What is an automatic parking system? Analysis of automatic parking path planning and tracking technology

(4) Parking path following control

Path tracking mainly executes path planning, converts relevant strategies into electrical signals and transmits them to the actuator, and guides the car to park along the planned path according to the instructions. This process continuously detects the environment through on-board sensors, estimates the vehicle position in real time, compares the actual running path with the ideal path, and makes local corrections when necessary.

Parking process control

Parking is an important part of APS, where the APS actuator controls the vehicle to enter the parking space according to the path planning. The path planning is made based on the distance information measured by the sensor, but its measurement results are greatly affected by the environment and are prone to errors. Therefore, in the process of parking, attention should be paid to the real-time control and adjustment of the vehicle parking process to ensure the timely update of environmental data and the timely adjustment of the path.

Automatic parking path planning and tracking

The two main components of the automated parking system (APAS) are shown. APAS models the surrounding environment and detects parking spaces where the vehicle can park. The two main tasks of APAS are: 1. APAS must calculate a feasible path 2. Based on the vehicle speed and path input by the driver, the steering angle is controlled through the electronic power steering system (EPAS) to follow this path in a closed loop, showing the continuous curve path planning problem and the solution based on time-scale following control. These components are part of the commercial application of APAS for passenger cars.

Keywords: Continuous curve path planning, following control, time stamping

1. Introduction

The parking space detection step, signal processing related to distance measurement, and vehicle position and direction calculation are not discussed. The parking space and feasible path calculation are realized by ultrasonic radar, and the path following uses the speed and angle data of the ABS sensor on the vehicle (there is a problem here: the angle should be sent by EPS or steering wheel angle sensor, not ABS.

To design an APAS, a mathematical model of the vehicle is required. Many vehicle kinematic and dynamic models are given in the literature, and a low-speed vehicle kinematic model during parking maneuvers is a complete approach.

If the vehicle model is known, path planning methods and following control algorithms can be designed based on the equations of motion. Motion planning can use deterministic or probabilistic methods. To obtain a path with continuous curvature, special curves are used. Algorithms based on soft computing can also calculate reference paths.

The following control of a semi-automatic system is more complex than that of a fully automated system. The following control of the fully automated mode uses two inputs to influence the vehicle behavior, while the semi-automatic mode has one less input, that is, the vehicle speed in the semi-automatic mode is controlled by the driver, whose longitudinal speed is very different from the reference speed used for path planning. This problem is solved by the time coordinate.

The goal was to develop a parking assistance system that could operate in both semi- and fully-automated modes and that could accommodate three different parking situations (parallel parking, perpendicular parking and diagonal parking).

First, the components of the system are presented (Chapter 2). Chapter 3 is the vehicle dynamics model, and the details of the path planning and following control algorithms are given in Chapters 4 to 6. Chapter 7 gives the results of the actual vehicle test and a brief summary of the entire paper.

2. System components

To ensure automatic control, many tasks need to be performed: the system should be able to detect obstacles in the environment; detect or estimate its position and orientation; plan a reference action; and finally follow the reference action with as high accuracy as possible. These tasks are jointly implemented by independent and interconnected subsystems in Figure 1.

The vehicle's ABS sensors detect the displacement of the wheels. Based on this data, the actual position and orientation of the vehicle in the world coordinate system are calculated and assumed. This assumed state is used for environmental modeling and control models. In order to build the environmental model, data about the environment is also required. Ultrasonic sensors are used to measure the distances to surrounding obstacles. Based on these distances, an environmental model can be built. A simple algorithm is then used to find parking areas (if any) in the environmental model.

Figure 1: Components of an automatic parking assist system

Motion planning first calculates a reference path, which is a curve connecting the initial position and the end point. In the planning stage, it is necessary to consider the existing constraints (such as: non-regulatory characteristics described by the model, collision avoidance, maximum values ​​of actuator signals, etc.). Finally, a following control algorithm is used to follow the reference path.

3. Vehicle dynamics model

Both the path planning and following control algorithms require a vehicle dynamics model. To compute the path geometry, the model needs to be slightly extended to ensure the behavior of continuous curves.

As is common in the literature, the reference point of the vehicle is the center of the rear axle, denoted by R. The vehicle configuration (q) is described by four state variables: the reference point position R(x,y), the vehicle's heading ψ, and the curvature κ (the inverse of the turning radius). Assuming that the Ackerman steering theory holds, the dynamics of the vehicle can be described by a two-degree-of-freedom model located at the vehicle's mid-axis (see Figure 2);

The longitudinal velocity of the vehicle is represented by v, the rate of change of curvature is σ, and the wheelbase is represented by b. This gives us the following relationship between curvature and its derivative.

Fig.2 Vehicle dynamics model on the xy plane

δ is the angle between the front wheel direction of the two-degree-of-freedom model and the longitudinal axis of the vehicle. Both the curvature and the curvature derivative have restrictions, such as:

To design the following control, we use a simplified version of Equation (1) where the curvature is reduced.

Since the longitudinal velocity is generated by the driver and is not affected by the controller, the (following) control of the semi-automatic system does not use the longitudinal velocity of the vehicle as a system input. Let vd represent the vehicle speed controlled by the driver. (We assume that the speed vd can be measured or estimated.)

4. Path Planning

The task of the path planning method is to determine the geometric parameters of the reference path. The goal is to obtain a curve with continuous curvature to avoid the vehicle having to stop when the wheels are turning. Other constraints include the upper limit of the curvature and the derivative with respect to time. Since the vehicle cannot turn with an arbitrarily small turning radius, and the speed of the turning radius (or curvature) change is also limited by the electronic steering system.

In order to plan a path that satisfies the above constraints, three different path prototypes are used, namely straight lines, circular segments and continuous curvature curves (CC turns). The curvature of a straight line is 0, the curvature of a circular segment is a non-zero fixed value and does not exceed a given upper limit, and the curvature of a continuous curvature curve changes linearly.

The geometry of a straight or circular segment is easy to describe if its parameters are known (e.g., length, radius). The calculation of the parameters of a continuous curvature curve is much more complicated. If the initial state of the motion is q0 = [0, 0, 0, 0]T, the velocity profile is fixed (e.g., v = 1), and the curvature change is less than the maximum allowed value σmax, then the characteristics of a continuous curvature curve are described by the following equation:

CF and SF represent Fresnel integrals, which cannot be expressed in approximate form. After differentiation, it can be seen that these equations satisfy the vehicle dynamics model given by (1).

Simple mathematical operations on formula (6-9) can yield the equation of motion for different initial positions and arbitrary fixed velocities. If the value of the Fresnel integral in (6-7) can be calculated in advance, the remaining calculations can be performed in real time.

Now let's discuss how to use these three path prototypes to obtain a reference path for parallel parking spaces: Use seven line segments to form the entire path (see Figure 3). Under the premise of ensuring universality, assume that the vehicle moves backward from the initial state qs = [0, 0, 0, κs]T. First, it moves along a continuous curvature curve until it reaches the maximum curvature (or minimum turning radius). Then it turns along an arc with the minimum turning radius, and the angle of rotation is represented by ψ1. After passing another continuous curvature curve, the curvature becomes 0. Then the vehicle turns to the opposite direction through a continuous curvature curve, and then passes through an arc with a turning angle of ψ2 and another continuous curvature curve, and the curvature returns to 0 again. Finally, the path ends with a straight line of length l.

Such a path consists of three parameters: the rotation angle of the arc segment (ψ1, ψ2) and the length of the straight line (l). If these parameters are known, the geometry of the path and the target position can be calculated.

Figure 3: Reference path for parallel parking