Non-holonomic interpolation motion planning for the car with trailers

In this paper we present new results on the path planning problem in the case study of the car with trailers. We formulate the problem in the framework of optimal nonholonomic interpolation and we use standard techniques of nonlinear optimal control theory for deriving hyperelliptic signals as controls for driving the system in an optimal way. The hyperelliptic curves contains as many loops as the number of nonzero Lie brackets generated by the system. We compare the hyperelliptic signals with the ordinary Lissajous-like signals that appear in the literature, we conclude that the former have better performance.