The complexity of motion planning amidst obstacles is a well modeled and understood notion. What is the increase of the complexity when the problem is to plan the trajectories of a nonholonomic robot? We show that this quantity can be seen as a function of paths and of the distance between the paths and the obstacles. We propose various definitions of it, from both topological and metric points of view, and compare their values. For two of them we give estimates which involve some E-norm on the tangent space to the configuration space. Finally we apply these results to compute the complexity needed to park a car-like robot with trailers.