A new approach to optimal planning of robot motion on a tree with obstacles

Abstract

In this paper we study the Graph Motion Planning of 1 Robot problem (GMP1R) on a tree. This problem consists in computing a minimum cost plan for moving a robot from one vertex to another in a tree whose vertices can have movable obstacles. Papadimitriou et alt. [FOCS 94] introduced the problem and gave an algorithm for the GMP1R on a tree. Their approach is based on flow arguments and yields an algorithm that solves O(n6) mincost flow problems on graphs with O(n) vertices. They also give a 7 approximation algorithm that solves O(n) mincost flow problems on graphs with O(n) vertices. We propose a new dynamic programming approach to GMPIR on a tree. Based on this approach we give a O(n4) algorithm for the GMP1R on a tree. Moreover, we give an O(n3) approximation algorithm that obtains a solution that is within a 7 factor from the optimum. We also discuss extensions of our work and pose a new open problem.