Sliced Configuration Spaces for Curved Planar Bodies

We present the nrst practlcal, implemented configuration space computation algorithm for a curved planar object translating and rotating amidst stationary obstacles, The bodies are rigid, compact, regular, and bounded by a finite number of rational parametrlc curve segments. The algorithm represents the three-dimensional configuration space as two-dimensional slices in which the moving object has a fixed orientation. It discretizes the configuration space into intervals of equivalent slices separated by critical slices_ The output is topologically correct and accurate to within a specified tolerance. We have implemented the algorithm for objects bounded by line segments and circular arcs, which is an important elMS for applications. The program is simple, fast, and robust. The slice representation is a natural and efficient abstract data type for geometric computations in robotics and engineering.