Linear Time-varying feedback Law for vehicles with Ackermann steering

In this paper, we propose an optimal state-feedback control law for addressing point stabilization and tracking problems of nonholonomic vehicles with Ackermann steering in a unified manner. Unlike other feedback controllers that perform dynamic linearization of vehicle models, the proposed optimal feedback controller provides the state-feedback control to the original nonlinear vehicle model for achieving excellent state-tracking performance. In addition, nonlinear control techniques suggested in the literature to date require that the desired trajectory of the robot is generated using persistently excited inputs. This may be too restrictive and non-realistic hypothesis to mimic a real scenario. Here, we address this issue by developing a smooth state-feedback control law that is formulated by modifying the classical Pontryagin’s minimum principle. The proposed control law can be applied for solving control problems of a general class of nonlinear affine systems. The proposed control scheme offers a modular solution to other control techniques for a large number of mobile robot applications. The theoretical results are validated through computer simulations.