Calculating optimal trajectories from contact transitions

The learning-from-demonstration method is focused on for a novel robot-programming style. It consists of two parts: to recognize human performance from ob-servation as sequential motion primitives and to ex-ecute the same performance. We already proposed a method to recognize assembly tasks. However, execu-tion requires the ability to convert motion primitives to collision free paths. In this paper, we describe a method to calculate collision free paths. Many researchers have proposed to calculate collision free paths using analytical methods, potential fields or probabilistic methods. Potential and probabilistic methods are very powerful tools on a computer, but their solutions are not optimal. We propose a method to calculate optimal collision free paths analytically.