Four-wheel steering vehicle trajectory tracking control method based on sliding mode control

Abstract

The invention discloses a four-wheel steering vehicle trajectory tracking control method based on sliding mode control, and the method comprises the steps: converting a mass center transverse error and a course error into a transverse error of front and rear axle virtual points, carrying out the design of a controller, and indirectly converging the transverse error and the course error of a mass center point through converging the transverse error of the front and rear axle virtual points. The front and rear axle rotation angle control quantity is decoupled, and controller design can be performed on a front axle virtual point and a rear axle virtual point. The sliding mode controller based on the front and rear axis virtual points is insensitive to parameter change and disturbance and has high robustness.

Description

Technical Field

[0001] The present invention belongs to the technical field of automatic driving, and in particular relates to a trajectory tracking control method for a four-wheel steering vehicle based on sliding mode control. Background Art

[0002] Single front-wheel active steering path tracking control is difficult to meet the motion requirements of intelligent vehicles under atypical working conditions. There are problems such as large tracking error and low stability. Therefore, the intervention of multiple actuators for joint control has become a research hotspot for intelligent vehicle motion control. Four-wheel steering vehicles have high controllable freedom, which is conducive to improving the high-speed stability of the vehicle. Previous studies on trajectory tracking control were mostly based on traditional front-wheel steering vehicle platforms, and less attention was paid to the stability control of the vehicle during the tracking process. If the trajectory tracking control problem of intelligent vehicles is studied based on the four-wheel steering vehicle platform, it will be of great help to improve the trajectory tracking performance and improve the vehicle stability.

[0003] The four-wheel steering control method is an effective means to improve the driving safety and handling stability of the vehicle. The traditional four-wheel steering control method often takes the center of mass sideslip angle of 0 as the control target, and achieves the requirements of "low-speed sensitivity and high-speed stability" by controlling the front and rear wheel steering angles. When the car speed is low or the steering angle of the steering wheel is large, the rear wheel steering angle is opposite to the front wheel steering angle, and the turning radius becomes smaller; when the car is driving at high speed or the steering angle is small, the rear wheel steering angle is in the same direction as the front wheel steering angle, and the turning radius becomes larger. The above four-wheel steering control method can improve the safety and stability of the vehicle in conditions such as entering and exiting corners and avoiding obstacles, and reduce the side slip and tail swing of the vehicle under extreme conditions.

[0004] For four-wheel steering vehicles, the rotation of its rear wheels will make the steering sensitivity of the vehicle (yaw angular velocity or / steering wheel steering angle) affected not only by the vehicle speed but also by the steering wheel steering angle. This change in steering sensitivity exceeds the driver's adaptability, increasing the driver's misoperation and driving burden. In addition, the high cost of four-wheel steering technology has prevented this technology from being popularized in non-autonomous driving vehicles. Considering that autonomous driving vehicles, i.e. unmanned vehicles, can ignore the interference and impact of changes in steering sensitivity on the driver, if four-wheel steering technology can be applied to autonomous driving vehicles, in addition to preventing driver misoperation caused by changes in steering sensitivity, it can also improve the safety and stability of autonomous driving vehicles in trajectory tracking.

[0005] In addition, traditional four-wheel steering vehicle control methods directly control the lateral error and heading error at the center of mass, and do not completely decouple the calculation of the front and rear axle angles. As a result, there are too many factors to consider when calculating the front and rear axle angles, too many control parameters need to be adjusted, and the actual vehicle calibration is huge, which is not conducive to the portability and platformization of the algorithm. Summary of the invention

[0006] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a four-wheel steering vehicle trajectory tracking control method based on sliding mode control, which uses the lateral offset of the front and rear virtual points as state variables to indirectly control the lateral offset and heading offset of the center of mass.

[0007] The present invention provides a four-wheel steering vehicle trajectory tracking control method based on sliding mode control, comprising the following steps:

[0008] Step S1. Establish a coordinate system, where X and Y are global coordinate systems, x and y are body coordinate systems, the x-axis direction is forward along the vehicle's center axis, the y-axis direction is to the right, and the center of the vehicle is at the center of mass; the vehicle's state information is expressed as (x, y, φ, v), i.e., the position, yaw angle and speed in the x and y directions;

[0009] Step S2. During the translation process, the vehicle is a point mass, and the force analysis of the point mass is performed according to Newton's second law, and the following is obtained:

[0010] in, is the inertial acceleration in the y-axis direction at the center of gravity of the vehicle,

[0011] F f and F r They represent the components of the forces acting on the front and rear wheels of the vehicle in the y-axis direction respectively;

[0012] The inertial acceleration of the vehicle along the y-axis and the centripetal acceleration of the vehicle rotating around the center of rotation are:

[0013]

[0014] The moment balance generated by the vehicle rotating around the Z axis, the corresponding yaw dynamics equation is:

[0015]

[0016] Among them, l f and l r is the distance from the front and rear tires to the center of gravity;

[0017] The force F on the vehicle tire in the y-axis direction f and F r , which is proportional to the side slip angle of the tire,

[0018] The lateral force on the front wheel of the vehicle is

[0019]

[0020] Among them, C f represents the cornering stiffness of each front wheel;

[0021] The lateral force on the rear wheels of the vehicle is

[0022]

[0023] Among them, C r Indicates the cornering stiffness of each rear wheel;

[0024] The lateral dynamic model can be derived as:

[0025]

[0026] Step S3. In the curved path, the error of the vehicle relative to the expected trajectory is

[0027]

[0028] Where ρ is the curvature of the desired trajectory;

[0029] The lateral error and heading error of the center of mass are converted into the lateral displacement of a virtual point close to the front and rear axes; the lateral error at the virtual point is converted to the vehicle coordinate system and is

[0030]

[0031] Among them, the distances from the center of mass to the front and rear virtual points are

[0032]

[0033] Therefore, the state equation of the error dynamics model for the decoupling of the front and rear axle angles can be obtained as follows:

[0034]

[0035] As a further technical solution of the present invention, the sliding surface of the sliding mode control is

[0036] Among them, C represents the speed at which the regulation state approaches zero;

[0037] Use exponential approach rate to control the front and rear wheel angles of four-wheel steering:

[0038]

[0039] Among them, sgn is the sign function, when s>0, sgns>0, otherwise it is less than 0;

[0040] Equivalent symbolic functions to continuous functions

[0041]

[0042] The front axle angle control amount and the rear axle angle control amount are obtained as follows:

[0043]

[0044] The advantages of the present invention are:

[0045] The front and rear axle angle control is decoupled, and the front axle angle controller and the rear axle angle controller are designed separately to facilitate parameter adjustment. The control parameters can be adjusted differently based on the steering characteristics of the front and rear axles.

[0046] The lateral error and heading error of the centroid are indirectly controlled through the front and rear virtual points, and the calibration parameters are few.

[0047] The sliding mode controller is highly robust to parameter changes and external disturbances and has better stability.

[0048] The virtual point controllers of the front and rear axles can compensate for the same-phase errors by superposition, so as to achieve rapid error convergence and high control accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a schematic diagram of the coordinate system of the present invention;

[0050] Figure 2 It is a schematic diagram of the sliding angle of the present invention;

[0051] Figure 3 It is a schematic diagram of the lateral displacement of a virtual point of the present invention;

[0052] Figure 4 It is a schematic diagram of the sliding surface of the sliding mode control of the present invention. DETAILED DESCRIPTION

[0053] This embodiment provides a four-wheel steering vehicle trajectory tracking control method based on sliding mode control of the present invention.

[0054] The modeling is based on the two-degree-of-freedom dynamics model of the vehicle, so the following assumptions are made:

[0055] ① The air force acting on the vehicle will only affect the movement in the x-axis direction of the vehicle body coordinate system. The y-axis direction and the rotation along the z-axis will not be affected by the air force.

[0056] ②The vehicle runs in a two-dimensional plane, that is, there is no speed on the z-axis.

[0057] ③The vehicle tire force operates in the linear range.

[0058] In the kinematic model, it is assumed that the velocity vectors of the front and rear wheels in the bicycle model are consistent with the direction of the wheels. However, when the vehicle speed is very high, the velocity vectors of the front and rear wheels in the bicycle model are no longer consistent with the direction of the wheels. At this time, the kinematic model cannot accurately describe the motion state of the vehicle, which requires the use of a dynamic model to model the vehicle.

[0059] Two dimensions of information need to be considered in the vehicle single vehicle model. These two dimensions refer to y, which represents the lateral position information of the vehicle, and φ, which represents the yaw angle information of the vehicle. They can be roughly divided into two categories: longitudinal force and lateral force. The longitudinal force is the force that makes the vehicle move forward and backward, while the lateral force makes the vehicle move laterally. In the process of force interaction, the tire plays a decisive role.

[0060] Establish as Figure 1 Coordinate system, X, Y represents the global coordinate system, x, y represents the body coordinate system, the x-axis direction is forward along the vehicle's center axis, the y-axis direction is to the right, and the center of the vehicle is at the center of mass. The vehicle's state information is represented by (x, y, φ, v), that is, the position, yaw angle and speed in the x, y directions.

[0061] First, we analyze the translation process, assuming that the vehicle is a point mass, and analyze the force on the point mass. According to Newton's second law, we get

[0062]

[0063] in,

[0064] is the inertial acceleration in the y-axis direction at the center of gravity of the vehicle

[0065] F f and F r They represent the components of the force on the front and rear wheels of the vehicle in the y-axis direction.

[0066] During translation, two forces work together to produce acceleration The inertial acceleration of the vehicle along the y-axis and the centripetal acceleration of the vehicle rotating around the center of rotation are as follows

[0067]

[0068] Then analyze the rotation process, assuming that the vehicle is a rigid body, and the rigid body rotates around the center of gravity. The motion process is described by torque and moment of inertia. The torque balance generated by the vehicle rotating around the Z axis, the corresponding yaw dynamics equation is

[0069]

[0070] Among them, l f and l r Indicates the distance from the front and rear tires to the center of gravity.

[0071] The experimental results show that the force F exerted on the vehicle tire in the y-axis direction is f and F r , which is proportional to the side slip angle of the tire. Figure 2 As shown;

[0072] According to the figure above, the lateral force on the front wheel of the vehicle can be expressed as

[0073]

[0074] Among them, C f Indicates the cornering stiffness of each front wheel.

[0075] Similarly, the lateral force on the rear wheel can be expressed as

[0076]

[0077] Among them, C r Indicates the cornering stiffness of each rear wheel.

[0078] Therefore, the derivation results of the lateral dynamics model are as follows:

[0079]

[0080] For a curved path, the error of the ego vehicle relative to the desired trajectory can be expressed as

[0081]

[0082] Where ρ is the curvature of the desired trajectory.

[0083] The goal of the autonomous driving control algorithm is to converge the lateral error and heading error of the center of mass to 0. Considering that the four-wheel steering system is basically a multi-input multi-output system, there is mutual interference between lateral motion and yaw motion and coupling terms between the front and rear steering angles. Therefore, in order to decouple the front and rear wheel steering angle control terms, the lateral error and heading error of the center of mass are converted into lateral displacements of virtual points close to the front and rear axes, such as Figure 3 shown.

[0084] The lateral error at the virtual point can be expressed as

[0085]

[0086] Among them, the distances from the center of mass to the front and rear virtual points are

[0087]

[0088] Therefore, the state equation of the error dynamics model for the decoupling of the front and rear axle angles can be obtained as follows:

[0089]

[0090] Variable structure control is a special nonlinear controller that is characterized by control discontinuity, also known as sliding mode control. The general steps are the design of the sliding surface, the design of the approach rate, and the solution of the controller.

[0091] Sliding mode control is a relatively simple control method with excellent control performance. Its excellent control effect is mainly reflected in two points: one is that the sliding mode can be designed, with fewer parameters to adjust and faster response speed. The second is that it is insensitive to disturbances. Sliding mode control is essentially a type of nonlinear control. Simply put, its nonlinearity is manifested as control discontinuity, that is, the "structure" of the system is not fixed, and can be purposefully changed according to the current state of the system during the dynamic process, forcing the system to move according to the state trajectory of the predetermined "sliding mode".

[0092] like Figure 4 As shown, s is the sliding surface. When the system state is at the sliding surface equal to 0 (or near it), the system is stable. So now our goal is to make s approach 0 so that the system is stable. The easiest way to think of is When s>0, On the contrary, when s<0, In this way, s eventually approaches 0.

[0093] The first step is to design the sliding surface. According to the four-wheel steering error dynamic state equation established earlier, the sliding surface is designed as

[0094]

[0095] Where C represents the speed at which the adjustment state approaches zero. The larger C is, the faster the speed is, and the state quantity eventually approaches zero at an exponential rate.

[0096] Then comes the design of the approach rate. The purpose of the approach rate design is to make the designed sliding surface s = 0. The easiest way to think of is When s>0, On the contrary, when s<0, In this way, s eventually approaches 0. The most commonly used approach rate design is:

[0097] Constant velocity approach rate:

[0098] Exponential Convergence Rate:

[0099] Power approach rate:

[0100] Where sgn is the sign function, when s>0, sgns>0, otherwise it is less than 0. All the above approach rates will eventually ensure that s approaches 0.

[0101] After comprehensive consideration, the exponential approach rate is used to control the front and rear wheel angles of the four-wheel steering:

[0102]

[0103] Since the sign function will produce a large jump at 0, we can consider replacing the sign function with the sign function function to achieve the same effect. Therefore, the sign function is equivalent to the following continuous function to avoid frequent sign switching.

[0104]

[0105] The last step is to solve the control quantity. Based on the sliding surface and approach rate designed previously, and the error dynamics equations, the front axle angle control quantity and the rear axle angle control quantity can be obtained as shown below.

[0106]

[0107] Simulation experiment

[0108] 1) Straight line working condition

[0109] For the working condition where the vehicle deviates from the straight trajectory by 0.5m, the front axle angle and rear axle angle calculated by the sliding mode controller based on the front and rear virtual points are output in a crab-like manner, which can quickly converge the error without overshoot.

[0110] 2) Large curvature curve

[0111] For large curvature curves with a curvature radius of 15m, the lateral error and heading error can also converge quickly. The front axle angle and the rear axle angle are output in different phases, which can greatly exert the advantages of four-wheel steering. The steady-state lateral error is only 1cm, and the steady-state heading error is only 0.2deg.

[0112] 3) U-shaped right angle bend

[0113] For the U-shaped right-angle bend with a curvature radius of 15m, there is a sudden change in the curvature radius when transitioning from a straight line to a curve, which leads to large disturbances in the lateral error and heading error at the center of mass. When faced with sudden changes in curvature, the controller can quickly converge the lateral error and heading error to ensure the accuracy of trajectory tracking. The steady-state lateral error is only 1cm, and the steady-state heading error is only 0.2deg.

[0114] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above specific embodiments. The above specific embodiments and the description in the specification are only for further illustrating the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of the present invention to be protected is defined by the claims and their equivalents.

Claims

1. A four-wheel steering vehicle trajectory tracking control method based on sliding mode control, characterized in that: The following steps are included: Step S1. Establish a coordinate system, where X and Y are global coordinate systems, x and y are body coordinate systems, the x-axis direction is forward along the vehicle's center axis, the y-axis direction is to the right, and the center of the vehicle is at the center of mass; the vehicle's state information is expressed as (x, y, φ, v), i.e., the position, yaw angle and speed in the x and y directions; Step S2. During the translation process, the vehicle is a point mass, and the force analysis of the point mass is performed according to Newton's second law, and the following is obtained: in, is the inertial acceleration in the y-axis direction at the center of gravity of the vehicle, F f and F r They represent the components of the forces acting on the front and rear wheels of the vehicle in the y-axis direction respectively; The inertial acceleration of the vehicle along the y-axis and the centripetal acceleration of the vehicle rotating around the center of rotation are: The moment balance generated by the vehicle rotating around the Z axis, the corresponding yaw dynamics equation is: Among them, l f and I r is the distance from the front and rear tires to the center of gravity; The force F on the vehicle tire in the y-axis direction f and F r , which is proportional to the side slip angle of the tire, The lateral force on the front wheel of the vehicle is Among them, C f represents the cornering stiffness of each front wheel; The lateral force on the rear wheels of the vehicle is Among them, C r Indicates the cornering stiffness of each rear wheel; The lateral dynamic model can be derived as: Step S3. In the curved path, the error of the vehicle relative to the desired trajectory is Where ρ is the curvature of the desired trajectory; The lateral error and heading error of the center of mass are converted into the lateral displacement of a virtual point close to the front and rear axes; the lateral error at the virtual point is converted to the vehicle coordinate system and is Among them, the distances from the center of mass to the front and rear virtual points are Therefore, the state equation of the error dynamics model for the decoupling of the front and rear axle angles can be obtained as follows:

2. The four-wheel steering vehicle trajectory tracking control method based on sliding mode control according to claim 1 is characterized in that: The sliding surface of sliding mode control is Among them, C represents the speed at which the regulation state approaches zero; Use exponential approach rate to control the front and rear wheel angles of four-wheel steering: Among them, sgn is the sign function, when s>0, sgns>0, otherwise it is less than 0; Equivalent symbolic functions to continuous functions The front axle angle control amount and the rear axle angle control amount are obtained as follows:

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