Motion planning amidst dynamic obstacles in three dimensions

Abstract

Motion planning amidst moving obstacles in three dimensions is considered. Each obstacle is a polyhedron in three dimensions that moves with a constant speed at a fixed direction. Three basic properties are established for time-minimal motions in three dimensions amidst slowly moving obstacles. Representing moving three-dimensional objects with full generality would require space-time for four dimensions. The discussion is based on the idea of three-dimensional collision fronts and does not make explicit use of the time dimension. This makes it possible to treat the problem as in the case of stationary obstacles.