Sliced configuration spaces for curved planar bodies

Abstract

We present the first practical, 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 parametric curve segments. The algorithm represents the three-dimensional configu-ration space as two-dimensional slices in which the moving object has a fixed orientation. It discretizes the configuration space into in-tervals of equivalent slices separated by critical slices. The output is topologically correct and accurate to within a specified toler-ance. 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 efficient abstract data type for geo-metric computations in robotics and engineering. 1