Studies On Reconfigurable Model Predictive Motion Controller For Autonomous Vehicles

As one of the key technologies for autonomous driving,motion control has made significant progress over the past few years.The motion control method based on model predictive control(MPC)has become the mainstream scheme in academia and industry.In recent years,the stability control strategy based on MPC has become a research hotspot,and it is developing towards integrated stability control.The path following control based on MPC has also increasingly integrated stability control.The motion control of the autonomous vehicle in this paper includes stability control and path following control.Although the motion control technology based on model predictive control has made significant progress,there are still many problems to be solved.First,the environment faced by autonomous vehicles is complicated and changeable,and the traditional MPC control relies on accurate prediction models.The steady-state error caused by model mismatch has not been solved properly.Second,lateral and longitudinal control are split in many research works,particularly in commercial deployment systems.Nonetheless,due to the coupling of lateral and longitudinal force constraints of tires,the vehicle will lose stability in extreme cases.The third point is MPC’s computational burden and stability because real-time performance is of great significance to the motion control of autonomous driving.Although nonlinear model predictive control has better control accuracy and can consider nonlinear constraints,its stability and efficiency are still the main reasons restricting the deployment of existing systems.The fourth point is that the configuration of four-wheel vehicles can be variable,and different configurations of vehicles commonly mean that the controller needs to be redesigned.Although the reconfigurable integrated stability control of vehicles with different configurations has been researched in recent years,the concept of reconfigurable controller is limited to stability control and not extended to motion control of autonomous driving.The primary purpose of this paper is to solve the above problems in motion model predictive control of autonomous vehicles.The main goal of this paper is to design a reconfigurable model predictive motion controller for four-wheel vehicles which can eliminate steady-state error and has high performance.The reconfigurable controller should be able to control four-wheel vehicles with different configurations and solve the problem of steady-state error in lateral and longitudinal coupling control.In order to design such a reconfigurable motion controller,it is necessary to establish a vectorized reconfigurable prediction model.The reconfigurability of the prediction model means that the prediction model can integrate the models of vehicles with different configurations into a unified model through the vectorization modeling method,and the configuration of vehicles can be changed by changing parameters.First,the dynamic equation of the vehicle body is established by the Newton-Euler equation,which includes three degrees of freedom: longitudinal,lateral,and yaw;Then,the vectorized modeling method is used to map the tire force to the vehicle body force.In the process of modeling,the traditional modeling method using the wheelbase and track is abandoned,and the coordinates of the wheels in the vehicle coordinate system are used instead.This is a very critical step to achieving vectorized modeling;Then,for the modeling of the actuator,the first-order delay system is used to model the driving and braking systems,the integration model is used to model the steering system,and the output of the actuator is mapped to the tire based on the reconfigurable matrix to achieve the reconfigurable modeling of the actuator;TM-Easy and TM-Simple models with simple parameters and clear physical meaning are adopted for the tire model.Finally,a unified reconfigurable model is established.Then,under different assumptions,the model is simplified and linearized with different complexity,and the different versions of the reconfigurable model with different complexity are obtained,which provides the basis for the subsequent design of the reconfigurable model predictive motion controller.Before designing the reconfigurable motion controller,there are two problems to be solved: the efficiency and stability of model predictive control.For the design of linear model predictive control solver,the process of transforming model predictive control problem into different forms of quadratic programming problem is derived,which is the basis of efficient linear model predictive controller design.Because the integration stiffness of vehicle dynamics in the lateral speed,yaw rate,and slip rate is large,there is an integration stability problem when the vehicle speed is low.Based on the stable Runge Kutta method,the semiimplicit Runge-Kutta method,and the split integration strategy,this paper proposes a strategy to solve the integration stability problem of nonlinear model predictive control applied to motion control.Based on the foundation mentioned above and offset-free model predictive control,different reconfigurable motion controllers are designed for different versions of reconfigurable models.Compared with the traditional model predictive control,the advantage of offset-free model predictive control is that it can eliminate the steady-state error.The offsetfree model predictive control includes a model predictive control solver,a reference generator,and a Kalman filter.The linear model predictive control solver is independently designed by us based on the quadratic programming solver OSQP,while the nonlinear model predictive control solver adopts the gradient-based solver GRAMPC.The reference generator is essential for eliminating the steady-state error,which generates the state reference and the control reference of the MPC control.Its solution process is modeled as a nonlinear programming problem.Since few parameters affect the nonlinear programming problem,to improve efficiency,a look-up table is obtained by offline calculation,then the state reference value and the control reference value are obtained by online interpolation.Simulation and actual vehicle experiments show that the designed reconfigurable model predictive motion controller can stably control the motion control of four-wheel vehicles with different configurations;It not only has high efficiency but also can successfully eliminate the steady-state error in the coupling control and has high control accuracy.The integration stability problem of the dynamic prediction model is also solved efficiently,and the controller can be applied to the motion control problem of vehicles with different configurations in the entire speed range from low speed to high speed.The innovations of this paper are as follows:(1)Using the vectorization modeling method,a reconfigurable vehicle dynamics prediction model is established,and a reconfigurable motion controller is proposed based on this.The reconfigurable vehicle dynamics model is significant for the design of the reconfigurable motion controller.The TM-Easy tire model is used for the tire model.In the most complex reconfigurable model version,the actuator’s dynamic behavior and the tire’s longitudinal slip ratio are considered.Then,different simplified versions of reconfigurable motion control models are obtained according to different simplified conditions.The reconfigurable motion controller designed based on the reconfigurable model can solve the motion control problem of vehicles with different configurations only by modifying the initialization parameters without recoding or modifying the control model,which significantly improves the applicability of the autonomous driving motion control system.(2)The offset-free MPC method is applied to the vehicle longitudinal and lateral coupling control to eliminate the steady-state error caused by model mismatch or external disturbances.Model predictive control relies on accurate dynamic models.Once the models are mismatched or encounter external disturbances,steady-state errors of longitudinal speed and lateral position will be generated.In order to eliminate the steady-state error,this paper proposes to use offset-free MPC.For offset-free MPC,one difficulty is the calculation of state and control reference value,especially for nonlinear model predictive control.The solution of steady-state reference value will be transformed into a nonlinear optimization problem,and the calculation of this nonlinear optimization problem itself is very time-consuming.It is found that the reference value of motion control depends on fewer parameters and can be calculated by offline calculation and then online interpolation,which significantly improves the real-time performance.(3)Based on explicit and semi-implicit Runge-Kutta methods,a split integration strategy is designed to solve the low speed integration stability problem based on NMPC motion control.For a long time,the problem of low-speed integration stability has not attracted enough attention,which is the main reason for the low efficiency and instability of motion control based on nonlinear model predictive control.In this paper,a split integration strategy is proposed to divide the state equation of the system into a stiff part and a non-stiff part.The stiff part is integrated by a semi-implicit method,while the non-stiff part is integrated by an explicit method.Since the dimension of the stiff part is significantly reduced,the low-speed integration stability of NMPC is solved effectively.