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Mixed logical dynamic based path-tracking model predictive control for autonomous vehicles

A novel model predictive control (MPC) strategy for autonomous vehicles path tracking based on mixed logical dynamic (MLD) system is proposed in this article. To simplify the vehicle lateral dynamics model and describe the complex nonlinear characteristics of tire lateral forces with higher accuracy, a piecewise linear affine (PWA) tire lateral force model is proposed by dividing the tire force curve into saturated, nonlinear and linear segments. In addition, to avoid excessive number of partitions caused by using segmented lateral force models for both front and rear tires, the front tire lateral force is used as the control input instead of steering angle in this article. In the PWA model, due to the coupling between the control input and partition, it will be difficult to perform state prediction according to the classical MPC method in this case where the control input and partition are unknown simultaneously. Therefore, an MLD system which is equivalent to the PWA model is constructed by designing new logical variables and auxiliary variables and using the conversion between Boolean algebraic logical expressions and the inequality set. In the optimization problem based on the MLD system, the control input and the logical variables characterizing the partition can be optimized together as independent variables. Then, the MLD-based optimization problem is transformed into a standard quadratic programming problem and the mixed-integer quadratic programming (MIQP) algorithm is employed to calculate its optimal solution. Furthermore, to reduce the online computational burden and improve the real-time performance, an explicit model predictive control (EMPC) strategy for MLD systems is given. Finally, the performance of the controller is evaluated in simulations. Simulation results show that the controller proposed in this article can track the reference path in real time and has a similar lateral error Root Mean Square (RMS) as the NMPC path tracking controller designed based on a complex nonlinear model.