Dan Halperin

k-color multi-robot motion planning

We present a simple and natural extension of the multi-robot motion planning problem where the robots are partitioned into groups (colors), such that in each group the robots are interchangeable. Every robot is no longer required to move to a specific target, but rather to some target placement that is assigned to its group. We call this problem k-color multi-robot motion planning and provide a sampling-based algorithm specifically designed for solving it. At the heart of the algorithm is a novel technique where the k-color problem is reduced to several discrete multi-robot motion planning problems. These reductions amplify basic samples into massive collections of free placements and paths for the robots. We demonstrate the performance of the algorithm by an implementation for the case of disc robots and polygonal robots translating in the plane. We show that the algorithm successfully and efficiently copes with a variety of challenging scenarios, involving many robots, while a simplified version of this algorithm, that can be viewed as an extension of a prevalent sampling-based algorithm for the k-color case, fails even on simple scenarios. Interestingly, our algorithm outperforms a well established implementation of PRM for the standard multi-robot problem, in which each robot has a distinct color.

On the hardness of unlabeled multi-robot motion planning

In unlabeled multi-robot motion planning, several interchangeable robots operate in a common workspace. The goal is to move the robots to a set of target positions such that each position will be occupied by some robot. In this paper, we study this problem for the specific case of unit-square robots moving amidst polygonal obstacles and show that it is PSPACE-hard. We also consider three additional variants of this problem and show that they are all PSPACE-hard as well. To the best of our knowledge, this is the first hardness proof for the unlabeled case. Furthermore, our proofs can be used to show that the labeled variant (where each robot is assigned a specific target position), again, for unit-square robots, is PSPACE-hard as well, which sets another precedent, as previous hardness results require the robots to be of different shapes (or at least in different orientations). Lastly, we settle an open problem regarding the complexity of the well-known Rush-Hour puzzle for unit-square cars in environments with polygonal obstacles.

Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time

Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons

tilde{O}(m^4+m^2n^2)

Finding a needle in an exponential haystack

, where

New perspective on sampling-based motion planning via random geometric graphs

m

Effective Metrics for Multi-Robot Motion-Planning

is the number of robots and

Sampling-Based Bottleneck Pathfinding with Applications to Fréchet Matching.

n

Effective metrics for multi-robot motion-planning

is the total complexity of the workspace. Moreover, the total length of the returned solution is at most

Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multi-robot motion planning

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