Practical Sliced Configuration Spaces for Curved Planar Pairs

Abstract

In this article, Ipresenta practical configuration-space computation algorithm for pairs of cwvedplanarparts, based on the general algorithm developed by Bajaj and me. The general algorithm advances the theoretical understanding of configuration-space computation, but is too slow andfragilefor some applications. The new algorithm solves these problems by restricting the analysis to parts bounded by line segments and circular arms, whereas the general algorithm handles rationalparametric curves. The trade-off is worthwhile, because the restricted class handles most robotics and mechanical engineering applications. The algorithm reduces run time by a factor of 60 on nine representative engineering pairs, and by a factor of 9 on two human-knee pairs. It also handles common specialpairs by specialized methods. A survey of 2,500 mechanisms shows that these methods cover 90%/O ofpairs and yield an additionalfactor of 10 reduction in average run time. The theme of this article is that application requirements, as well as intrinsic theoretical interest, should drive configuration-space research.