2-D motorcade dynamic performance sliding mode control method for performing error adjustment based on virtual position

Abstract

The invention discloses a 2-D motorcade dynamic performance sliding mode control method for error adjustment based on a virtual position, and relates to the field of motorcade cooperative control. According to the method, a virtual position following strategy is designed under a 2-D motorcade cooperative control technical framework for the first time. A virtual position corresponding to each following vehicle is set, so that the following vehicles can predict the path change of a motorcade in advance through the respective corresponding virtual positions, and the vehicle course angle error in the following process is remarkably reduced; a novel finite time performance function is designed, a convergence region can be sensitively transformed according to an initial value of a spacing tracking error, and control parameters are automatically adjusted in real time according to an error state. Through the function, the vehicle distance error can be quickly and stably converged to a predefined area within finite time under the condition that a traditional pilot-front vehicle following strategy is adopted. The motorcade can automatically adapt to control requirements under different driving conditions, and stable operation of the motorcade under various complex road conditions is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle fleet cooperative control, and in particular to a sliding mode control method for dynamic performance of a 2-D vehicle fleet based on error adjustment of virtual positions. Background Art

[0002] As a core technology in intelligent transportation systems, 2-D platooning cooperative control technology enables multiple functions, including vehicle autonomy, informationization, and safety. It demonstrates significant potential in reducing vehicle energy consumption, shortening inter-vehicle distances, and increasing driving speeds. This technology transforms platooning applications from a one-dimensional scenario, which primarily considers vehicle spacing, to a two-dimensional one that more closely reflects real-world road conditions and takes into account both inter-vehicle spacing errors and vehicle heading angle errors. This enables complex operations widely demanded in the intelligent transportation sector, such as overtaking, obstacle avoidance, and lane changes. Its core approach is to achieve 2-D coordinated control between vehicles through inter-vehicle communication systems and intelligent control algorithms, ensuring that inter-vehicle spacing errors and vehicle heading angle errors remain within acceptable limits. In this mode, the following vehicle receives real-time driving data from the preceding vehicle and automatically maintains a preset following distance and driving direction through appropriate control methods. This enables efficient, orderly platooning that adapts to complex road conditions.

[0003] In recent years, 2-D platooning cooperative control technology has become a key area of research in intelligent transportation systems due to its significant benefits in alleviating traffic congestion and reducing exhaust emissions. Existing research primarily employs methods such as sliding mode control, backstepping control, and model predictive control. Their core goal is to achieve rapid convergence of vehicle spacing errors and vehicle heading angle errors, ensuring that the following vehicle accurately follows the trajectory of the leading vehicle. However, the vehicle error feedback mechanism and originally designed performance functions employed in traditional platooning control methods have inherent flaws, which can easily lead to serpentine oscillations in dynamic scenarios such as lane changes, seriously compromising the safety and stability of the platoon. While current research on finite-time control for 2-D platooning cooperative control has made progress, much of the focus has been on optimizing controller design steps (such as improving existing finite-time performance function parameters and designing new finite-time sliding mode surfaces). While recent research has improved control efficiency through novel finite-time sliding mode controllers, they still rely on traditional error feedback mechanisms for vehicle heading error control. For vehicle spacing error control, a fixed finite-time performance function design is used that cannot flexibly change the convergence region based on the initial value of the tracking error and cannot automatically adjust control parameters in real time based on the error state. This makes it difficult to overcome phase lag and trajectory oscillation during lane changes. The convergence rates for vehicle spacing error and vehicle heading error are slow, making them incapable of adapting to complex traffic conditions. In complex traffic situations, the platoon's stability and robustness are weak. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention provides a sliding mode control method for the dynamic performance of a 2-D convoy based on error adjustment of virtual position, which can solve the serpentine oscillation problem during the lane change of the following vehicle and optimize the efficiency and performance of the convoy collaborative control.

[0005] The technical solution of the present invention is:

[0006] A sliding mode control method for dynamic performance of a 2-D vehicle fleet with error adjustment based on virtual position, the method comprising the following steps:

[0007] Step 1: Establish a 2-D convoy dynamics model based on the vehicle's driving conditions;

[0008] Step 2: Define the coordinates of the virtual position of each following vehicle according to the 2-D convoy dynamics model and set the virtual position for each following vehicle;

[0009] Step 3: Define the formula for calculating the distance between adjacent vehicles, and based on the virtual position following strategy, define the formula for calculating the azimuth angle between the actual position and the virtual position of the following vehicle, thereby determining the formula for calculating the distance tracking error between vehicles and the constraints of the distance tracking error, and determining the formula for calculating the azimuth tracking error between vehicles;

[0010] Step 4: Based on the constraints of the spacing tracking error, design the finite time performance function according to the preset performance control (PPC) method;

[0011] Step 5: Based on the definitions of the spacing tracking error and the orientation tracking error, and the relationship between the finite-time performance function and the spacing tracking error, determine the control objectives of the convoy.

[0012] Step 6: Based on the error transformation principle and the finite-time performance function, the constrained inter-vehicle distance tracking error is converted into an unconstrained inter-vehicle distance tracking error;

[0013] Step 7: Based on the unconstrained inter-vehicle tracking error, a finite-time composite sliding mode controller is designed to achieve the control objective of the platoon.

[0014] Furthermore, according to the sliding mode control method for dynamic performance of a 2-D convoy, the 2-D convoy dynamic model in step 1 includes a dynamic model of a leading vehicle and a dynamic model of a following vehicle; the dynamic model of the leading vehicle is shown in formula (1); the dynamic model of the following vehicle is shown in formula (2);

[0015]

[0016] where x0(t), y0(t), φ0(t), v0(t), a0(t), l0(t) and Represent the horizontal coordinate, vertical coordinate, heading angle, speed, acceleration, angular velocity and angular acceleration of the leading vehicle respectively;

[0017]

[0018] f i (v i ,a i ,t)=f i0 (v i ,a i ,t)+Δf i (v i ,a i ,t) (3)

[0019] Where: x i (t), y i (t),φ i (t), v i (t), a i (t), l i (t), and Represent the horizontal coordinate, vertical coordinate, heading angle, velocity, acceleration, angular velocity and angular acceleration of the following vehicle i respectively; represents the angle controller input signal of the following vehicle i; m i is the mass of the following vehicle i; is the input signal of the distance controller following vehicle i; τ i is the engine time constant of the following vehicle i; is the error caused by the throttle or brake of the following vehicle i; is the steering wheel error of the following vehicle i; t is the time; f i (v i ,a i ,t) represents the remaining errors of the following vehicle i except the errors caused by the accelerator or brake; f i0 (v i ,a i ,t) is the error that affects the acceleration of the following vehicle i and can be obtained by calculation; Δf i (v i ,a i ,t) is the unknown error that affects the acceleration of the following vehicle i and cannot be calculated.

[0020] Furthermore, according to the sliding mode control method for the dynamic performance of the 2-D convoy, the coordinates of the virtual position of each following vehicle i are And there are:

[0021]

[0022] in The horizontal coordinate representing the virtual position of the following vehicle i; The vertical coordinate representing the virtual position of the following vehicle i; d * Represents the expected distance between adjacent vehicles and satisfies 0 <d i min <d * <d i max , d i min To ensure the minimum distance between adjacent vehicles without collision, d i max The maximum distance between adjacent vehicles to ensure smooth communication between vehicles. For ease of description, the continuous time parameter (t) is omitted.

[0023] Furthermore, according to the sliding mode control method for dynamic performance of a 2-D convoy, the virtual position following strategy is: based on the preset virtual position of the following vehicle i, the heading angle of the following vehicle i is changed, so that the actual position of the following vehicle i continuously approaches the virtual position of the following vehicle i.

[0024] Furthermore, according to the sliding mode control method for the dynamic performance of the 2-D fleet, we define represents the azimuth angle between the actual position of the following vehicle i and its virtual position. The azimuth angle between the actual position and the virtual position of the following vehicle i is calculated as follows:

[0025]

[0026] For the convenience of description, the continuous time parameter (t) is omitted.

[0027] Furthermore, according to the sliding mode control method for the dynamic performance of the 2-D convoy, the tracking error between the vehicles in step 4 is The calculation formula is (8); the orientation tracking error between the vehicles The calculation formula is formula (9);

[0028]

[0029] For the convenience of description, the continuous time parameter (t) is omitted.

[0030] According to formula (8), the spacing tracking error is further obtained The constraints are as follows:

[0031]

[0032] in, Λ i =d * -d i min , d iis the distance between the following vehicle i and the adjacent vehicle i-1. When i=1, it represents the distance between the following vehicle 1 and the leading vehicle 0. For the convenience of description, the continuous time parameter (t) is omitted.

[0033] Furthermore, according to the sliding mode control method for the dynamic performance of a 2-D fleet, the control objectives of the fleet in step 5 are as follows:

[0034] 1) Following vehicle i in the convoy at a given time It has a finite time stability;

[0035] 2) Pitch tracking error Strictly satisfy the relationship between it and the finite time performance function;

[0036] 3) Ensure the fleet arrives at the given time Finite-time string stability within .

[0037] Furthermore, according to the 2-D fleet dynamic performance sliding mode control method, the constraint condition based on the spacing tracking error in step 4 is used to design a finite time performance function according to the preset performance control PPC method as follows:

[0038] The relationship between the finite time performance function and the spacing tracking error constraining and being constrained is as follows:

[0039]

[0040] in B i (t), A i (t) represents the finite time performance function, which are as follows:

[0041]

[0042]

[0043] in δ i ,∈ i is the positive parameter of the design, For artificially set time parameters, when When the spacing tracking error Complete convergence; is the tracking error between the following vehicle i and its immediately preceding vehicle at the initial moment; δ i is a stable and relatively small constant that satisfies The relationship between i Pitch tracking error After the convergence is completed, the upper bound of the convergence region satisfies k1, k2, k3, k4, u1, u2, n1, and n2 are parameters designed to adjust the performance of the function and can be modified and adjusted according to different application scenarios. exp(·) represents the natural exponential function, that is, the exponential function with the real number e as the base. Its expression is exp(·) = e (·) ; tanh(·) is the hyperbolic tangent function, and its expression is For the convenience of description, the continuous time parameter (t) is omitted.

[0044] Furthermore, according to the sliding mode control method for the dynamic performance of a 2-D convoy, the unconstrained inter-vehicle tracking error in step 6 is as follows:

[0045]

[0046] Furthermore, according to the sliding mode control method for dynamic performance of a 2-D fleet, the design process of the finite-time sliding mode controller in step 7 is as follows:

[0047] First, define the following coupling variables:

[0048]

[0049] where q i is the design parameter, satisfying 0 i <1; N is the total number of vehicles in the fleet;

[0050] Then the finite-time sliding surface is designed as follows:

[0051]

[0052] in

[0053]

[0054] where |·| represents the absolute value of a real number, sig * (·)=|·| * sign(·); ι ij ,C i1 ,C i2 , is the set sliding surface parameter, and ι ij >0,C i1 >0,C i2 >0, For the convenience of description, the continuous time parameter (t) is omitted.

[0055] Design parameters: And order Then on the sliding surface S i1 and S​i2 On the basis of , a new composite sliding surface is introduced as follows:

[0056]

[0057] in

[0058]

[0059] in α ij , γ1,γ2 are the set parameters, α ij >0, and sig * (·)=|·| * sign(·); for the convenience of description, the continuous time parameter (t) is omitted.

[0060] Finally, the finite-time composite sliding mode controller is obtained as follows:

[0061]

[0062] And the following adaptive law:

[0063]

[0064] where σ iη1 , σ iη2 , σ iω1 , σ iω2 are positive parameters in the adaptive rate, and the adaptive law can be improved by changing the specific values of these parameters; α rij , β rij , ρ i 0<ρ i <1,α rij >1, β rij Positive constant > 1; For the convenience of description, the continuous time parameter (t) is omitted.

[0065] in

[0066]

[0067] To estimate D i and The size of the parameter D is introduced i0 and is an unknown constant such that D i0 ≥|D i |,

[0068] in and is the parameter η defined as follows i and parameter ω i Estimated value of:

[0069]

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] (1) For the first time, the present invention introduces and designs a specific two-dimensional coordinate representation of virtual positions within the framework of 2-D convoy collaborative control technology, and designs a virtual position following strategy based on the virtual position. By setting a corresponding virtual position for each following vehicle, each following vehicle can predict the path changes of the convoy in advance through its corresponding virtual position, thereby significantly reducing the vehicle heading angle error during the vehicle following process. This mechanism effectively solves the snake-like oscillation caused by pose coupling and dynamic response delay in the error feedback mechanism provided by the pilot-leading vehicle following strategy widely used in the prior art to control the vehicle heading angle error.

[0072] (2) The present invention designs a novel finite-time performance function, which can sensitively transform the convergence region according to the initial value of the spacing tracking error and automatically adjust the control parameters in real time according to the error state. Through this function, the vehicle spacing error defined based on the traditional pilot-leader following strategy can converge quickly and smoothly to the predefined region within a finite time. By coordinating the optimization of the longitudinal and lateral control of the following vehicles in the convoy, the problem of the fixed boundary performance function used in the prior art being unable to respond in time to the rapidly changing parameters in the vehicle dynamics model, resulting in slow convergence of the spacing tracking error, limited adaptability to complex scenarios, and low robustness is solved.

[0073] Of particular note, the proposed sliding mode control method for 2D platoon dynamic performance, using error adjustment based on virtual positions, successfully addresses the dynamic constraints of vehicle platoons in two-dimensional scenarios. By introducing a pre-set error adjustment mechanism and a finite-time performance function that tracks the error state, the platoon can automatically adapt to control requirements under varying driving conditions, ensuring stable operation in a variety of complex road conditions. This innovation provides new technical insights and solutions for vehicle cooperative control in intelligent transportation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 Schematic diagram of a two-dimensional convoy dynamics model with error adjustment based on virtual positions in an embodiment of the present invention;

[0075] Figure 2 Schematic diagram of the flow of the sliding mode control method for dynamic performance of a 2-D vehicle fleet with error adjustment based on virtual position according to the present invention;

[0076] Figure 3 A two-dimensional position information curve diagram of each vehicle in a fleet at different times provided by an embodiment of the present invention;

[0077] Figure 4 A graph showing the heading angle information of each vehicle in a fleet at different times provided by an embodiment of the present invention;

[0078] Figure 5 A graph showing steering wheel input information of each vehicle in a fleet at different times provided by an embodiment of the present invention;

[0079] Figure 6 A graph showing control input information of each vehicle in a fleet at different times provided by an embodiment of the present invention;

[0080] Figure 7 A graph showing the tracking error information of the distance between vehicles in a fleet at different times provided by an embodiment of the present invention;

[0081] Figure 8 This is a graph showing the position tracking error information of each vehicle in a fleet at different times, provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0082] To facilitate understanding of the present application, a more comprehensive description of the present application will be provided below with reference to the accompanying drawings. The accompanying drawings illustrate preferred embodiments of the present application. However, the present application can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and comprehensive understanding of the disclosure of the present application.

[0083] Figure 1 Schematic diagram of a two-dimensional convoy dynamics model for error compensation based on virtual positions in an embodiment of the present invention. Figure 2 FIG. 1 is a flow chart of a sliding mode control method for 2-D fleet dynamic performance based on virtual position error adjustment according to the present invention. Figure 1 and Figure 2 As shown, the sliding mode control method for 2-D convoy dynamic performance based on virtual position error adjustment includes the following steps:

[0084] Step 1: Establish a 2-D fleet dynamics model based on vehicle operation conditions;

[0085] This embodiment considers a two-dimensional planar convoy consisting of N vehicles, which consists of a leader vehicle marked as 0 and N-1 following vehicles, such as Figure 1 shown.

[0086] In this system, the dynamic model of the leading vehicle 0 is shown in formula (1), and the dynamic model of the following vehicle i is shown in formula (2).

[0087]

[0088] Among them: x0(t), y0(t), φ0(t), v0(t), a0(t), l0(t), and They represent the horizontal coordinate, vertical coordinate, heading angle, velocity, acceleration, angular velocity and angular acceleration of the leading vehicle, respectively.

[0089] The dynamic model of the following vehicle i is shown in formula (2):

[0090]

[0091] in

[0092]

[0093] This parameter can also be rewritten as:

[0094] f i (v i ,a i ,t)=f i0 (v i ,a i ,t)+Δf i (v i ,a i ,t) (3)

[0095] Where: x i (t), y i (t),φ i (t), v i (t), a i (t), l i (t), and Represent the horizontal coordinate, vertical coordinate, heading angle, velocity, acceleration, angular velocity and angular acceleration of the following vehicle i respectively; represents the angle controller input signal of the following vehicle i; m i is the mass of the following vehicle i; is the input signal of the distance controller following vehicle i; τ i is the engine time constant of the following vehicle i; is the error caused by the throttle or brake of the following vehicle i; is the steering wheel error of the following vehicle i; t is the time; f i (v i ,a i,t) represents the remaining errors of the following vehicle i except the errors caused by the accelerator or brake; f i0 (v i ,a i ,t) is the error that affects the acceleration of the following vehicle i and can be obtained by calculation; Δf i (v i ,a i ,t) is the unknown error that affects the acceleration of the following vehicle i and cannot be calculated.

[0096] Step 2: According to the 2-D convoy dynamics model, the virtual position of each following vehicle i is obtained by defining the horizontal and vertical coordinate expressions of the virtual position of each following vehicle i.

[0097] For the convenience of description, the continuous time parameter (t) is omitted, and the horizontal coordinates of the virtual position of the following vehicle i shown in formula (4) are defined as The vertical coordinate of the virtual position of the following vehicle i is shown in formula (5) That is, the virtual position of the following vehicle i is stably lagged behind the lateral position of the leading vehicle 0 by i d * The distance, d * is the desired distance between adjacent vehicles set artificially. The longitudinal position of the virtual position of the following vehicle i is aligned with the longitudinal position of the leading vehicle 0:

[0098]

[0099] In summary, the virtual position coordinates of the following vehicle i are defined as in The horizontal coordinate representing the virtual position of the following vehicle i; The vertical coordinate representing the virtual position of the following vehicle i; d * Represents the expected distance between adjacent vehicles and satisfies 0 <d i min <d * <d i max , d i min To ensure the minimum distance between adjacent vehicles without collision, d i max The maximum distance between adjacent vehicles to ensure smooth communication between vehicles.

[0100] Step 3: Based on the platoon dynamics model, the pilot-follow strategy is used to define the formula for calculating the distance between adjacent vehicles. Based on the virtual position following strategy of the following vehicle i, the formula for calculating the azimuth angle between the actual position of the following vehicle i and the virtual position of the following vehicle i is defined. This determines the distance tracking error between vehicles. The calculation formula and azimuth tracking error Calculation formula and determine the spacing tracking error constraints.

[0101] Based on the above dynamic model and the defined virtual position of the following vehicle i, for the error in the distance between adjacent vehicles, this embodiment adopts a pilot-leading vehicle following strategy, that is, the following vehicle closely follows the position of the leading vehicle, and dynamically adjusts and optimizes the distance between adjacent vehicles in the queue as the distance between adjacent vehicles changes, thereby minimizing the error in the distance between adjacent vehicles (that is, the absolute value of the difference between the actual distance between adjacent vehicles and the artificially set expected distance between adjacent vehicles). For the vehicle heading angle error, a following strategy based on the virtual position of the following vehicle i was designed for the first time, that is, the heading angle of the tracking vehicle i is changed based on the preset path and direction of the virtual position of the following vehicle i, so that the actual position of the following vehicle i continues to approach the virtual position of the following vehicle i, thereby reducing the vehicle heading angle error. Figure 1 As shown, this embodiment defines the adjacent vehicle distance d as shown in formula (6) i That is, the distance between vehicle i and vehicle i-1 (when i=1, it means the distance between the following vehicle 1 and the leading vehicle 0). Definition is the azimuth angle between the actual position of the following vehicle i and the virtual position of the following vehicle i, as shown in (7). For the convenience of description, the continuous time parameter (t) is omitted in Equations (6) and (7).

[0102]

[0103] where d i is the distance between the following vehicle i and the adjacent vehicle i-1. When i=1, it represents the distance between the following vehicle 1 and the leading vehicle 0.

[0104] For simplicity, the continuous time parameter (t) is omitted, and the spacing tracking error shown in equation (8) is determined as The calculation formula and the azimuth tracking error shown in formula (9) Calculation formula.

[0105]

[0106] where d * Represents the expected distance between adjacent vehicles set manually, that is, d * It is a parameter set artificially, indicating the distance d between adjacent vehicles. i The expected value of , and satisfies 0 <d i min <d * <d i max .d i min To ensure the minimum distance between adjacent vehicles without collision, d i max The maximum distance between adjacent vehicles to ensure smooth communication between vehicles.

[0107] According to formula (8), the spacing tracking error can be further obtained Constraints:

[0108]

[0109] in: Λ i The specific expression is The specific expression is For the convenience of description, the continuous time parameter (t) is omitted.

[0110] Step 4: Based on the constraints of the spacing tracking error, a finite-time performance function is designed according to the PPC (Prescribed Performance Control) method. This function can sensitively transform the convergence region of the spacing tracking error according to the initial value of the spacing tracking error and automatically adjust the control parameters in real time according to the error state.

[0111] In order to meet the error constraints shown in formula (10), according to the requirements of PPC (Prescribed Performance Control), the finite time performance function and The relationship between the constraint and the constrained is as follows:

[0112]

[0113] in: B i (t), A i (t) represents the finite-time performance function. The specific expression is as follows. For simplicity, the continuous-time parameter (t) is omitted in the specific expression. |·| represents the absolute value of a real number.

[0114]

[0115]

[0116] in δ i ,∈ i is the positive parameter of the design, For artificially set time parameters, when When the spacing tracking error Complete convergence; is the tracking error between the following vehicle i and its immediately preceding vehicle at the initial moment; δ i is a stable and relatively small constant that satisfies The relationship between iPitch tracking error After the convergence is completed, the upper bound of the convergence region satisfies k1, k2, k3, k4, u1, u2, n1, and n2 are parameters designed to adjust the performance of the function and can be modified and adjusted according to different application scenarios. exp(·) represents the natural exponential function, that is, the exponential function with the real number e as the base, and its expression is exp(·) = e (·) ; tanh(·) is the hyperbolic tangent function, and its expression is For the convenience of description, the continuous time parameter (t) is omitted.

[0117] Step 5: Tracking Error Based on Pitch and azimuth tracking error Definition of , and finite time performance function and spacing tracking error The relationship between them determines the control objectives of the fleet;

[0118] In this implementation, the fleet has three control objectives:

[0119] 1) Following vehicle i in the convoy at a given time It has finite time stability, that is, all vehicles (i∈V N ) tracking error and In the given Synchronous convergence is completed within , where V N ={1,2,…,N} represents the set of integers from 1 to N, It is a time parameter set by humans;

[0120] 2) Pitch tracking error Strictly satisfy the performance constraints shown in formula (11);

[0121] 3) Ensure the fleet arrives at the given time Finite time string stability (also called queue stability) within the platoon, that is, ensuring that the distance d between adjacent vehicles in the platoon is i (t) and the azimuth angle between the actual position and the virtual position of the following vehicle When state variables are disturbed (such as the preceding vehicle suddenly braking or turning), the disturbance will not propagate backward along the queue and amplify, but will gradually decay, thus maintaining the safety and efficient operation of the entire queue.

[0122] It is worth noting that in a large number of past studies and actual experiments, it is often only necessary to ensure The convergence of Therefore, this method is only applicable to Design finite-time performance functions, constrain, and suppress fluctuations.

[0123] Step 6: Based on the error transformation principle and finite time performance function, Based on this, we deduce the same convergence The constrained spacing tracking error is converted into an unconstrained error to reduce the difficulty of sliding mode controller design. Solve for its first and second derivatives with respect to time t.

[0124] Since it is extremely difficult to design a controller directly based on the constrained pitch tracking error shown in Equation (8), the constrained pitch tracking error shown in Equation (8) is converted into the unconstrained pitch tracking error shown in Equation (16) through mathematical error transformation techniques:

[0125]

[0126] It should be noted that the two variables and have the same convergence properties. This means that by Convergence, to ensure Convergence, reducing design difficulty.

[0127] To prepare for controller design in the next step, take The first and second order derivatives of time t are:

[0128]

[0129] The specific expression is:

[0130]

[0131] For simplicity of description, the continuous time parameter (t) is omitted.

[0132] Where: R i , σ i , X i , Γ i The letters introduced here are for the sake of simplicity. Their specific expressions are as follows:

[0133]

[0134] where R i According to formula (11), R i Always greater than zero.

[0135]

[0136] For simplicity, the continuous time parameter (t) is omitted in the following two equations:

[0137]

[0138] Step 7: Based on the unconstrained vehicle spacing tracking error expressed in the transformed equation (16), a finite-time composite sliding mode controller is designed using the existing composite sliding mode surface theory and finite-time stability theory (also known as finite-time stability theory) to achieve the control objective of the platoon.

[0139] To ensure the string stability of the fleet, the following coupling variables are defined:

[0140]

[0141] Where: q i is the design parameter, which satisfies 0 i ≤1, N is the total number of vehicles in the fleet. In the process, it is necessary to ensure that the defined coupling variables and Have the same convergence and dispersion properties.

[0142] This embodiment proposes a finite-time composite sliding mode surface with a faster convergence speed as follows:

[0143]

[0144] in:

[0145]

[0146] In this formula, |·| represents the absolute value of a real number, sig * (·)=|·| * sign(·)

[0147] where ι ij ,C i1 ,C i2 , The sliding surface parameters are set. The characteristics of the sliding surface can be changed by setting the parameters. The detailed value rules are as follows: ij >0,C i1 >0,C i2 >0, More specific values can be obtained based on simulation experiments. For the convenience of description, the continuous time parameter (t) is omitted.

[0148] Further design parameters according to the following rules: To facilitate the subsequent elaboration of technical content,​

[0149] On the second-order sliding surface S i1 and S i2 Based on the new composite sliding surface, a new composite sliding surface is introduced.

[0150]

[0151] in:

[0152]

[0153] in α ij , γ1 and γ2 are set parameters. The characteristics of the sliding surface can be changed by setting parameters. The design should meet the following requirements: α ij >0, and More specific values can be simulated based on simulation experiments. * (·)=|·| * sign(·); the continuous time parameter (t) is omitted.

[0154] On this basis, the finite time composite sliding mode controller is designed:

[0155] To ensure π ij The convergence of π ij The time derivative is as follows:

[0156]

[0157] Furthermore, for the sliding surface Π i1 The derivative is, for the convenience of description, the continuous time parameter (t) is omitted:

[0158]

[0159] D i ,Λ i1 The letters introduced are for the convenience of expression. The specific expression is:

[0160]

[0161] Where: f i0 f i0 (v i ,a i ,t), which is the error that affects the acceleration of the following vehicle i and can be calculated. For the convenience of description, the continuous time parameter (t) is omitted.

[0162] in:

[0163]

[0164] For the convenience of description, the continuous time parameter (t) is omitted.

[0165] Similarly, the sliding surface Π i2 The time derivative of can be expressed as:

[0166]

[0167] in: For the convenience of description, the continuous time parameter (t) is omitted.

[0168] This implementation considers the following convergence law:

[0169]

[0170] Where: α rij , β rij ,ρ is 0<ρ i <1,α rij >1, β rij A positive constant > 1. For ease of description, the continuous time parameter (t) is omitted.

[0171] To estimate D i and The size of the parameter D is introduced i0 and is an unknown constant such that D i0 ≥|D i |, For the convenience of description, the continuous time parameter (t) is omitted.

[0172] The adaptive technique is used to estimate the bounds of these parameters. Defined as:

[0173]

[0174] in and is the parameter η defined as follows i and parameter ω i Estimated value:

[0175]

[0176] Subsequently, the finite-time compound sliding mode controller is designed as follows:

[0177]

[0178] And the following adaptive law:

[0179]

[0180] where σ iη1 , σ iη2 , σ iω1 , σ iω2 are positive parameters in the adaptive rate, and the adaptive rate can be improved by changing the specific values of these parameters. In this step, only σ iη1 , σ iη2 , σ iω1 , σ iω2 It can be greater than zero, and a more specific value can be simulated based on simulation experiments. For the convenience of description, the continuous time parameter (t) is omitted.

[0181] Example

[0182] This embodiment is as follows Figure 1 Taking the 5-vehicle convoy model with 4 following vehicles and 1 leading vehicle as an example, the control of the convoy is realized by using the method of the present invention, and the corresponding numerical simulation is performed. In the simulation, the parameters of the following vehicle i are set as follows: the mass m of the following vehicle i i = 1605 kg, the engine time constant τ of vehicle i i = 0.2s, the front cross-sectional area A of the following vehicle i i =2.2m 2 , the air density at the location of the following vehicle i Drag coefficient of following vehicle i g=9.8m / s 2 , the road resistance coefficient b of the road where the following vehicle i is located i = 0.02, the distance d between the following vehicle i and its immediately preceding vehicle i (t) = 0.1tanh(t), the remaining error f of the following vehicle i except the error caused by the accelerator or brake i (v i ,a i ,t)=0.5f i0 (v i ,a i ,t). The slope angle Θ of the road followed by vehicle i i = 0. The fleet parameters are: the expected distance d between adjacent vehicles * =15m, minimum distance between adjacent vehicles d i min =9m, maximum distance between adjacent vehicles d i max = 23m. The acceleration (m / s) of the leader vehicle 0 is set as follows:

[0183]

[0184] After the parameters in the finite time performance function are determined through simulation, the finite time performance function is designed as follows:

[0185]

[0186] In this embodiment, a practical scenario of multi-lane vehicle reflow is considered.

[0187] Multi-lane vehicle merging: In this case, the initial state of each vehicle in the platoon, that is, the initial conditions of each vehicle in the platoon, are shown in Table 1, and the control parameters of each vehicle, that is, the control parameters of the following vehicle, are shown in Table 2.

[0188] Table 1 Initial conditions of each vehicle in the fleet

[0189]

[0190]

[0191] Table 2 Control parameters of the following vehicle

[0192]

[0193] Based on the above parameters, this embodiment uses the 2-D fleet dynamic performance sliding mode control method based on virtual position error adjustment of the present invention to perform simulation verification. The simulation results are as follows: Figure 3-8 As shown. Figure 3 In order to see the specific position distribution of each vehicle on the two-dimensional plane in detail, Figure 4 The heading angle information of each vehicle is accurately displayed. Obviously, the method of the present invention can successfully form a vehicle queue in a relatively short and limited time, and ensure that adjacent vehicles always maintain a safe distance and no collision occurs.

[0194] Controller and The relevant performances are presented in Figure 5 and Figure 6 In the example, the outputs of both controllers increase over time, then oscillate and decay until they reach zero. This indicates that the controller can adjust its output in real time as the vehicle spacing error and vehicle heading angle error in the platoon change until the vehicle spacing error and vehicle heading angle error in the platoon fall within the required range.

[0195] observe Figure 7 , Figure 8It can be clearly seen that the spacing tracking error and the spacing tracking error are always effectively controlled within the specified area, with minimal overshoot, indicating that the vehicle fleet has good stability and responsiveness under the control of the present invention's method. The performance function designed in this embodiment can sensitively change the convergence region based on the initial value of the tracking error, so that the error can converge quickly and smoothly to the predefined area within a preset time. It is worth mentioning that the tracking error successfully converges to a region extremely close to zero within a limited time and strictly meets the conditions, achieving vehicle platoon stability. This fully demonstrates that not only the stability of the operating state of each vehicle is achieved, but also the stability of the entire vehicle platoon is guaranteed, achieving the desired control goal.

[0196] This embodiment also theoretically analyzes the convergence of the cooperative controller designed by the present invention and the string stability (also called queue stability) of the fleet.

[0197] Theorem 1: Considering the two-dimensional planar vehicle platoon shown in equations (1) and (2), by adopting the performance transformation specified by equations (12) and (13) and the sliding mode control method for the dynamic performance of the 2-D platoon based on error adjustment based on virtual position proposed in this invention, the method includes the sliding mode surfaces shown in equations (25), (26) and (29), the controller shown in equations (40), (41) and the adaptive law shown in equation (42), the three control objectives of the platoon can be achieved:

[0198] 1) Following vehicle i in the convoy at a given time It has finite time stability, that is, all vehicles (i∈V N ) tracking error and At a given time Synchronous convergence is completed within , where V N ={1,2,…,N} represents the set of integers from 1 to N, where It is a time parameter set by humans;

[0199] 2) Pitch tracking error Strictly meet performance constraints (11);

[0200] 3) Ensure the fleet arrives at the given time Finite-time string stability within ;

[0201] The proof consists of the following three parts. For the convenience of description, the continuous time parameter (t) is omitted.

[0202] Part I, prove objective 1).

[0203] First, define a Lyapunov function:

[0204]

[0205] V ij Taking the derivative, substituting equations (32) and (36) into equation (48) yields:

[0206]

[0207] From formula (42), we can get:

[0208]

[0209] From formula (38) and formula (50), we can get:

[0210]

[0211] Using Young's inequality, we can get:

[0212]

[0213] Similarly, we can get:

[0214]

[0215] Substituting the mathematical transformation results of equations (50)(51)(52)(53) into equation (49), we obtain:

[0216]

[0217] in:

[0218]

[0219] Based on the finite time stability theorem, determine V ij is a practical finite-time stable function. Therefore, there exists a function that satisfies 0<κ i A constant κ < 1 i , so that Π i1 、Π i2 、 and In a finite time T i1 Converges to Ω i region. Here, Ω i and T i1 The definition of is as follows:

[0220]

[0221] Therefore, for the signal π within the convoy i1 ,Π i2 , and are bounded within a finite time. By selecting appropriate design parameters, it can be ensured that Π i1 and Π i2 converge to a very small region close to zero. Since Π ij and S ij are equivalent, it can be considered that Π ij ≈0. When t ≥ T i1 , the sliding mode surfaces shown in Eqs. (25) and (26) become:

[0222]

[0223] Next, a classification discussion is carried out according to the values of |z di | and |e i2 |:

[0224] Case 1: When |z di | ≥ ι ij , |e i2 | ≥ ι ij , the following two Lyapunov functions are defined:

[0225]

[0226] Taking the derivative of Eq. (59) gives:

[0227]

[0228] 2) By configuring the parameters C i1 , C i2 , such that e i2 and can converge to zero along the sliding mode surfaces S i1 = 0 and S i2 = 0 within a finite time and . Therefore, the parameters can be artificially set such that At this time is the maximum time expected to complete convergence. In this case, z di , e i2 can complete synchronous convergence within the given .

[0229] Case 2: When |z di [[ID=8))|< ι ij , |e i2 |< ι ij , Eqs. (25) and (26) are rewritten as Eqs. (61) and (62):

[0230]

[0231] Among them: sig * (·)=|·| * sign(·).

[0232] 3) When parameters α1 and α2 are selected as hour, Convergence speed is faster than The time to complete convergence is less than that in case 1. Therefore, in case 2, e i2 You can also specify Complete synchronous convergence within.

[0233] In summary, the error e i2 and is finite-time stable, i.e., within a finite time converges to a small region near the origin. i2 and are equivalent, so In time Finite time convergence is also achieved within . e i2 and tracking error have the same convergence and divergence, so the tracking error can be obtained and Can be given Complete synchronous convergence within.

[0234] Part II proves the following objective:

[0235] The performance shown in formula (11) is achieved (i.e., the spacing tracking error Can the performance constraints (11) be strictly met?

[0236] From formula (16), we can get:

[0237]

[0238] After mathematical transformation, we can further obtain:

[0239]

[0240] After simplifying formula (64), we can get:

[0241]

[0242] Therefore, when ε is reached diWhen the stability of the model is guaranteed, the predefined constraint requirements shown in formula (11) can be met.

[0243] Part III Proof Objective 3):

[0244] 3) Can the team be guaranteed to arrive at the designated time? Finite-time string stability within ;

[0245] based on hour The fact that, combined with formula (14) and ε di and e di The equivalence relationship between them can be obtained:

[0246]

[0247] Due to 0 i ≤1, thus achieving the goal of finite-time string stability.

[0248] It should be understood that, inspired by the technical concept of the present invention, those skilled in the art may make various improvements or changes based on the above description without departing from the content of the present invention, which still fall within the scope of protection of the present invention.​

Claims

1. A sliding mode control method for 2-D fleet dynamic performance based on error adjustment of virtual position, characterized by: The method comprises the following steps: Step 1: Establish a 2-D convoy dynamics model based on the vehicle's driving conditions; Step 2: Define the coordinates of the virtual position of each following vehicle according to the 2-D convoy dynamics model and set the virtual position for each following vehicle; Step 3: Define the formula for calculating the distance between adjacent vehicles, and based on the virtual position following strategy, define the formula for calculating the azimuth angle between the actual position and the virtual position of the following vehicle, thereby determining the formula for calculating the distance tracking error between vehicles and the constraints of the distance tracking error, and determining the formula for calculating the azimuth tracking error between vehicles; Step 4: Based on the constraints of the spacing tracking error, design the finite time performance function according to the preset performance control (PPC) method; Step 5: Based on the definitions of the spacing tracking error and the orientation tracking error, and the relationship between the finite-time performance function and the spacing tracking error, determine the control objectives of the convoy. Step 6: Based on the error transformation principle and the finite-time performance function, the constrained inter-vehicle distance tracking error is converted into an unconstrained inter-vehicle distance tracking error; Step 7: Based on the unconstrained inter-vehicle tracking error, a finite-time composite sliding mode controller is designed to achieve the control objective of the platoon.

2. The sliding mode control method for dynamic performance of a 2-D vehicle fleet according to claim 1, characterized in that: The 2-D convoy dynamics model in step 1 includes a dynamics model of the leading vehicle and a dynamics model of the following vehicle; the dynamics model of the leading vehicle is shown in formula (1); the dynamics model of the following vehicle is shown in formula (2); where x0(t), y0(t), φ0(t), v0(t), a0(t), l0(t) and Represent the horizontal coordinate, vertical coordinate, heading angle, speed, acceleration, angular velocity and angular acceleration of the leading vehicle respectively; f i (v i ,a i ,t)=f i0 (v i ,a i ,t)+Δf i (v i ,a i ,t) (3) Where: x i (t), y i (t),φ i (t), v i (t), a i (t), l i (t), and Represent the horizontal coordinate, vertical coordinate, heading angle, velocity, acceleration, angular velocity and angular acceleration of the following vehicle i respectively; represents the angle controller input signal of the following vehicle i; m i is the mass of the following vehicle i; is the input signal of the distance controller following vehicle i; τ i is the engine time constant of the following vehicle i; is the error caused by the throttle or brake of the following vehicle i; is the steering wheel error of the following vehicle i; t is the time; f i (v i ,a i ,t) represents the remaining errors of the following vehicle i except the errors caused by the accelerator or brake; f i0 (v i ,a i ,t) is the error that affects the acceleration of the following vehicle i and can be obtained by calculation; Δf i (v i ,a i ,t) is the unknown error that affects the acceleration of the following vehicle i and cannot be calculated.

3. The sliding mode control method for dynamic performance of a 2-D vehicle fleet according to claim 2, characterized in that: The coordinates of the virtual position of each following vehicle i are And there are: in The horizontal coordinate representing the virtual position of the following vehicle i; The vertical coordinate representing the virtual position of the following vehicle i; d * Represents the expected distance between adjacent vehicles and satisfies 0 <d imin <d * <d imax , d imin To ensure the minimum distance between adjacent vehicles without collision, d imax The maximum distance between adjacent vehicles to ensure smooth communication between vehicles.

4. The sliding mode control method for dynamic performance of a 2-D vehicle fleet according to claim 3, characterized in that: The virtual position following strategy is: based on the preset virtual position of the following vehicle i, the heading angle of the following vehicle i is changed so that the actual position of the following vehicle i continuously approaches the virtual position of the following vehicle i.

5. The sliding mode control method for dynamic performance of a 2-D vehicle fleet according to claim 4, characterized in that: definition represents the azimuth angle between the actual position of the following vehicle i and its virtual position. The azimuth angle between the actual position and the virtual position of the following vehicle i is calculated as follows:

6. The sliding mode control method for dynamic performance of a 2-D vehicle fleet according to claim 5, characterized in that: The distance tracking error between vehicles in step 4 The calculation formula is (8); the orientation tracking error between the vehicles The calculation formula is (9), where the continuous time parameter (t) is omitted for the convenience of description; According to formula (8), the spacing tracking error is further obtained The constraints are as follows: in, Λ i =d * -d imin , d i is the distance between the following vehicle i and the adjacent vehicle i-1. When i=1, it represents the distance between the following vehicle 1 and the leading vehicle 0.

7. The sliding mode control method for dynamic performance of a 2-D vehicle fleet according to claim 6, characterized in that: The control objectives of the fleet described in step 5 are as follows: 1) Following vehicle i in the convoy at a given time It has finite time stability; 2) Pitch tracking error Strictly satisfy the relationship between it and the finite time performance function; 3) Ensure the fleet arrives at the given time Finite-time string stability within .

8. The sliding mode control method for dynamic performance of a 2-D vehicle fleet according to claim 6, characterized in that: Based on the constraint of the spacing tracking error described in step 4, the finite time performance function is designed according to the preset performance control PPC method as follows: The relationship between the finite time performance function and the spacing tracking error constraining and being constrained is as follows: in B i (t), A i (t) represents the finite time performance function, which are as follows: in δ i ,∈ i is the positive parameter of the design, For artificially set time parameters, when When the spacing tracking error Complete convergence; is the tracking error between the following vehicle i and its immediately preceding vehicle at the initial moment; δ i is a stable and relatively small constant that satisfies The relationship between i Pitch tracking error After the convergence is completed, the upper bound of the convergence region satisfies k1, k2, k3, k4, u1, u2, n1, and n2 are parameters designed to adjust the performance of the function and can be modified and adjusted according to different application scenarios. exp(·) represents the natural exponential function, that is, the exponential function with the real number e as the base, and its expression is exp(·) = e (·) ; tanh(·) is the hyperbolic tangent function, and its expression is 9. The sliding mode control method for dynamic performance of a 2-D vehicle fleet according to claim 8, characterized in that: The unconstrained vehicle-to-vehicle distance tracking error described in step 6 is as follows:

10. The sliding mode control method for dynamic performance of a 2-D vehicle fleet according to claim 9, characterized in that: The design process of the finite-time sliding mode controller described in step 7 is as follows: First, define the following coupling variables: where q i is the design parameter, satisfying 0 i <1; N is the total number of vehicles in the fleet;​ Then the finite-time sliding surface is designed as follows: in where |·| represents the absolute value of a real number, sig * (·)=|·| * sign(·);l ij ,C i1 ,C i2 , is the set sliding surface parameter, and ι ij >0,C i1 >0,C i2 >0, Design parameters: And order Then on the sliding surface S i1 and S i2 On the basis of , a new composite sliding surface is introduced as follows: in in α ij , γ1,γ2 are the set parameters, α ij >0, and sig * (·)=|·| * sign(·); Finally, the finite-time composite sliding mode controller is obtained as follows: And the following adaptive law: where σ iη1 , σ iη2 , σ iω1 , σ iω2 are positive parameters in the adaptive rate, and the adaptive law can be improved by changing the specific values of these parameters; α rij , β rij , ρ i 0<ρ i <1,α rij >1, β rij Positive constant > 1; in where f i0 f i0 (v i ,α i ,t), which is the error that affects the acceleration of the following vehicle i and can be obtained by calculation; in order to estimate D i and The size of the parameter D is introduced i0 and is an unknown constant such that D i0 ≥|D i |, in and is the parameter η defined as follows i and parameter ω i Estimated value of:

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