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

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.

Keywords:

• Approximation algorithms
• Robot motion planning
• Rod robot
• d ₁-optimal motion

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).