LQR Trajectory Tracking Control of Unmanned Wheeled Tractor Based on Improved Quantum Genetic Algorithm

In the process of trajectory tracking using the linear quadratic regulator (LQR) for driverless wheeled tractors, a weighting matrix optimization method based on an improved quantum genetic algorithm (IQGA) is proposed to solve the problem of weight selection. Firstly, the kinematic model of the wheeled tractor is established according to the Ackermann steering model, and the established model is linearized and discretized. Then, the quantum gate rotation angle adaptive strategy is optimized to adjust the rotation angle required for individual evolution to ensure a timely jumping out of the local optimum. Secondly, the populations were perturbed by the chaotic perturbation strategy and Hadamard gate variation according to their dispersion degree in order to increase their diversity and search accuracy, respectively. Thirdly, the state weighting matrix Q and the control weighting matrix R in LQR were optimized using IQGA to obtain control increments for the trajectory tracking control of the driverless wheeled tractor with circular and double-shifted orbits. Finally, the tracking simulation of circular and double-shifted orbits based on the combination of Carsim and Matlab was carried out to compare the performance of LQR optimized by five algorithms, including traditional LQR, genetic algorithm (GA), particle swarm algorithm (PSO), quantum genetic algorithm (QGA), and IQGA. The simulation results show that the proposed IQGA speeds up the algorithm's convergence, increases the population's diversity, improves the global search ability, preserves the excellent information of the population, and has substantial advantages over other algorithms in terms of performance. When the tractor tracked the circular trajectory at 5 m/s, the root mean square error (RMSE) of four parameters, including speed, lateral displacement, longitudinal displacement, and heading angle, was reduced by about 30%, 1%, 55%, and 3%, respectively. When the tractor tracked the double-shifted trajectory at 5 m/s, the RMSE of the four parameters, such as speed, lateral displacement error, longitudinal displacement error, and heading angle, was reduced by about 32%, 25%, 37%, and 1%, respectively.