Sliced Con guration Spaces for Curved Planar Bodies

We present the rst practical, implemented con guration space computation algorithm for a curved planar object translating and rotating amidst stationary obstacles. The bodies are rigid, compact, regular, and bounded by a nite number of rational parametric curve segments. The algorithm represents the three-dimensional con guration space as two-dimensional slices in which the moving object has a xed orientation. It discretizes the con guration space into intervals of equivalent slices separated by critical slices. The output is topologically correct and accurate to within a speci ed tolerance. We have implemented the algorithm for objects bounded by line segments and circular arcs, which is an important class for applications. The program is simple, fast, and robust. The slice representation is a natural and e cient abstract data type for geometric computations in robotics and engineering. To appear in International Journal of Robotics Research