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.
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Average case constant factor time and distance optimal multi-robot path planning in well-connected environments
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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- NSF-PAR ID:
- 10111596
- Date Published:
- Journal Name:
- Autonomous Robots
- ISSN:
- 0929-5593
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s10514-019-09858-z
