Practical Sliced Configuration Spaces for Curved Planar Pairs

In this article, the author presents a practical configuration-space computation algorithm for pairs of curved planar parts, based on the general algorithm developed by Bajaj and the author. The general algorithm advances the theoretical understanding of configuration-space computation, but is too slow and fragile for some applications. The new algorithm solves these problems by restricting the analysis to parts bounded by line segments and circular arcs, whereas the general algorithm handles rational parametric 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 special pairs by specialized methods. A survey of 2,500 mechanisms shows that these methods cover 90% of pairs and yield an additional factor 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.