Modeling and Optimal Control of 4 Wheel Steering Vehicle Using LQR and its Comparison with 2 Wheel Steering Vehicle

In this paper, kinetic and kinematic modeling of a 4 wheel steering vehicle is done and its movement is controlled in an optimal way using Linear Quadratic Regulator (LQR). The results are compared with the same control of two-wheel steering case and the advantages are analyzed. In 4 wheel steering vehicles which are nowadays more applicable the number of controlling actuators are more than the required actuators for controllability of the system. As a result, the possible path through which he vehicle can move to transfer between two boundaries is not unique and this fact provides the possibility of optimization of a desired cost function. In this paper after extracting the model of these vehicles based on Jacobian matrix a compromise between the accuracy and controlling effort is selected as the mentioned objective function and the optimal control and its related optimal path is extracted through which the best accuracy and the least input is required. The correctness of modeling and efficiency of the designed optimal controller is verified by the aid of a series of simulation scenarios and also comparing the results between 4 wheel steering vehicles and 2 wheel steering ones.