Most researches concerning the yaw stability and rollover prevention for autonomous vehicles are studied separately and decoupled the longitudinal and lateral vehicle dynamics control. However, the roll motion influences the yaw stability during high speed curve steering manoeuvres. With this in mind, a curve trajectory stable tracking controller for autonomous vehicles using linear time-varying model predictive control (LTV MPC) is proposed in this paper. The lateral dynamics control employs the LTV MPC to generate a sequence of optimal steering angles considering the constraints of control input, state output, yaw stability and roll stability together in the cost function, in which the prediction model utilizes an 8 degrees of freedom (DOF) vehicle model and the plant utilizes a 14-DOF vehicle model. The longitudinal control adopts PID control embedded in the MPC framework to update the speed at each optimization step and generate the total wheel torque for speed tracking. The trajectory tracking simulation results demonstrate that the vehicle tracks the reference trajectory and speed well with the proposed controller, which satisfies the constraints of control input, state output as well as the boundaries of yaw stability envelope, sideslip angle and roll angle, thereby reducing the risk of vehicle skid and rollover.

Most controllers concerning lateral stability and rollover prevention for autonomous vehicles are designed separately and used simultaneously. However, roll motion influences lateral stability in cornering maneuvers, especially at high speed. Typical rollover prevention control stabilizes the vehicle with differential braking to create an understeering condition. Although this method can prevent rollover, it can also lead to deviation from a reference path specified for an autonomous vehicle. This contribution proposes and implements a coupled longitudinal and lateral controller for path tracking via model predictive control (MPC) to simultaneously enforce constraints on control input, state output, lateral stability, and rollover prevention. To demonstrate the approach in simulation, an 8 degrees of freedom (DOF) vehicle model is used as the MPC prediction model, and a high-fidelity 14-DOF model as the plant. The MPC-based lateral control generates a sequence of optimal steering angles, while a PID speed controller adjusts the driving or braking torque. The lateral stability envelope is determined by the phase plane of yaw rate and lateral velocity, while the roll angle threshold is derived from the load transfer ratio (LTR) and tire vertical force under the condition of quasi-steady-state rollover. To track the desired trajectory as fast as possible, a minimum-time velocity profile is determined using a forward-backward integration approach, subject to tire friction limit constraints. We demonstrate the approach in simulation, by having the vehicle track an arbitrary course of continuously varying curvature thus highlighting the accuracy of the controller and its ability to satisfy lateral and roll stability requirements. The MATLAB® code for the 8-DOF and 14-DOF vehicle models, along with the implementation of the proposed controller are available as open source in the public domain.

Model predictive control (MPC) algorithm is established based on a mathematical model of a plant to forecast the system behavior and optimize the current control move, thus producing the best future performance. Hence, models are core to every form of MPC. An MPC-based controller for path tracking is implemented using a lower-fidelity vehicle model to control a higher-fidelity vehicle model. The vehicle models include a bicycle model, an 8-DOF model, and a 14-DOF model, and the reference paths include a straight line and a circle. In the MPC-based controller, the model is linearized and discretized for state prediction; the tracking is conducted to obtain the heading angle and the lateral position of the vehicle center of mass in inertial coordinates. The output responses are discussed and compared between the developed vehicle dynamics models and the CarSim model with three different steering input signals. The simulation results exhibit good path-tracking performance of the proposed MPC-based controller for different complexity vehicle models, and the controller with high-fidelity model performs better than that with low-fidelity model during trajectory tracking.

In order to investigate how model fidelity in the formulation of model predictive control(MPC) algorithm affects the path tracking performance, a bicycle model and an 8 degrees of freedom(DOF) vehicle model, as well as a 14-DOF vehicle model were employed to implement the MPC-based path tracking controller considering the constraints of input limit and output admissibility by using a lower fidelity vehicle model to control a higher fidelity vehicle model. In the MPC controller, the nonlinear vehicle model was linearized and discretized for state prediction and vehicle heading angle, lateral position and longitudinal position were chosen as objectives in the cost function. The wheel step steering and sine wave steering responses between the developed vehicle models and the Carsim model were compared for validation before implementing the model predictive path tracking control. The simulation results of trajectory tracking considering an 8-shaped curved reference path were presented and compared when the prediction model and the plant were changed. The results show that the trajectory tracking errors are small and the tracking performances of the proposed controller considering different complexity vehicle models are good in the curved road environment. Additionally, the MPC-based controller formulated with a high-fidelity model performs better than that with a low-fidelity model in the trajectory tracking.

In order to track the desired path as fast as possible, a novel autonomous vehicle path tracking based on model predictive control (MPC) and PID speed control was proposed for high-speed automated vehicles considering the constraints of vehicle physical limits, in which a forward-backward integration scheme was introduced to generate a time-optimal speed profile subject to the tire-road friction limit. Moreover, this scheme was further extended along one moving prediction window. In the MPC controller, the prediction model was an 8-degree-of-freedom (DOF) vehicle model, while the plant was a 14-DOF vehicle model. For lateral control, a sequence of optimal wheel steering angles was generated from the MPC controller; for longitudinal control, the total wheel torque was generated from the PID speed controller embedded in the MPC framework. The proposed controller was implemented in MATLAB considering arbitrary curves of continuously varying curvature as the reference trajectory. The simulation test results show that the tracking errors are small for vehicle lateral and longitudinal positions and the tracking performances for trajectory and speed are good using the proposed controller. Additionally, the case of extended implementation in one moving prediction window requires shorter travel time than the case implemented along the entire path.

In this paper, a new coupled lateral and longitudinal controller based on model predictive control (MPC) framework was proposed for an autonomous vehicle to track the desired trajectory and speed. Considering the constraints of control input limit and state output admissible, we used a spatial-based 8 degrees of freedom (DOF) vehicle model as the prediction model and used a high-fidelity model, i.e., a 14-DOF vehicle model as the plant model in the formulation of MPC algorithm. For the lateral control, the MPC controller generates the optimal road-wheel steering angle; for the longitudinal control, the PID controller embedded in the optimization solution generates the total driving or braking wheel torque. All these control inputs were passed to the plant simultaneously. The developed vehicle models were simulated with step steering input and compared with the simulation result of CarSim vehicle model for validation. We implemented the proposed controller for path tracking and speed control with MATLAB considering an 8-shaped curved trajectory as the reference. The simulation results showed that the path tracking and speed tracking performance were good using the combined lateral and longitudinal control strategy.

This technical contribution represents a step up in relation to work reported in [1]. Therein, the trajectory tracked was an 8-shaped curve with constant curvature and the optimization step in the model predictive control (MPC) algorithm was carried out without bound constraints. In this report, we consider the trajectory to be an arbitrary curve of continuously varying curvature. The MPC-based path tracking is implemented considering constraints on the control input and state outputs. For the lateral control, the MPC controller generates the optimal wheel steering angle. For the longitudinal control, the PID controller embedded in the solution generates the total accelerating or braking wheel torque. The speed-over-time control was carried out to maximize the speed at which the vehicle moves along the given curve. The speed profile generation was done in a moving prediction window, which was also used for path tracking and speed control. We present simulation results and compare them with reference objectives. We report small tracking errors between the plant and the objectives for the heading angle ‘ψ’, the lateral position ‘Y ’ and the longitudinal position ‘X’ of vehicle center of mass (C.M.). The work presented here draws on MPC concepts introduced earlier [2], [3] and goes one step beyond the studies reported in [4], [5]. To that end, it uses three vehicle models discussed in [6].

通过分析路面附着条件和道路曲率等因素对车辆转向特性和稳定性的影响,建立了高速车辆的等效动力学模型.提出了一种变步长的模型离散化方法,能够在保证车辆模型预测精度的基础上,实现较长的预测时域,并满足计算实时性的要求.通过对高速车辆稳定行驶状态进行分析,推导了基于包络线的滑移稳定性约束条件,并设计了基于模型预测控制的高速无人驾驶车辆的轨迹跟踪控制器.仿真结果表明,该方法可有效保证高速无人驾驶车辆在不同地面附着情况及道路曲率下的操控稳定性.

In this report, we implemented a model predictive control (MPC) strategy for path tracking and PID control for speed tracking to ensure the autonomous vehicle follows a desired path (an 8-shaped curve ) and speed profile. In addition, we generated a minimum-time speed profile as the speed reference for the vehicle to track the path as fast as possible. In the simulation, we considered three cases for the speed reference: Case A – the longitudinal velocity is constant at 10m/s; Case B – the longitudinal velocity is varied along the curved path; and, Case C – designing a minimum-time travel speed profile. For the path tracking, we used MPC controller to generate the optimal front wheel steering angle; for the speed tracking, we used a PID controller embedded in the model predictive control to generate the total accelerating or braking wheel torque. The front wheel steering angle and total wheel torque are passed simultaneously to the plant as inputs to calculate the vehicle state. The simulation results of tracking performance in these three cases are presented and compared with the reference objectives. The tracking errors between the plant and the objectives, such as the heading angle ‘ψ’, the lateral displacement ‘Y ’ of vehicle center of mass (C.M.) and the speed, are relatively small. The work presented here draws on MPC concepts introduced earlier [1,2] and goes one step beyond the studies reported in [3,4]. To that end, it uses three vehicle models discussed in [5].

This report focuses on implementing the model predictive control (MPC) and state estimation with cosimulation of Chrono and Matlab/Simulink R © for a mass-springdamper example and a pendulum example. The plants in the examples were generated using Chrono and the MPC controller with state estimator was designed in Matlab/Simulink R ©. With the plant measurement and optimal control input, the estimator used least squares estimation to estimate the plant state inputted to the MPC controller. With the estimated plant state and tracking objective, the regulator used model predictive control to calculate the optimal control signal inputted to the plant. In the simulation, firstly, the output of the model was compared with that of the plant to ensure the model provided a good approximation to the plant. Then without the disturbances in the control input and the output measurement, the estimated state and the plant state compared with the tracking objective using cosimulation of Chrono and Matlab/Simulink R © were illustrated. After that, when the process and measurement noise were considered, the estimated state, the plant state and the output measurement were compared with the tracking objectives respectively, which illustrated that the displacement of the mass m1 in the mass-spring-damper example and the rotation angle of the pendulum tracked the given objective using the proposed controller.

In this report, we discuss a model predictive control (MPC) strategy for path tracking by using a lower fidelity vehicle model to control the dynamics of a higher fidelity vehicle model. The vehicle models included a bicycle model, an 8-DOF model and a 14-DOF model. The paths included a straight line and a circle. These models are discussed in detail in [1]. In the MPC controller, the model is linearized and discretized for state prediction and the tracking objectives were the heading angle and the lateral displacement of the vehicle center of mass (C.M.) in global coordinates. We discuss the path tracking performance of the proposed controllers. This exercise is implemented in Matlab © and uses MPC concepts discussed in [2, 3].

提出一种越野地形下智能车辆的动力学建模与轨迹跟踪控制方法.针对越野地形建立了考虑路面倾角的智能车辆动力学模型,并推导了基于零力矩点的车辆侧倾安全约束.然后考虑上述车辆动力学模型及安全约束条件,设计了基于模型预测的智能车辆轨迹跟踪控制器.仿真试验表明该方法可以有效地适应复杂的越野地形,并能够在实现无碰撞轨迹的同时防止车辆发生侧翻危险.

A Model Predictive Control (MPC) approach is used in conjunction with two examples – mass-spring-damper and pendulum, to gauge the robustness of the MPC approach in the context of simple multibody dynamics problems. For the mass-springdamper example, a sensitivity analysis with respect to the weight factor and the value m2 of the second mass in the system was carried out to assess their influence on tracking performance. For the pendulum example, the solution used the same MPC controller used in the mass-spring-damper example.

在高速无人驾驶车辆的运动规划与跟踪控制过程中,滑移和侧倾是很难克服的高度非线性约束,特别是在复杂地形条件下,容易导致车辆失稳甚至侧翻。通过研究地形因素对车辆转向特性和稳定性的影响,建立高速车辆的等效动力学模型,并提出了一种变步长的模型离散化方法,能够在保证及时动态响应的基础上,实现较长的轨迹预测时域以及计算的实时性。针对高速无人驾驶车辆的滑移和侧倾等动力学安全因素,通过对车辆稳定行驶状态进行分析,推导了基于包络线和零力矩点的高速车辆稳定性约束条件。根据在高速、滑移、侧倾等复杂约束下车辆安全行驶的要求,运用模型预测控制算法求解最优运动轨迹及跟踪控制序列,在保证道路环境约束的同时满足车辆的滑移和侧倾等稳定性约束。仿真试验表明,该方法可以有效的考虑道路曲率和地形对高速车辆动力学特性的影响,保证车辆无碰撞行驶,同时防止车辆出现滑移和侧倾等现象。

This paper presents a model predictive control (MPC) scheme for the stabilization of high-speed autonomous ground vehicles (AGVs) considering the effect of road topography. Accounting for the road curvature and bank angle, a single-track dynamic model with roll dynamics is derived. Variable time steps are utilized for vehicle model discretization, enabling collision avoidance in the long-term without compromising the prediction accuracy in the near-term. Accordingly, safe driving constraints including the sideslip envelope, zero-moment-point and lateral safety corridor are developed to handle stability and obstacle avoidance. Taking these constraints into account, an MPC problem is formulated and solved at each step to determine the optimal steering control commands. Moreover, feedback corrections are integrated into the MPC to compensate the unmodeled dynamics and parameter uncertainties. Comparative simulations validate the capability and real-time ability of the proposed control scheme.

Intelligent vehicle,which has great advantages in enhancing the driving safety and diminishing road accidents,has become an emerging research focus worldwide.The development and research current status of lateral control for intelligent vehicles at home and abroad are reviewed.The research process and modeling of vehicle lateral dynamics and tire dynamics,the theory and methods of lateral control,and the automatic steering actuator design are discussed and summarized.Several research issues and development trends of lateral control of intelligent vehicles are presented,in which the modeling of vehicle lateral dynamics and the lateral controller design concerning the nonlinearity,uncertainties and time-varying characteristics,particularly in high speed lateral control,and the integrated design combining sensing,perception and decision-making systems with vehicle system dynamics will be research focuses in the future.