Time optimal paths for a mobile robot with one trailer

Optimal paths are in many ways interesting to motion planning. Not only they are obviously the most interesting ones with respect to the optimized criterion, but also they offer a way of studying the topological aspects associated to the controllability of the system. Many works have been carried out successfully on the optimal paths for unicyle and carlike system. This paper aims to extend those results when adding trailers. Characterizing the time optimal paths for a mobile robot with n-trailers is an ambitious task. As a first step, we give an explicit description of the abnormal and singular extremals for a mobile robot with one trailer. This is done with the help of the maximum principle.