A Numerical Approach for Solving the Inversion Problem for n-Trailer Systems

Planning feasible trajectories is a necessity for developing autonomous vehicles. This especially becomes a difficult task when arbitrary trailers are involved. This paper proposes a sequential approach to solve the inversion problem for the so-called n-trailer systems. The idea is to specify the movement of the rearmost axle and convert the vehicle chain into concatenated axle pairs. Starting from the rearmost axle, the hitching angles and their time derivatives can be computed using geometric relations as well as either numerical differentiation or integration depending on the hitching type. The algorithm constructs the vehicle motion trajectories and the required control signals. Additionally, a method for generating the reference paths is provided. The results are validated for a truck with three trailers and different hitching types.