Most nonholonomic path planning algorithms in the presence of obstacles use a local planner, that is, a method returning feasible paths between pairs of configurations without taking obstacles into account. To ensure convergence of the global method, however, the local planner has to account for small-time controllability: the length of the path joining two configurations has to tend toward zero with the distance between these configurations. In this paper, we present such a Local method for a robot towing n trailers, based on differential flatness and significantly more efficienct than former methods.