Model predictive navigation for position and orientation control of nonholonomic vehicles

In this paper we consider a nonholonomic system in the form of a unicycle and steer it to the origin so that both position and orientation converge to zero while avoiding obstacles. We introduce an artificial reference field, propose a discontinuous control policy consisting of a receding horizon strategy and implement the resulting field-based controller in a way that theoretically guarantees for collision avoidance; convergence of both position and orientation can also be established. The analysis integrates an invariance principle for differential inclusions with model predictive control. In this approach there is no need for the terminal cost in receding horizon optimization to be a positive definite function.