2 Path tracking control
In order for the vehicle to follow the desired path smoothly, precise control of the steering of the vehicle is required in the lateral direction when the vehicle speed is known. The principle of path tracking control is to calculate according to the real-time feedback state information of the vehicle, obtain the optimal control amount of front wheel angle or steering wheel angle, and feed the control amount to the vehicle to control the vehicle to track the desired path.
The process of path tracking is actually a process of tracking a series of points on the desired path one by one. When the vehicle speed changes during the path tracking process, the tracking effect will be affected. When many researchers study the path tracking control method, they regard the vehicle speed as a constant speed condition, ignoring the influence of the vehicle speed change on the tracking effect. During the parking process, the vehicle may encounter dynamic obstacles such as pedestrians and animals. At this time, it needs to stop and avoid. In the traditional path tracking control strategy, the speed of the vehicle is relatively high, and the vehicle speed needs to be kept as constant as possible during the parking process. The state, the change of the corner is related to time, and the tracking ability is lost after braking.
In order to reduce the impact of vehicle speed changes on the tracking effect and consider the obstacle avoidance control of dynamic obstacles encountered during parking, this paper designs a path tracking controller based on the model predictive control algorithm. The model predictive control algorithm can be based on the vehicle pose information. Adjust the prediction model in real time with the vehicle speed information, correct the corner control amount, and reduce the impact of vehicle speed on the path tracking effect.
2.1 Model Predictive Control Theory
Model Predictive Control (MPC) is an advanced process control method and a feedback control strategy that has been widely discussed in recent years. applied.
The mechanism of MPC can be described as: at each sampling time, according to the measurement information obtained at the current sampling time, a finite-time open-loop optimization problem is solved, and the first element of the solved control sequence is applied to the controlled object , repeat the above process at the next sampling time, refresh the optimization problem with the new measurement value and solve it again, so as to realize the optimization solution of the whole time domain. MPC is actually a kind of time-dependent, which uses the current state of the system and the current control quantity to realize the control of the future state of the system. The future state of the system is uncertain, so in the control process, it is necessary to continuously adjust the future control amount according to the system state. Moreover, compared with classical PID control, it has the ability to optimize and predict, that is to say, MPC is a kind of optimization control problem dedicated to decomposing longer time span, even infinite time, into several shorter time spans. , or an optimal control problem with a finite time span, and still seeks an optimal solution to a certain extent.
Three key steps are needed in the process of realizing MPC:
(1) Prediction model: The prediction model is the basis of MPC, and its main function is to predict the future output of the system according to the historical information and future input of the system.
(2) Rolling optimization: Due to the influence of external disturbance and model uncertainty in finite time domain prediction, the solved control sequence cannot be directly applied to the system, but the first component of each sampling time must be applied to the system. Therefore, the predictive control does not adopt a constant global optimization objective, but adopts a limited time period optimization strategy that rolls forward in time, which is carried out repeatedly online.
(3) Feedback correction: In order to prevent the deviation of the control from the ideal state caused by model mismatch or environmental interference, the actual output of the object needs to be detected at the new sampling time first, and this real-time information is used for correction, and then new optimization is carried out. , which constitutes a closed-loop optimization.
2.2 Linear time-varying vehicle model
Compared with nonlinear MPC, the linear time-varying MPC is simpler to calculate and has better real-time effect. Therefore, in order to ensure the real-time performance of the parking system and the stability of the vehicle tracking the desired path, this paper uses the linear time-varying model as the MPC algorithm. prediction model. Since the vehicle is moving at a low speed during the parking process, the vehicle kinematics model can be used as the prediction model, but whether the vehicle model is kinematic modeling or dynamic modeling, the final result is a nonlinear system. The kinematic model is linearized. The methods of nonlinear system linearization can be roughly divided into two types: exact linearization and approximate linearization. Because the approximate linearization method is simple and has strong applicability, the approximate linearization method is generally adopted.
It can be known from the vehicle kinematics model:
Equation (3.6) is the linearized vehicle error model. In order to make the error model applicable to the design of the model predictive controller, Equation (3.6) needs to be discretized. The discretization method is divided into the exact discretization method and the approximate discretization method. Since the vehicle kinematics model is used in this paper, the model is relatively simple, so the approximate discretization method is adopted.
Suppose there is a continuous system equation of state as shown below:
2.3 Vehicle Prediction Model
2.4 Transformation of quadratic programming problem
2.5 Constraint problem transformation
2.6 Construction and Simulation of Path Tracing Controller
(The code in this section will be linked later) The matlab code and simulink model in this section
In the automatic parking path tracking problem, the MPC-based path tracking controller used in this paper is shown in the figure below.
In order to verify the tracking effect of the control model, combined with the parameters of the target vehicle, a vehicle kinematics model is built in Simulink as the target vehicle model of the controller, and the controller is preliminarily tested. The structure of the built simulink model is shown in the figure below. The model consists of a model prediction controller and a vehicle kinematics model. First, set the vehicle speed to -1m/s, and input the vehicle speed signal into the vehicle kinematic model; then, calculate the horizontal displacement, longitudinal displacement, The yaw angle and yaw angular velocity are input into the model prediction controller, and the controller calculates the optimal front wheel angle control amount according to the set reference path and the vehicle state amount, and feeds it back to the vehicle motion In the learning model and the model predictive controller, the loop operation is performed thereby to complete the path tracking process.
Running the above model, the simulation results are shown in the following figure. As can be seen from Figure (a), when the vehicle travels along the desired path, the motion trajectories of the vertices of the vehicle body do not contact the parking space line and the road boundary line, and the vehicle contour does not collide with the parking space boundary and the road boundary. It can be seen from Figure (b) that the Y-axis coordinate of the center of the rear axle of the vehicle changes continuously with time, and the error range in the Y-axis direction remains within. It can be seen from Figure © that the yaw angle of the vehicle changes continuously with time, and the error range between the actual yaw angle of the vehicle and the yaw angle of the desired path is kept within the range of the yaw angle of the desired path. keep it parallel. It can be seen from Figure (d) that the change of the front wheel angle of the vehicle with time is continuous without sudden change, and the variation range of the front wheel angle can meet the requirements of the vehicle steering mechanism. When the vehicle reaches the end point of the path, the front wheel angle is in a positive state. , avoiding the situation of turning in situ. It can be seen from Figure (e) that the rotation speed of the front wheel of the vehicle changes continuously with time, and there is no sudden change, and the variation range of the rotation angle of the front wheel can meet the requirements of the steering mechanism of the vehicle. In summary, the model predictive controller can better control the vehicle kinematic model to track the desired path, which preliminarily verifies the effectiveness of the controller, and provides a reference for the subsequent use of the dynamic model as the target vehicle to verify the controller.
