TY - GEN

T1 - Unlabeled Multi-Robot Motion Planning with Tighter Separation Bounds

AU - Banyassady, Bahareh

AU - de Berg, Mark

AU - Bringmann, Karl

AU - Buchin, Kevin

AU - Fernau, Henning

AU - Halperin, Dan

AU - Kostitsyna, Irina

AU - Okamoto, Yoshio

AU - Slot, Stijn

N1 - Publisher Copyright:
© Bahareh Banyassady, Mark de Berg, Karl Bringmann, Kevin Buchin, Henning Fernau, Dan Halperin, Irina Kostitsyna, Yoshio Okamoto, and Stijn Slot; licensed under Creative Commons License CC-BY 4.0

PY - 2022/6/1

Y1 - 2022/6/1

N2 - We consider the unlabeled motion-planning problem of m unit-disc robots moving in a simple polygonal workspace of n edges. The goal is to find a motion plan that moves the robots to a given set of m target positions. For the unlabeled variant, it does not matter which robot reaches which target position as long as all target positions are occupied in the end. If the workspace has narrow passages such that the robots cannot fit through them, then the free configuration space, representing all possible unobstructed positions of the robots, will consist of multiple connected components. Even if in each component of the free space the number of targets matches the number of start positions, the motion-planning problem does not always have a solution when the robots and their targets are positioned very densely. In this paper, we prove tight bounds on how much separation between start and target positions is necessary to always guarantee a solution. Moreover, we describe an algorithm that always finds a solution in time O(n log n + mn + m2) if the separation bounds are met. Specifically, we prove that the following separation is sufficient: any two start positions are at least distance 4 apart, any two target positions are at least distance 4 apart, and any pair of a start and a target positions is at least distance 3 apart. We further show that when the free space consists of a single connected component, the separation between start and target positions is not necessary.

AB - We consider the unlabeled motion-planning problem of m unit-disc robots moving in a simple polygonal workspace of n edges. The goal is to find a motion plan that moves the robots to a given set of m target positions. For the unlabeled variant, it does not matter which robot reaches which target position as long as all target positions are occupied in the end. If the workspace has narrow passages such that the robots cannot fit through them, then the free configuration space, representing all possible unobstructed positions of the robots, will consist of multiple connected components. Even if in each component of the free space the number of targets matches the number of start positions, the motion-planning problem does not always have a solution when the robots and their targets are positioned very densely. In this paper, we prove tight bounds on how much separation between start and target positions is necessary to always guarantee a solution. Moreover, we describe an algorithm that always finds a solution in time O(n log n + mn + m2) if the separation bounds are met. Specifically, we prove that the following separation is sufficient: any two start positions are at least distance 4 apart, any two target positions are at least distance 4 apart, and any pair of a start and a target positions is at least distance 3 apart. We further show that when the free space consists of a single connected component, the separation between start and target positions is not necessary.

KW - computational geometry

KW - motion planning

KW - simple polygon

UR - http://www.scopus.com/inward/record.url?scp=85134297628&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.SoCG.2022.12

DO - 10.4230/LIPIcs.SoCG.2022.12

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AN - SCOPUS:85134297628

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 38th International Symposium on Computational Geometry, SoCG 2022

A2 - Goaoc, Xavier

A2 - Kerber, Michael

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 38th International Symposium on Computational Geometry, SoCG 2022

Y2 - 7 June 2022 through 10 June 2022

ER -