Toward an exact incremental geometric robot motion planner

In this paper we introduce a new class of geometric robot motion planning problems that we call incremental problems. We also introduce the concept of incremental algorithms to solve this class of problems. As an example, we describe an incremental critical curve based exact cell decomposition algorithm for a line segment robot moving freely amidst polygonal obstacles. In the example, after computing an initial representation of the robot's free space, the algorithm maintains the representation as obstacles are moved between planning problems. The cost to maintain the representation is expected to be small relative to the cost of its initial construction.