Inner wheel differential control method based on asynchronous sampling during vehicle turning

Abstract

The present invention discloses an inner wheel difference control method based on asynchronous sampling during vehicle turning. The present invention establishes a mathematical model of a vehicle system under incomplete constraints with the rear wheel axle center as the vehicle position reference point, avoids the space occupation of the turning area during the vehicle turning process by tracking and controlling the rear wheel axle center for the expected trajectory, and reduces the inner wheel difference during the turning process of the existing vehicle; in the design process of the asynchronous sampling control law of the steering subsystem and the position subsystem, the present invention is different from the idea of ​​avoiding the rear wheel axle center as the reference point in the existing vehicle control design, and uses the constructed coordinate transformation to pre-process the incomplete vehicle model to reduce the design difficulty of the sampling control law. The steering control law and position control law obtained by design not only realize the precise control of the position of the center point of the rear wheel axle of the vehicle, but also use the transmission mechanism based on asynchronous sampling to reduce the difficulty of hardware selection and digital realization in the actual engineering application process.

Description

Technical Field

[0001] The present invention belongs to the technical field of vehicle control in traffic control systems, and in particular to a trajectory tracking control method for an autonomous driving vehicle based on asynchronous sampling, which is suitable for controlling the inner wheel difference of an autonomous driving vehicle during a turn. Background Art

[0002] As the general trend of future automobile development, autonomous driving technology has received extensive attention from academia and industry at home and abroad. However, the problem of inner wheel difference caused by the different driving trajectories of the front and rear wheels due to the length of the vehicle body has not been well solved. The main reason is that in order to reduce the difficulties in control design, the existing autonomous driving vehicle's tracking control design for the lane centerline is mainly carried out around the vehicle's center of mass, avoiding the use of the center point of the rear wheel axle under non-complete constraints as a reference point, resulting in the wheel difference area becoming larger as the length of the vehicle body increases.

[0003] The relatively fixed rear wheel on the rear axle of the vehicle, which can only move forward and backward and cannot turn freely, brings certain challenges to the control problem of vehicle dynamics. From the perspective of vehicle dynamics, it can be seen that the relatively fixed mechanical structure of the rear wheel makes the existing vehicle system essentially a non-holonomic system. Although there are many discussions and studies on the stabilization control problem and trajectory tracking control problem of such systems (Brockett RW, Asymptotic Stability and Feedback Stabilization, Differential Geometric Control Theory, Birkhauser, 1983, 181-19; Kolmanovsky, IV & McClamroch, NH, Developments in nonholonomic control problems, IEEE Control Systems Magazine, 1995, 15, 20-36), due to the difficulty of control design brought by non-holonomic constraints and the limitations of the current sampling control method, the inner wheel difference problem in the turning process of autonomous driving vehicles has not been studied from the perspective of nonlinear systems, and there is no report on the turning control problem under asynchronous sampling of the vehicle steering system and the vehicle driving system. Summary of the invention

[0004] Technical problem: The purpose of the present invention is to avoid the occupation of the turning space area during the turning process of an unmanned vehicle, to provide a trajectory tracking control method based on asynchronous sampling during the turning process of an autonomous driving vehicle, to achieve accurate tracking of the desired trajectory by the center of the rear wheel axle of the vehicle, and to reduce the risk of traffic accidents by reducing the inner wheel difference of the vehicle when turning.

[0005] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A method for controlling inner wheel differential based on asynchronous sampling during vehicle turning comprises the following steps:

[0007] S1. Taking the center of the rear wheel axle of the vehicle as the reference point, a mathematical model of the vehicle system in which the position subsystem and the steering subsystem are cascaded under non-holonomic constraints is established. Then, the continuous system cascade mathematical model is preprocessed using the constructed coordinate transformation to establish a discrete state space model of the non-holonomic vehicle cascade system.

[0008] S2. Based on the asynchronous sampling transmission conditions of the steering subsystem and the position subsystem, sampling control laws are designed for the steering subsystem and the position subsystem respectively to achieve the stabilization of the non-holonomic constrained vehicle system with respect to the target point;

[0009] S3. Based on the eigenvalue analysis method of discrete closed-loop system, the system matrix of the steering subsystem and the position subsystem under the asynchronous sampling transmission condition is analyzed, and the appropriate control gain parameters and subsystem sampling period are selected to ensure the stability of the steering subsystem and the position subsystem, so as to realize the inner wheel difference control of the vehicle system based on asynchronous sampling under non-complete constraints.

[0010] Compared with the existing vehicle system line tracking control technology, the present invention has the following advantages and effects:

[0011] Compared with the existing vehicle system line-finding and tracking control technology, the mathematical modeling of the present invention uses the center point of the rear wheel axle under non-complete constraints as the vehicle position reference point. Through the precise control of the center position of the rear wheel axle, the space occupied by the vehicle in the turning area during turning can be effectively reduced, and the inner wheel difference of the existing vehicle during turning can be reduced; in terms of vehicle control technology, the present invention constructs sampling stabilization control laws for the steering subsystem and the position system under the asynchronous sampling mechanism, avoiding the strict requirements of the traditional synchronous sampling control law for hardware implementation; at the same time, the present invention uses the control gain adjustable parameters introduced by constructing coordinate transformation to further relax the selection range of the sampling period under asynchronous sampling control, which facilitates the hardware selection and digital implementation in the control law implementation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A flowchart of the steps for implementing the present invention;

[0013] Figure 2 It is a schematic diagram of the tracking control of the rear wheel center of the controlled vehicle system along the lane line of the present invention;

[0014] Figure 3 Schematic diagram of error model preprocessing;

[0015] Figure 4It is a schematic diagram of the vehicle state and sampling input changes when the steering subsystem is fast sampled and the position subsystem is slow sampled;

[0016] Figure 5 Schematic diagram of the vehicle state and sampling input changes when the steering subsystem is sampled slowly and the position subsystem is sampled quickly.

[0017] Figure 6 for Figure 5 b Schematic diagram of the corresponding circular trajectory tracking;

[0018] Figure 7 for Figure 4 b Schematic diagram of the corresponding circular trajectory tracking. DETAILED DESCRIPTION

[0019] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0020] A method for controlling inner wheel differential based on asynchronous sampling during vehicle turning comprises the following steps:

[0021] S1. Taking the center of the rear wheel axle of the vehicle as the reference point, a mathematical model of the vehicle system in which the position subsystem and the steering subsystem are cascaded under non-holonomic constraints is established. Then, the continuous system cascade mathematical model is preprocessed using the constructed coordinate transformation to establish a discrete state space model of the non-holonomic vehicle cascade system.

[0022] S2. Based on the asynchronous sampling transmission conditions of the steering subsystem and the position subsystem, sampling control laws are designed for the steering subsystem and the position subsystem respectively to achieve the stabilization of the non-holonomic constrained vehicle system with respect to the target point;

[0023] S3. Based on the eigenvalue analysis method of discrete closed-loop system, the system matrix of the steering subsystem and the position subsystem under the asynchronous sampling transmission condition is analyzed, and the appropriate control gain parameters and subsystem sampling period are selected to ensure the stability of the steering subsystem and the position subsystem, so as to realize the inner wheel difference control of the vehicle system based on asynchronous sampling under non-complete constraints.

[0024] Figure 1 The flowchart of the steps for implementing the present invention is as follows:

[0025] Step 1: Establish a tracking model for unmanned vehicles under non-holonomic constraints.

[0026] 11) Continuous mathematical model of unmanned vehicle tracking control:

[0027] like Figure 2 In the geodetic coordinate system XOY shown in the figure, the following mathematical model of the unmanned vehicle is established with the center of the rear wheel axle of the vehicle as the reference point:

[0028]

[0029] Among them, (x, y) is the coordinate of the midpoint of the rear axle, θ is the angle of the vehicle body relative to the horizontal direction, and v and ω represent the vehicle's linear velocity and the steering angular velocity of the vehicle body respectively.

[0030] The desired turning path is divided into equal intervals, and the vehicle is driven to a series of division points (x ir ,y ir ),i=1,2,…N to realize the tracking control of the desired path, (x ir ,y ir ) is the coordinate of the i-th desired position point. Based on the mathematical model of the rear wheel of the vehicle, the vehicle relative to the dividing point (x ir ,y ir ) error model

[0031]

[0032] where e xi =xx ir ,e yi =yy ir In view of the convenience of describing the above errors in the vehicle body coordinate system during vehicle target point tracking, the following coordinate transformation is used

[0033]

[0034] Get as Figure 3 The following error model in the body coordinate system X1O1Y1 is shown (where x2, x3 are as Figure 3 (shown)

[0035]

[0036] In the above formula, let u1=ω,u2=-ωx2+v, and further obtain the following chain error model:

[0037]

[0038] Or the following two subsystems

[0039]

[0040]

[0041] Cascading form.

[0042] 12) Continuous state space model preprocessing:

[0043] In order to ensure the controllability of the continuous cascade system (3) with respect to the control law u1, the following coordinate transformation is used (L1, L2 are unknown constants, T1 is the sampling period of the steering subsystem, and k is the sampling sequence count):

[0044]

[0045] The cascade system (3) can be rewritten in continuous form as follows:

[0046]

[0047] and discrete form (T2 is the sampling period of the position subsystem)

[0048]

[0049] Step 2: Design of multi-sampling control law.

[0050] 21) Design of sampling control law for steering subsystem (4):

[0051] In order to ensure the controllability of the position subsystem under different values ​​of x1(0), in the design process of the steering control law, according to the different values ​​of x1(0), the design of the steering sampling control law u1 is divided into the following two cases:

[0052] (1) When x1(0)≠0, the following steering sampling control law is designed for the steering subsystem (4) in the sampling interval [kT1, (k+1)T1):

[0053] u1(t)=-L1x1(kT1) (7)

[0054] The corresponding closed-loop system can be obtained as

[0055]

[0056] By integrating both sides of the above equation in the sampling interval [kT1, (k+1)T1), we can obtain x1((k+1)T1) = (1-L1T1)x1(kT1). By iteratively repeating the above integration process in each sampling interval, we can obtain the analytical solution of the closed-loop system x1(kT1) = (1-L1T1) k+1 x1(0), and then we can get

[0057] The necessary and sufficient condition for x1(kT1)→0 is 0<|L1T1|<2.

[0058] (2) When x1(0) = 0, first use u1(t) = c, t∈[0, T1) (where the constant c≠0) to “pull” x1(t) away from the initial zero point, and then apply the sampling control law (7) designed in the above situation.

[0059] 22) Design of sampling control law for position subsystem (3):

[0060] For the position subsystem (6), the following sampling control law is designed on the sampling interval t∈[kT2,(k+1)T2)

[0061] v(t)=v(k)=-k2z2(k)-k3z3(k)

[0062] Where k2 and k3 are constants greater than zero. Substituting the above sampling control law into the discrete position system (6) can obtain its corresponding closed-loop system

[0063]

[0064] Since the closed-loop system (8) is a linear steady-state discrete system, the global exponential stability of the closed-loop system (8) can be achieved by selecting appropriate control gain and sampling period (see step 3 for details), and then the sampling stabilization control law of the position subsystem (3) is obtained as follows:

[0065]

[0066] Step 3: Parameter selection of multi-sampling control law.

[0067] 31) Steering subsystem sampling control law (7) Selection of control gain and sampling period:

[0068] When x1(0)≠0, due to the analytical solution of the steering subsystem x1(kT1)=(1-L1T1) k+1 x1(0)≠0, so the steering sampling control law (7) can ensure the controllability of the position subsystem (3). At this time, the selection scheme of the control gain and sampling period of the steering subsystem sampling control law (7) only needs to ensure the stability of the closed-loop system, and then the steering sampling control law (7) is obtained as follows:

[0069] 0<|L1T1|<2.

[0070] When x1(0)=0, the constant control law of u1(t)=c (c is a constant, t∈[0,T1)) is first used in the first sampling control cycle to "pull" the initial state of the subsystem (4) away from the origin, and then the steering sampling control law (7) obtained by the above design is applied.

[0071] 32) Position subsystem sampling control law (9) Selection of control gain and sampling period:

[0072] In order to ensure the simplicity of parameter selection of sampling control law of position subsystem, setting k2=k3=1 can further simplify the closed-loop subsystem (8) to

[0073]

[0074] in,

[0075] Based on the following characteristic polynomial of the closed-loop system (10)

[0076]

[0077] Applying the Jury criterion for the stability of linear steady-state discrete systems, we can obtain the necessary and sufficient conditions for the characteristic roots of the characteristic polynomial (11) to be within the unit circle or the stability of the discrete closed-loop system (10) as follows:

[0078]

[0079] Further simplifying the necessary and sufficient conditions (12) can lead to the following control gain and sampling period selection scheme of the position subsystem sampling control law (9):

[0080]

[0081] In order to further understand the present invention, the following Figure 4 and Figure 5 The vehicle system control examples shown are used to verify the embodiments of the present invention. However, it should be understood that these verifications are only used to further illustrate the features and advantages of the present invention, rather than to limit the claims of the present invention. Figure 4 is a curve diagram of the change of system state and control input under the conditions of fast sampling of the steering subsystem and slow sampling of the position subsystem, where Figure 4 a is a schematic diagram of the change of vehicle state variables over time when the steering subsystem is sampled quickly (T1=0.05) and the position subsystem is sampled slowly (T2=0.1). Figure 4 b is a schematic diagram of the change of control input over time when the steering subsystem is fast sampled (T1=0.2) and the position subsystem is slow sampled (T2=0.4); L1=1, L2=2; it can be seen that under the conditions of fast sampling of the steering subsystem and slow sampling of the position subsystem, the control method of the present invention can achieve stabilization of the vehicle trajectory tracking error over a larger sampling period range.

[0082] Figure 5 is the curve diagram of the system state and control input under the conditions of slow sampling of the steering subsystem and fast sampling of the position subsystem, where Figure 5 a is a schematic diagram of the change of vehicle state variables over time when the steering subsystem is sampled slowly (T1=0.1) and the position subsystem is sampled quickly (T2=0.05). Figure 5b is a schematic diagram of the control input changing with time when the steering subsystem is sampled slowly (T1=0.4) and the position subsystem is sampled quickly (T2=0.2); L1=1, L2=2; it can be seen that under the conditions of slow sampling of the steering subsystem and fast sampling of the position subsystem, the control method of the present invention can also achieve stabilization of the vehicle trajectory tracking error over a larger sampling period range. It can be seen from the above simulation results that based on the inner wheel difference control method based on asynchronous sampling proposed by the present invention, the tracking control of the vehicle rear wheel center to the desired lane line can be achieved by stabilizing the desired reference point.

[0083] Under the same initial conditions, the tracking diagram of the circular trajectory is drawn under the conditions of slow sampling of the steering subsystem (T1 = 0.4), fast sampling of the position subsystem (T2 = 0.2), and fast sampling of the steering subsystem (T1 = 0.2), and slow sampling of the position subsystem (T2 = 0.4). Figure 6 , Figure 7 As shown), it can be seen that the asynchronous sampling control given by the present invention can ultimately effectively realize the tracking control of the trajectory error. At the same time, the subsystems with different sampling laws ( Figure 6 , Figure 7 From the transient performance of the steering system (as shown in the figure), it can be found that fast sampling of the steering system helps to reduce the overshoot phenomenon (overshoot) during vehicle turning.

[0084] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the attached claims rather than the above description, and it is intended to include all changes within the meaning and scope of the equivalent elements of the claims. Although the embodiments of the present invention have been shown and described, it is understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the attached claims and their equivalents.

Claims

1. The inner wheel differential control method based on asynchronous sampling during vehicle turning is characterized in that: The following steps are involved: S1. Taking the center of the rear wheel axle of the vehicle as the reference point, a mathematical model of the vehicle system in which the position subsystem and the steering subsystem are cascaded under non-holonomic constraints is established, and then the mathematical model of the cascaded vehicle system is preprocessed by using the constructed coordinate transformation to establish a discrete state space model of the non-holonomic vehicle cascade system; S2. Based on the asynchronous sampling transmission conditions of the steering subsystem and the position subsystem, sampling control laws are designed for the steering subsystem and the position subsystem respectively to achieve the stabilization of the non-holonomic constrained vehicle system with respect to the target point; S3. Based on the eigenvalue analysis method of discrete closed-loop system, the system matrix of the steering subsystem and the position subsystem under the asynchronous sampling transmission condition is analyzed, and the appropriate control gain parameters and subsystem sampling period are selected to ensure the stability of the steering subsystem and the position subsystem, so as to realize the inner wheel difference control of the vehicle system based on asynchronous sampling under non-complete constraints.

2. The inner wheel differential control method based on asynchronous sampling during vehicle turning according to claim 1, characterized in that: The step S1 is specifically as follows: S11. Based on the equally spaced division of the turning path, the tracking problem of the unmanned vehicle on the desired path is transformed into a stabilization problem for the target point, and the position subsystem of the vehicle rear wheel axle center relative to the target point under non-holonomic constraints is established. Steering subsystem Mathematical model of cascaded vehicle systems; where x1 = θ, x2 = e xi sinθ-e yi cosθ,x3=e xi cosθ+e yi sinθ;e xi =xx ir ,e yi =yy ir , (x, y) is the coordinate of the midpoint of the rear axle, θ is the angle of the vehicle body relative to the horizontal direction, (x ir ,y ir ) is the coordinate of the i-th expected position point; S12. Use the following coordinate transformation Preprocess the continuous position subsystem and construct the following discrete position subsystem: Where L1 and L2 are unknown constants, T1 is the sampling period of the steering subsystem, T2 is the sampling period of the position subsystem, and k is the sampling sequence count.

3. The inner wheel differential control method based on asynchronous sampling during vehicle turning according to claim 2, characterized in that: The step S2 is specifically as follows: S21. For the steering subsystem, the following control law is constructed to ensure the convergence of the steering subsystem and the controllability of the position subsystem When x1(0)≠0, u1(t)=-L1x1(kT1),t∈[kT1,(k+1)T1),k=0,1,2,…; When x1(0)=0, Where c is a constant not equal to 0; S22. For the position subsystem, construct the following sampling control law to achieve the stabilization of the position system t∈[kT2,(k+1)T2),k=0,1,2,…。 4. The inner wheel differential control method based on asynchronous sampling during vehicle turning according to claim 3, characterized in that: The step S3 is specifically as follows: S31. Analyze the selection scheme of control gain and sampling period in the sampling control law of the steering subsystem, and obtain the following parameter selection scheme to ensure the stability of the steering subsystem 0<|L1T1|<2; S32. Using the characteristic polynomial of the discrete position closed-loop system, the selection scheme of control gain and sampling period in the sampling control law of the position subsystem is analyzed, and the following parameter selection scheme is obtained to ensure the stability of the position subsystem.

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