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Original Articles

An approximation algorithm for d1-optimal motion of a rod robot with fixed rotations

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Pages 357-370 | Received 01 Nov 2004, Accepted 01 Jun 2006, Published online: 17 Feb 2007
 

Abstract

Given a translating and rotating rod robot in a plane in the presence of polygonal obstacles with the initial and final placements of the rod known, the d 1-optimal motion planning problem is defined as finding a collision-free motion of the rod such that the orbit length of a fixed but arbitrary point F on the rod is minimized. In this paper we study a special case of this problem in which the rod can translate freely, but can only rotate by some pre-specified given angles around F. We first characterize the d 1-optimal motion of the robot under the given conditions and then present a (1 + ε)–approximation algorithm for finding the optimal path. The running time of the algorithm is bounded by a polynomial in terms of some parameters related to the problem input.

Acknowledgements

The authors wish to thank the anonymous referees for many useful comments.

Additional information

Notes on contributors

Mohammad Ghodsi

This author's work was partially supported by a grant from IPM school of CS (No. CS1384-2-01).

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