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. W e also introduce the concept of incremental algorithms to solve this class of problems. As a n example, we describe an incremental critical curve based exact cell decomposition algorithm for a line segment robot moving freely amidst polpgonal obstacles. In the example, after computing a n initial representation of the robot’s free space, the algorithm maintains the representation as obstacles are moved between planning problems. The co:it t o maintain the representation is expected to be small relative t o the cost of i ts initial construction.