Evaluation of model-based predictive control methods in high-speed automated ground vehicle path following

Abstract

Ensuring safe driving in autonomous vehicles is one of the most important requirements. Providing trajectory tracking plays a key role in this issue. A number of technological instruments such as electronic anti-skid systems, electronic stability programs and electric-hydraulic-supported steering systems are used to obtain the safest trajectory for a vehicle. These systems developed by automotive manufacturers are controlled by different methods. For example, proportional-integral-derivative (PID) control, Fuzzy logic, linear-quadratic-regulator (LQR), linear-quadratic-integrator (LQI), artificial neural networks, H-infinity and model predictive control are utilized for directional control in vehicles. With the help of these control methods, parameters such as steering angle and/or wheel moments are optimized, and human intervention in driving is partially or completely prevented. Model predictive control (MPC), one of the listed methods, differs from other control methods due to its suitability for autonomous driving systems. It is a model-based control method. In this approach, the control action is provided by considering the difference between the predicted and current outputs of the system. The control signal is generated according to the selection of the MPC parameters (prediction horizon, control horizon, appropriate sampling time and weighting parameters). In addition, the MPC is capable of working with multiple system and controller outputs, multiple constraints on the control signal and multiple set-points. Furthermore, the base model of the MPC can be in linear or nonlinear formulations. In linear MPC systems, the base model formulation remains constant throughout the control action. In nonlinear MPC systems, the base model is updated at each sampling depending on the outputs of the system. With this implementation, nonlinear and complex systems can be controlled with MPC. Due to these advantages, MPC is frequently used in solving of trajectory tracking problems of the autonomous vehicles. In this Ph.D. thesis, the MPC-based control systems for a military vehicle cruising at constant speed in the NATO double lane change (DLC) maneuver are presented, considering successful trajectory tracking and fast control signal generation. This vehicle is entitled "system" and it is represented by a two-track nonlinear vehicle model. The system model has 4 degrees of freedom in the vehicle body (longitudinal motion, lateral motion, yaw motion and roll motion) and 8 degrees of freedom in each wheel (rotation). The inputs to the system are the steering angle for the front wheels and the torque outputs of each wheel. Magic Formula (2002) version is used to model the tires of the vehicle. This semi-experimental model is used to calculate the lateral and longitudinal forces that can be produced by the tire using the experimentally-determined tire parameters. The friction between the tire and ground and combined slip properties are also considered in the tire modelling. The system model has been validated using the experimental data generated by a NATO Research Task Group on Applied Vehicle Technology. The data include outputs such as steering wheel angle, wheel moments, lateral acceleration, roll angle, roll rate, yaw angle, yaw rate and global position. Six control systems based on discrete-time MPC are developed. These are "linear MPC", "adaptive nonlinear MPC" (with two tuning methods), "robust linear MPC", "classical nonlinear MPC with multiple controller outputs" and "explicit tunable nonlinear MPC". In all controllers, the vehicle model with two degrees of freedom is used as the base model. The degrees of freedom are the yaw motion of the body and the lateral motion of the center of gravity. In all controller designs, except for the "classical nonlinear MPC" and "explicit tunable nonlinear MPC" designs, the base model is configured as a single-track vehicle model. In addition, the steering angle is used as the only control signal. In the "classical nonlinear MPC" and "explicit tunable nonlinear MPC" designs, the base model is a two-track vehicle model. The steering angle and direct yaw moment are determined in coordination. In the "explicit tunable nonlinear MPC" design, the control law is not obtained using online approaches. However, in other controllers, the control signal is generated online by minimizing the cost function in the MPC structure. In all controller designs, the lateral position of the center of gravity and the yaw angle of the body are used as desired system outputs. In addition, the system model is always assumed to be at constant speed during the DLC maneuver. In the first controller design, "linear MPC", the system is expected to approach the set points at two different speeds. The base model of the controller is linear. No tuning method is used to determine the controller parameters. In the simulation studies, it is observed that the "linear MPC" can provide improved trajectory tracking performance compared to the proportional-integral-derivative (PID) control method. In the second controller design, "adaptive nonlinear MPC (version 1)", it is aimed to increase the experimentally-determined maximum NATO DLC speed of the system. The parameters of this controller are tuned by artificial neural networks (ANN) and determined online at each sampling instant according to the outputs of the system. In addition, during the control signal generation phase, the nonlinear base model is linearized at each sampling instant. This process is completed by considering the instantaneous values of the control signal and the system states. These features make the controller adaptive. Steering angle is the only control signal. Simulations show that the maximum NATO DLC speed can be increased using "adaptive nonlinear MPC (version 1)" compared to experiments and PID controller, without lateral skidding, wheel lift-off and roll-over. The third controller design, "adaptive and nonlinear MPC (version 2)", is an enhanced version of the "adaptive and nonlinear MPC (version 1)". The weights of this controller are tuned using a combined structure of ANN and the Big Bang-Big Crunch (BB-BC) algorithm. It includes 2 layers: In the first layer, controller weights are determined by ANN. These weights are then evaluated as the initial center of mass in the first iteration of the BB-BC algorithm. The BB-BC algorithm also works in two stages: In the first stage, "Big Bang", the initial population is obtained. Then the "Big Crunch" phase starts and candidate solutions are gathered around the center of mass. The BB-BC algorithm is inspired by the formation of the universe and it determines the controller weights with low computational load and fast convergence. The combined tuning mechanism is adaptive and online. The results showed that, all controller weights are tuned online and updated during the maneuvers, and path following performance of the vehicle is enhanced at different NATO DLC speeds using the developed tuning mechanism, compared to working with ANN only. The fourth design, "robust linear MPC", aims to provide a control action where controller performance is maintained at different vehicle speeds. Steering angle is the only controller output. The robustness of the controller is ensured by ANN in 2 steps. In the first step, controller weights and sampling time are determined for a given range of vehicle speeds to achieve maximum tracking performance. These parameters are determined to be same for all speeds. In addition, a smoothed control signal is obtained by adaptively selecting the prediction horizon according to the vehicle speed. In the simulation studies, it is observed that the "robust linear MPC" is more successful in trajectory following and more flexible in terms of completing the control action at three different vehicle speeds, compared to a set of linear-quadratic-integrator (LQI) and two discrete integrators. The fifth design, the "classical nonlinear MPC with multiple controller outputs", aims to optimize the steering angle and the direct yaw moment (DYM) to ensure trajectory tracking in the NATO DLC maneuver at 2 different speeds. The DYM is then determined as rear wheel torques using the wheel torque distribution algorithm and transmitted to the system model. No method is used to tune controller parameters. In order to reduce the high computational burden caused by the online control signal generation, multiple controller outputs and base model complexity, the sixth design, the "tunable explicit nonlinear MPC", is used. In this design, the behavior of the "classical nonlinear MPC" on the control action is completely modeled by ANN. Furthermore, in order to improve the trajectory tracking performance, the weights of the controller are adjusted by two mechanisms: ANN and fuzzy logic. The simulation results show that the "tunable explicit nonlinear MPC" is more successful than the "classical nonlinear MPC" in terms of trajectory tracking and computational efficiency. All simulations in this Ph.D. thesis were performed in MATLAB / SIMULINK environment. It has been determined that the controllers designed based on MPC show effective results in terms of trajectory tracking performance and computational load. They are candidates for the control of autonomous vehicles.