Steering Nonholonomic Systems via Nilpotent Approximations: The General Two-Trailer System

Existing methods for nonholonomic motion planning can only be applied to exactly nilpotentizable or flat systems. For nonholonomic systems that do not fall into the above classes, we conjecture that globally defined nilpotent approximations will allow the synthesis of efficient steering and stabilization strategies. In this paper, a car towing two off-hooked trailers is considered as a case study. First, it is shown how to derive a nilpotent approximation that is valid in the neighborhood of both regular and singular points. Then, such approximate model is used to compute steering controls. Simulation results are reported to show the satisfactory performance of the method.