Linear time-varying model predictive controller improving precision of navigation path automatic tracking for agricultural vehicle

Abstract: Automatic driving for agricultural vehicle has become a research hotspot. Automatic driving technology includes vehicle position technology and automatic steering technology. Vehicle position technology usually uses the global positioning system (GPS) to realize. Automatic steering technology is realized by controlling vehicle lateral motion which can keep vehicle driving in a desired trajectory. So the result of automatic steering control directly embodies the intelligent behavior of agricultural vehicle. Recently more and more papers have proposed all kinds of algorithms to realize agricultural vehicle automatic driving. All of them show that in straight path tracking experiments, when the velocity is 1 m/s, the maximum error is 5 cm; in circular path tracking experiments, when the velocity is 1 m/s, the maximum error is 10 cm. With the increase of velocity, the tracking error is bound to further increase. To improve the precision, iterative learning control has been applied to path tracking. This method can achieve an almost perfect tracking performance in theory. But iterative learning control is an open-loop control which cannot effectively deal with interference. Model predictive control is a new control method which has attracted more and more researchers to study. The method can resolve the problem with constraints using the rolling optimization technique. It can not only predict the next-time system state, but also minimize tracking errors. With the rolling optimization technique and feedback adjustment, it can also overcome some uncertainty interferences. So to improve the precision of navigation control system for agricultural vehicle, an intelligent method of path tracking based on linear time-varying model predictive control is proposed. Although agricultural vehicle model usually has high nonlinearity, the method selects the linear timing-varying error model of the dynamic model as the prediction model of model predictive control to improve operation velocity. Objective function that selects control increment as state variable is established and relaxation factor is used to ensure the feasibility of solution. With the design of the constraints of control variable, control increment variable and state variable, the solution of objective function is changed into quadratic programming problem with some constraints which is solved using interior point method. After selecting the first element of control input increment as the input signal and repeating the above process to achieve the optimal control, model predictive controller is designed based on MATLAB/Simulink. Experimental results of straight and circular path tracking show that the controller can realize perfect tracking of straight path; the average error of lateral direction under 1 m/s is 7.5 cm and that under 3 m/s is 10 cm in circular path tracking; the front wheel angle is always in constraint dimensions, which shows the controller has not only a higher tracking precision but also a better stability. Experimental results of different controller parameters show that increasing prediction horizon and control cycle can reduce the tracking error and front wheel angle changes, and control horizon does not affect the controller's response speed. Meanwhile ground experiments based on the designed controller have been also completed. Results show that in straight path tracking, when the tracking velocity is 1 m/s, the average error of lateral direction is 0.865 cm; in circular path tracking, when the tracking velocity is less than 1 m/s, the average error of lateral direction is less than 10 cm; with the increase of velocity, the tracking error is further increased and the main reason is that when the velocity is lower, the experimental vehicle is linear, which is agreed well with the prediction model (using linear timing-varying error model), but when the velocity increases, the nonlinear features of vehicle is apparent gradually, which is not agreed well with the prediction model. The solution is using nonlinear model predictive control but it has larger computation. In practical path tracking, the velocity of agricultural vehicle is generally less than 1 m/s, so the designed controller can meet practical requirements.