes solutions with sub-linear makespan. SplitAndGroup is capable of handling cases when the density of robot is extremely high - in a graph-theoretic setting, the algorithm supports cases where all vertices of the underlying graph are occupied by robots. SplitAndGroup attains its desirable properties through a careful combination of divide-and-conquer technique and network flow based methods for routing the robots.more » « less
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