Movement Planning in the Presence of Flows

This paper investigates the problem of time-optimum movement planning in two and three dimensions for a point robot which has bounded control velocity through a set of n polygonal regions of given translational flow velocities. This intriguing geometric problem has immediate applications to macro-scale motion planning for ships, submarines and airplanes in the presence of significant flows of water or air. Also, it is a central motion planning problem for many of the meso-scale and micro-scale robots that recently have been constructed, that have environments with significant flows that affect their movement. In spite of these applications, there is very little literature on this problem, and prior work provided neither an upper bound on its computational complexity nor even a decision algorithm. It can easily be seen that an optimum path for the 2D version of this problem can consist of at least an exponential number of distinct segments through flow regions. We provide the �...

• Type: Conference
• Year: 2001
• Where: WADS
• Authors: John H. Reif, Zheng Sun
• Keywords: Algorithms, Computational Complexity, Decision Algorithm, Intriguing Geometric Problem, WADS 2001