TY - CHAP

T1 - Motion Planning for Multiple Unit-Ball Robots in$$\mathbb {R}^{{\varvec{d}}}$$

AU - Solomon, Israela

AU - Halperin, Dan

N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020

Y1 - 2020

N2 - We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in, for any. We assume that the robots have revolving areas in the vicinity of their start and target positions: Revolving areas are regions where robots can maneuver in order to give way to another moving robot. Given that this assumption is fulfilled, the algorithm is complete, namely it is guaranteed to find a solution or report that none exists. A key goal in our design is to make the revolving areas as economical as possible and in particular to allow different revolving areas to overlap. This makes the analysis rather involved but in return makes the algorithm conceptually fairly simple. We show that for the case of m unit-discs moving among polygonal obstacles of total complexity n in, the algorithm can be executed in time. We implemented the algorithm for this case and tested it on several scenarios, for which we show experimental results for up to 1000 robots. Finally, we address the problem of choosing the order of execution of the paths in decoupled algorithms that locally solve interferences and show that finding the optimal order of execution is NP-hard. This motivated us to develop a heuristic for choosing the order; we describe the heuristic and demonstrate its effectiveness in certain scenarios.

AB - We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in, for any. We assume that the robots have revolving areas in the vicinity of their start and target positions: Revolving areas are regions where robots can maneuver in order to give way to another moving robot. Given that this assumption is fulfilled, the algorithm is complete, namely it is guaranteed to find a solution or report that none exists. A key goal in our design is to make the revolving areas as economical as possible and in particular to allow different revolving areas to overlap. This makes the analysis rather involved but in return makes the algorithm conceptually fairly simple. We show that for the case of m unit-discs moving among polygonal obstacles of total complexity n in, the algorithm can be executed in time. We implemented the algorithm for this case and tested it on several scenarios, for which we show experimental results for up to 1000 robots. Finally, we address the problem of choosing the order of execution of the paths in decoupled algorithms that locally solve interferences and show that finding the optimal order of execution is NP-hard. This motivated us to develop a heuristic for choosing the order; we describe the heuristic and demonstrate its effectiveness in certain scenarios.

UR - http://www.scopus.com/inward/record.url?scp=85107077978&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-44051-0_46

DO - 10.1007/978-3-030-44051-0_46

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AN - SCOPUS:85107077978

T3 - Springer Proceedings in Advanced Robotics

SP - 799

EP - 816

BT - Springer Proceedings in Advanced Robotics

PB - Springer Science and Business Media B.V.

ER -