Non-linear optimal control of articulated-vehicle planar motion based on braking utilizing the state-dependent Riccati equation method

Abstract

In this paper, a new non-linear optimal controller for the planar motion of an articulated vehicle is proposed. The main goal of the control system is to enhance the planar stability through active braking of the wheels. The controller was designed such that the states of the system are forced to follow the reference values using an input-constrained non-linear model including the longitudinal dynamics, the lateral dynamics and the yaw dynamics of both units. Using the state-dependent Riccati equation method a servomechanism was designed which results in reasonable trade-offs between the control efforts and the allowable state errors while representing the non-linearities of the system. Furthermore, the brake torques were derived from the state-dependent Riccati equation control law by imposing constraints on the control inputs. Through proper selection of a weighting matrix, the control system distributes the brake forces optimally among the axles considering the coupling between the longitudinal tyre forces and the lateral tyre forces. In order to evaluate the performance and the effectiveness of the proposed controller, simulations were performed using the non-linear vehicle model. Additionally, the robustness of the controller is evaluated by analysis of its performance in the presence of parameter uncertainties. The simulation results prove the efficacy of the proposed controller in improving the yaw–roll stability, the handling and the manoeuvrability of the tractor–semitrailer.