This paper addresses the choice of the control horizon in a Nonlinear Model Predictive Control (NMPC) strategy for nonholonomic vehicles. The latter can be modeled by chained systems. We establish a relation between the degree of nonholonomy and the minimum length of the control horizon so as to make the full-state control possible. A necessary condition on the control horizon of NMPC is given and theoretically proved whatever the dimension of the chained system considered. The theoretical results are illustrated through simulations on a (2,5) chained system, describing a car-like vehicle with one trailer. Difficult motion objectives that require a lateral displacement are considered, as well as robustness to modeling errors.
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