3-D world modeling based on combinatorial geometry for autonomous robot navigation

In applications of robotics to surveillance and mapping at nuclear facilities the scene to be described is three-dimensional. Using range data a 3-D model of the environment can be built. First, each measured point on the object surface is surrounded by a solid sphere with a radius determined by the range to that point. Then the 3-D shapes of the visible surfaces are obtained by taking the (Boolean) union of the spheres. Using this representation distances to boundary surfaces can be efficiently calculated. This feature is particularly useful for navigation purposes. The efficiency of the proposed approach is illustrated by a simulation of a spherical robot navigating in a 3-D room with static obstacles