A fixed time vehicle cooperative control method maintaining connectivity

Abstract

The application provides a fixed-time vehicle cooperative control method for keeping communication, and relates to the technical field of vehicle cooperative control.The application constructs a new dynamic model for vehicles in a vehicle group, and obtains an error dynamic model of the system according to the new dynamic model.A control optimization problem and a communication distance constraint function are defined according to a control target and a requirement, and then an upper optimization controller is designed, and a lower tracking controller is further determined.The upper design is a zero-gradient and distributed optimization algorithm based on a sliding mode, and is combined with a logarithmic barrier penalty function method, and is used for solving the optimization problem under the communication distance constraint, and the lower layer is combined with a predefined time command filter in the vehicle controller, so that the derivative of the control signal is approximated, and complexity explosion is prevented.The double-layer design jointly constitutes an improved double-layer fixed-time vehicle cooperative control strategy, and a group of vehicles can realize optimal consistency of zero-spacing error while keeping communication connection.

Description

Technical Field

[0001] This invention relates to the field of vehicle cooperative control technology, specifically a fixed-time vehicle cooperative control method for maintaining connectivity. Background Technology

[0002] Cooperative control of autonomous vehicles is an important branch of intelligent transportation systems and has attracted widespread attention. Currently, most research on vehicle cooperative control (such as: [R. Rajamani, H.-S. Tan, B. Law, et al., “Demonstration of integrated longitudinal and lateral control for the operation of automated vehicles in platoons,” IEEE Trans. Control Syst. Technol., vol. 8, no. 4, pp. 695-708, Jul. 2000] and [S. Wen and G. Guo, “Distributed trajectory optimization and sliding mode control of heterogenousvehicular platoons,” IEEE Trans. Intell. Transp. Syst., vol. 23, no. 7, pp.7096-7111, Jul. 2022.]) only considers longitudinal control, that is, using information from surrounding vehicles to adjust the distance between the driver vehicle and the vehicle in front. However, in real-world scenarios, such as merging and lane changing, vehicle movement occurs in a two-dimensional space, involving both longitudinal and lateral coordinated control. Existing longitudinal and lateral coordinated vehicle control (e.g., [W.-D. Xu, X.-G. Guo, J.-L. Wang, et al., “Nonlinear disturbance observer-based fault-tolerant sliding-modecontrol for 2-D plane vehicular platoon with UTVFD and ANAS,” IEEE Transactions on Cybernetics, Apr. 2024.(DOI: 10.1109 / TCYB.2022.3222496)]) is a coordinated method defined by Euclidean distance and azimuth angle. However, due to the lack of direct connection with the azimuth angle of the preceding vehicle, the trajectory of the following vehicle is not unique. Furthermore, reliable inter-vehicle communication is fundamental to achieving coordinated control. However, the transmission capacity of onboard communication equipment is limited by various factors, hindering the propagation of wireless signals.Many cooperative control strategies that consider communication distance constraints (e.g., [Q. Zhang and G. Guo, “Prescribed-time cooperative control of connected and autonomous vehicles on rough roads,” IEEE Transactions on Vehicular Technology, Sep. 2024. (DOI: 10.1109 / TVT.2024.3454969)]) neglect the influence of the Euclidean distance between vehicles. Vehicle cooperative control requires a high convergence speed for the cooperative error; if the response rate is too slow, effective control performance cannot be guaranteed. Existing research on vehicle cooperative control (e.g., [C.-L. Zhang and G. Guo, “Prescribed performance sliding mode control of vehicular platoons with input delays,” IEEE Transactions on Intelligent Transportation Systems, Mar. 2024. (DOI: 10.1109 / TITS.2024.3368520)]) is mostly asymptotically stable.

[0003] Current research on vehicle cooperation mainly focuses on the unrealistic problem of longitudinal cooperation, and has not yet achieved longitudinal and lateral cooperative control that satisfies Euclidean distance constraints while ensuring the uniqueness of vehicle trajectories. Furthermore, it has neglected the convergence speed requirements of connected vehicle cooperative control. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to propose a fixed-time vehicle cooperative control method for maintaining connectivity, comprising:

[0005] Step 1: Perform force analysis on each vehicle in the target convoy, construct a dynamic model for each vehicle, obtain the dynamic model of the lead vehicle and the dynamic models of all other vehicles except the lead vehicle. The target convoy contains multiple vehicles, each vehicle is assigned a number, all vehicles are arranged according to their numbers, the vehicle with the smallest number is designated as the lead vehicle, and all vehicles are led by the lead vehicle according to their numbers.

[0006] Step 2: Determine the leading vehicle's forward position Based on the leading vehicle's forward position The dynamic model of the leading vehicle is transformed to obtain the transformed dynamic model of the leading vehicle, and the third dynamic model of the other vehicles is determined.i The front position of the vehicle According to the i The front position of the vehicle For the vehicles other than the lead vehicle, the first i The vehicle's dynamics model is transformed to obtain the first... i The transformation dynamics model of the vehicle is obtained, and then the transformation dynamics models of other vehicles except the lead vehicle are obtained. The distance error between adjacent vehicles is determined. Based on the distance error, the transformation dynamics model of the lead vehicle and the transformation dynamics models of other vehicles except the lead vehicle, an error dynamics model is constructed.

[0007] Step 3: Define the communication constraints in the Euclidean sense, and determine the control optimization problem and the communication distance constraint function;

[0008] Step 4: Based on the error dynamics model, the optimization problem, and the communication distance constraint function, design the upper-level optimization controller. ;

[0009] Step 5: Based on the error dynamics model and the upper-level optimization controller A lower-level tracking controller is designed to control the vehicle.

[0010] Optionally, the dynamic model of the leading vehicle described in step 1 is expressed by the following formula:

[0011] ;

[0012] ;

[0013] ;

[0014] in,

[0015] ;

[0016] ;

[0017] ;

[0018] in, yes Time derivative, This indicates the position and orientation of the lead vehicle in the inertial coordinate system. The ordinate represents the position of the lead vehicle in the inertial coordinate system. The x-coordinate represents the position of the lead vehicle in the inertial coordinate system. This indicates the orientation angle of the lead vehicle in the inertial coordinate system. This indicates the speed of the lead vehicle in the moving coordinate system. This represents the linear velocity of the lead vehicle in the moving coordinate system. This represents the angular velocity of the lead vehicle in the moving coordinate system. yes Time derivative, This represents the acceleration of the lead vehicle in the moving coordinate system. This represents the linear acceleration of the lead vehicle in the moving coordinate system. This represents the angular acceleration of the lead vehicle in the moving coordinate system.

[0019] Optionally, the dynamic models of the vehicles other than the lead vehicle mentioned in step 1 are specifically represented by the following formula:

[0020] ;

[0021] ;

[0022] ;

[0023] in,

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] in, yes Time derivative, This indicates the number of vehicles other than the lead vehicle. The position and orientation of the vehicle in the inertial coordinate system. , N This indicates the number of vehicles other than the lead vehicle. Indicates the first The ordinate of the vehicle's position in the inertial coordinate system. Indicates the first The x-coordinate of the vehicle's position in the inertial coordinate system. Indicates the first The vehicle's orientation angle in the inertial coordinate system. Indicates the first The speed of the vehicle in the moving coordinate system. Indicates the first The linear velocity of the vehicle in the moving coordinate system. Indicates the first The angular velocity of the vehicle in the moving coordinate system. yes Time derivative, Indicates the first The acceleration of the vehicle in the moving coordinate system. Indicates the first The linear acceleration of the vehicle in the moving coordinate system. Indicates the first The angular acceleration of the vehicle in the moving coordinate system. yes The time derivative, Indicates the first i Vehicle input, It is the first The vehicle's accelerator or brake input, It is the first The car's steering wheel input, It is the first The vehicle's quality, It is the first The engine time constant of a vehicle. It is the first Air density in a car It is the first The cross-sectional area of ​​a vehicle. It is the first The aerodynamic drag coefficient of a vehicle. It is the first The rolling resistance coefficient of a vehicle's tires. It is the gravitational constant. It refers to the road slope.

[0034] Optionally, the transformation dynamics model of the leading vehicle in step 2 is expressed by the following formula:

[0035] ；

[0036] ;

[0037] in,

[0038] ；

[0039] ；

[0040] ;

[0041] in, yes Time derivative, This indicates the forward position of the lead vehicle after the conversion. This indicates the longitudinal position of the lead vehicle after the conversion. Indicates the lateral position of the lead vehicle after the conversion; yes Time derivative, The speed of the leading vehicle after the conversion. This indicates the longitudinal speed of the leading vehicle after the conversion. This indicates the lateral speed of the leading vehicle after the conversion. This indicates the acceleration of the leading vehicle after the conversion. This represents the longitudinal acceleration of the lead vehicle after the conversion. This indicates the lateral acceleration of the leading vehicle after the conversion.

[0042] Optionally, in step 2, among the vehicles other than the lead vehicle, the [number]th [vehicle]... i The front position of the vehicle This can be expressed by the following formula:

[0043] ;

[0044] in, Represents the transformed th The longitudinal position of the vehicle Represents the transformed th The lateral position of the vehicle, Indicates the first The straight-line distance between the vehicle's center of gravity and its front end;

[0045] Based on this, the first i The transformation dynamics model of a vehicle is expressed by the following formula:

[0046] ;

[0047] ;

[0048] ;

[0049] in,

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] in, yes Time derivative, yes Time derivative, Represents the transformed th The speed of the car Represents the transformed th The longitudinal speed of the vehicle, Represents the transformed th The vehicle's lateral speed, yes Time derivative, Represents the transformed th The acceleration of the vehicle, Represents the transformed th The longitudinal acceleration of the vehicle, Represents the transformed th The vehicle's lateral acceleration, and Indicates the transformed th Vehicle control inputs, for The first time derivative, for The second time derivative, yes The inverse matrix;

[0059] Optionally, the distance error between two adjacent vehicles in step 2 is expressed by the following formula:

[0060] ;

[0061] in, , Indicates the first Car and thei -1 longitudinal spacing error of vehicles on a two-dimensional plane; Indicates the first Car and the i -1 lateral spacing error of vehicles on a two-dimensional plane; It is the first Car and the The expected constant distance between vehicles Indicates the first Car and the i -1 The expected constant distance of a vehicle in the longitudinal direction on a two-dimensional plane; Indicates the first Car and the i -1 The expected constant distance that a vehicle travels laterally in a two-dimensional plane; Indicates the first i -1 vehicle's front position;

[0062] Based on this, the error dynamics model is expressed by the following formula:

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] in, express The first derivative in time, Indicates the first Vehicle speed error, Indicates the first The acceleration error of the vehicle, for The first time derivative, for The first time derivative, for Third-order time derivative for The third time derivative, Indicates the first i -1. Time derivative of the longitudinal acceleration of the vehicle. Indicates the first i -1 The time derivative of the lateral acceleration of the vehicle.

[0069] Optionally, the communication constraint condition described in step 3 is... Vehicle and the Euclidean distance between -1 vehicles Less than the maximum effective communication distance Specifically, it is expressed by the following formula:

[0070] ;

[0071] in, t represents time. This can be expressed by the following formula:

[0072] ;

[0073] in, Represents the transformed th -1. The longitudinal position of the vehicle. Represents the transformed th The lateral position of the vehicle;

[0074] The control optimization problem can be expressed by the following formula:

[0075] ;

[0076] ;

[0077] in, , For the first The objective function of the vehicle, It is all spacing errors stack vector, For the first Vehicle spacing error, It is the optimal solution to the control optimization problem. It is the communication distance constraint function, specifically expressed by the following formula:

[0078] .

[0079] Optionally, the upper-level optimization controller described in step 4 Specifically, it is expressed by the following formula:

[0080] ;

[0081] in,

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] The definition of the power sign function is: α1, α2, and α3 are constants and 0 < α1, α2 < 1. T1 and T2 are predefined time constants satisfying T1, T2 > 0. The two-dimensional column vector s... i It is a sliding flow pattern, L bf,i (e i ) is the constructed logarithmic barrier penalty function, {e i |g i ,com(e i )<0}, It is function L bf,i (e i ) on its independent variable e i The derivative of It is function L bf,i (e i ) on its independent variable e i The second derivative, It is the inverse of the second derivative matrix. It is an auxiliary variable, k 1+ , k 1- ρ and k are control parameters. bf,i As a preset positive value, N represents the number of vehicles other than the lead vehicle. i Let i represent the set of vehicles whose numbers are adjacent to the i-th vehicle.

[0088] Optionally, the lower-level tracking controller mentioned in step 5 is specifically represented by the following formula:

[0089] ;

[0090] ;

[0091] in

[0092] ;

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] in, u ε,i For vehicles i The input signal, i.e., the acceleration control signal, u h,i For virtual speed control signals, speed deviation error E v,i = ( E v,x,i , E v,y,i ), E v,x,i express x Velocity deviation error in the axial direction; E v,y,i express y Velocity deviation error in the axial direction; acceleration deviation error E a,i = ( E a,x,i , E a,y,i ), E a,x,i express x Acceleration deviation error in the axial direction; E a,y,i express y Acceleration deviation error in the axial direction; k Ev , k Ea and α 3 is a preset parameter, and it satisfies... k Ev ≥1 / 2, k Ea ≥1 / 2, 0< α 3 < 1; T 3 is a predefined time constant, and T 3>0; k ε1 and k ε2 These are preset parameters. T ε For a predefined time constant, and T ε >0; subscript , and This represents the filter output signal. for Time derivative, for Time derivative, Represents the filter error, satisfying eε1,1,i =( e ε1,1,x,i , e ε1,1,y,i )= - ε 1,1,i , e 𝜀1,2,i =( e ε1,2,x,i , e ε1,2,y,i )= u ε,i - ε 1,2,i , e ε1,1,x,i Indicates the corresponding virtual control signal Filter error e ε1,1,i exist x Dimensions in the axial direction e ε1,1,y,i Indicates the corresponding virtual control signal Filter error e ε1,1,i exist y Dimensions along the axial direction; e ε1,2,x,i Indicates correspondence u ε,i Filter error e ε1,2,i exist x Dimensions along the axial direction; e ε1,2,y,i Indicates correspondence u ε,i Filter error e ε1,2,i exist y Dimensions along the axial direction.

[0099] The beneficial effects of adopting the above technical solution are as follows:

[0100] This invention provides a fixed-time vehicle cooperative control method that maintains connectivity. Specifically, it designs a sliding mode-based zero-gradient and distributed optimization algorithm, combined with the logarithmic obstacle penalty function method, to solve the optimization problem under communication distance constraints, achieving the desired vehicle spacing within a specified time. A predefined time command filter is incorporated into the vehicle controller to approximate the derivative of the control signal, preventing complexity explosion. Furthermore, an improved two-layer fixed-time vehicle cooperative control strategy is proposed, which can achieve optimal consistency with zero spacing error while maintaining communication connectivity. Attached Figure Description

[0101] Figure 1This is a schematic flowchart of a fixed-time vehicle cooperative control method for maintaining connectivity in an embodiment of the present invention;

[0102] Figure 2 This is a schematic diagram of the front position in an embodiment of the present invention;

[0103] Figure 3 The motion trajectories of the four vehicles under the hierarchical controller in this embodiment of the invention;

[0104] Figure 4 Figure (a) is a schematic diagram of the evolution of speed deviation over time in an embodiment of the present invention, Figure (b) is a schematic diagram of the evolution of speed deviation over time in vehicle 1, Figure (c) is a schematic diagram of the evolution of speed deviation over time in vehicle 2, and Figure (c) is a schematic diagram of the evolution of speed deviation over time in vehicle 3.

[0105] Figure 5 Figure 1 is a schematic diagram of the evolution of the spacing error over time in an embodiment of the present invention. Figure 2 is a schematic diagram of the evolution of the spacing error of vehicle 1 over time, Figure 3 is a schematic diagram of the evolution of the spacing error of vehicle 2 over time, and Figure 4 is a schematic diagram of the evolution of the spacing error of vehicle 3 over time.

[0106] Figure 6 The filtering error in the embodiments of the present invention e ε1,1,i A schematic diagram illustrating the evolution over time, where Figure (a) shows the filtering error of vehicle 1. e ε1,1,i A schematic diagram illustrating the evolution over time; Figure (b) shows the filtering error of vehicle 2. e ε1,1,i A schematic diagram illustrating the evolution over time; Figure (c) shows the filtering error of vehicle 3. e ε1,1,i A schematic diagram illustrating the evolution over time;

[0107] Figure 7 The filtering error in the embodiments of the present invention e ε1,2,i A schematic diagram illustrating the evolution over time, where Figure (a) shows the filtering error of vehicle 1. e ε1,2,i A schematic diagram illustrating the evolution over time; Figure (b) shows the filtering error for vehicle 2. e ε1,2,i A schematic diagram illustrating the evolution over time; Figure (c) shows the filtering error of vehicle 3. e ε1,2,i A diagram illustrating the evolution over time. Detailed Implementation

[0108] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0109] To address the problems existing in current technologies, this invention aims to solve the problem of rapid cooperative control of connected vehicles with distance constraints. It proposes a novel distributed two-layer fixed-time control strategy that can achieve the desired cooperative relationship while maintaining communication connectivity. Specifically, this invention provides a fixed-time vehicle cooperative control method that maintains connectivity, combined with… Figure 1 This may include the following steps:

[0110] Step 1: Perform force analysis on each vehicle in the target convoy, construct a dynamic model for each vehicle, obtain the dynamic model of the lead vehicle and the dynamic models of all other vehicles except the lead vehicle. The target convoy contains multiple vehicles, each vehicle is assigned a number, all vehicles are arranged according to their numbers, the vehicle with the smallest number is designated as the lead vehicle, and all vehicles are led by the lead vehicle according to their numbers.

[0111] The dynamic model of the leading vehicle described in step 1 is expressed by the following formula:

[0112] ；

[0113] ；

[0114] ；

[0115] in,

[0116] ；

[0117] ；

[0118] ;

[0119] in, yes Time derivative, This indicates the position and orientation of the lead vehicle in the inertial coordinate system. The ordinate represents the position of the lead vehicle in the inertial coordinate system. The x-coordinate represents the position of the lead vehicle in the inertial coordinate system. This indicates the orientation angle of the lead vehicle in the inertial coordinate system. This indicates the speed of the lead vehicle in the moving coordinate system. This represents the linear velocity of the lead vehicle in the moving coordinate system. This represents the angular velocity of the lead vehicle in the moving coordinate system. yes Time derivative, This represents the acceleration of the lead vehicle in the moving coordinate system. This represents the linear acceleration of the lead vehicle in the moving coordinate system. This represents the angular acceleration of the lead vehicle in the moving coordinate system.

[0120] The dynamic models of the vehicles other than the lead vehicle mentioned in step 1 are specifically represented by the following formula:

[0121] ；

[0122] ;

[0123] ;

[0124] in,

[0125] ；

[0126] ；

[0127] ；

[0128] ；

[0129] ；

[0130] ；

[0131] ；

[0132] ；

[0133] ;

[0134] in, yes Time derivative, This indicates the number of vehicles other than the lead vehicle. The position and orientation of the vehicle in the inertial coordinate system. , NThis indicates the number of vehicles other than the lead vehicle. Indicates the first The ordinate of the vehicle's position in the inertial coordinate system. Indicates the first The x-coordinate of the vehicle's position in the inertial coordinate system. Indicates the first The vehicle's orientation angle in the inertial coordinate system. Indicates the first The speed of the vehicle in the moving coordinate system. Indicates the first The linear velocity of the vehicle in the moving coordinate system. Indicates the first The angular velocity of the vehicle in the moving coordinate system. yes Time derivative, Indicates the first The acceleration of the vehicle in the moving coordinate system. Indicates the first The linear acceleration of the vehicle in the moving coordinate system. Indicates the first The angular acceleration of the vehicle in the moving coordinate system. yes The time derivative, Indicates the first i Vehicle input, It is the first The vehicle's accelerator or brake input, It is the first The car's steering wheel input, It is the first The vehicle's quality, It is the first The engine time constant of a vehicle. It is the first Air density in a car It is the first The cross-sectional area of ​​a vehicle. It is the first The aerodynamic drag coefficient of a vehicle. It is the first The rolling resistance coefficient of a vehicle's tires. It is the gravitational constant. It refers to the road slope.

[0135] Step 2: Determine the leading vehicle's forward position Based on the leading vehicle's forward position The dynamic model of the leading vehicle is transformed to obtain the transformed dynamic model of the leading vehicle, and the third dynamic model of the other vehicles is determined. iThe front position of the vehicle According to the i The front position of the vehicle For the vehicles other than the lead vehicle, the first i The vehicle's dynamics model is transformed to obtain the first... i The transformation dynamics model of the vehicle is obtained, and then the transformation dynamics models of other vehicles except the lead vehicle are obtained. The distance error between adjacent vehicles is determined. Based on the distance error, the transformation dynamics model of the lead vehicle and the transformation dynamics models of other vehicles except the lead vehicle, an error dynamics model is constructed.

[0136] The transformation dynamics model of the leading vehicle in step 2 is expressed by the following formula:

[0137] ；

[0138] ;

[0139] in,

[0140] ；

[0141] ；

[0142] ;

[0143] in, yes Time derivative, This indicates the forward position of the lead vehicle after the conversion. This indicates the longitudinal position of the lead vehicle after the conversion. Indicates the lateral position of the lead vehicle after the conversion; yes Time derivative, The speed of the leading vehicle after the conversion. This indicates the longitudinal speed of the leading vehicle after the conversion. This indicates the lateral speed of the leading vehicle after the conversion. This indicates the acceleration of the leading vehicle after the conversion. This represents the longitudinal acceleration of the lead vehicle after the conversion. This indicates the lateral acceleration of the leading vehicle after the conversion.

[0144] In step 2, among the vehicles other than the lead vehicle, the first... i The front position of the vehicle This can be expressed by the following formula:

[0145] ;

[0146] in, Represents the transformed th The longitudinal position of the vehicle Represents the transformed th The lateral position of the vehicle, Indicates the first The straight-line distance between the vehicle's center of gravity and its front end, combined with Figure 2 , where point Point is the location of the centroid. This refers to the front of the vehicle.

[0147] Based on this, the first i The transformation dynamics model of a vehicle is expressed by the following formula:

[0148] ;

[0149] ;

[0150] ;

[0151] in,

[0152] ;

[0153] ;

[0154] ;

[0155] ;

[0156] ;

[0157] ;

[0158] ;

[0159] ;

[0160] in, yes Time derivative, yes Time derivative, Represents the transformed th The speed of the car Represents the transformed th The longitudinal speed of the vehicle, Represents the transformed th The vehicle's lateral speed, yes Time derivative, Represents the transformed th The acceleration of the vehicle, Represents the transformed th The longitudinal acceleration of the vehicle, Represents the transformed th The vehicle's lateral acceleration, and Indicates the transformed th Vehicle control inputs, for The first time derivative, for The second time derivative, yes The inverse matrix;

[0161] The distance error between two adjacent vehicles in step 2 is expressed by the following formula:

[0162] ;

[0163] in, , Indicates the first Car and the i -1 longitudinal spacing error of vehicles on a two-dimensional plane; Indicates the first Car and the i -1 lateral spacing error of vehicles on a two-dimensional plane; It is the first Car and the The expected constant distance between vehicles Indicates the first Car and the i -1 The expected constant distance of a vehicle in the longitudinal direction on a two-dimensional plane; Indicates the first Car and the i -1 The expected constant distance that a vehicle travels laterally in a two-dimensional plane; Indicates the first i -1 vehicle's front position;

[0164] Based on this, the error dynamics model is expressed by the following formula:

[0165] ;

[0166] ;

[0167] ;

[0168] ;

[0169] ;

[0170] in, express The first derivative in time, Indicates the first Vehicle speed error, Indicates the first The acceleration error of the vehicle, for The first time derivative, for The first time derivative, for Third-order time derivative for The third time derivative, Indicates the first i -1. Time derivative of the longitudinal acceleration of the vehicle. Indicates the first i -1 The time derivative of the lateral acceleration of the vehicle.

[0171] Step 3: Define the communication constraints in the Euclidean sense, and determine the control optimization problem and the communication distance constraint function;

[0172] The communication constraints described in step 3 Vehicle and the Euclidean distance between -1 vehicles Less than the maximum effective communication distance Specifically, it is expressed by the following formula:

[0173] ;

[0174] in, t represents time. This can be expressed by the following formula:

[0175] ;

[0176] in, Represents the transformed th -1. The longitudinal position of the vehicle. Represents the transformed th The lateral position of the vehicle;

[0177] The control optimization problem can be expressed by the following formula:

[0178] ;

[0179] ;

[0180] in, , For the first The objective function of the vehicle, It is all spacing errors stack vector, For the first Vehicle spacing error, It is the optimal solution to the control optimization problem. It is the communication distance constraint function, specifically expressed by the following formula:

[0181] .

[0182] If the above optimization problem can be solved, then the cooperative control of connected vehicles with communication maintenance constraints will be realized.

[0183] Step 4: Based on the error dynamics model, the optimization problem, and the communication distance constraint function, design the upper-level optimization controller. ;

[0184] The upper-level optimization controller mentioned in step 4 Specifically, it is expressed by the following formula:

[0185] ;

[0186] in,

[0187] ;

[0188] ;

[0189] ;

[0190] ;

[0191] ;

[0192] The definition of the power sign function is: α1, α2, and α3 are constants and 0 < α1, α2 < 1. T1 and T2 are predefined time constants satisfying T1, T2 > 0. The two-dimensional column vector s... i It is a sliding flow pattern, L bf,i (e i ) is the constructed logarithmic barrier penalty function, {e i |g i ,com(e i )<0}, It is function L bf,i (e i ) on its independent variable e iThe derivative of It is function L bf,i (e i ) on its independent variable e i The second derivative, It is the inverse of the second derivative matrix. It is an auxiliary variable, k 1+ , k 1- ρ and k are control parameters. bf,i As a preset positive value, N represents the number of vehicles other than the lead vehicle. i Let i represent the set of vehicles whose numbers are adjacent to the i-th vehicle.

[0193] Determine the upper-level optimization controller At that time, for those with error dynamics The vehicle fleet designed the aforementioned upper-level optimization controller. And prove the upper-level optimized controller The convergence of the expression is demonstrated in the following specific steps:

[0194] Design a Lyapunov function: ,when When, its time derivative satisfies

[0195] ;

[0196] According to the pre-defined time stability theory, in Within a time period, the first The end sliding surface of the vehicle It converges to 0.

[0197] when At that time, the Lyapunov function was designed as follows: Its time derivative satisfies

[0198] ;

[0199] in, It is a matrix (∇) ee L bf,i ( e i )) -1 The minimum eigenvalue, therefore the optimization problem will be solved in a fixed time. T con The solution is obtained in time, and In conclusion, the convergence of the upper-level optimization design has been proven.

[0200] Step 5: Based on the error dynamics model and the upper-level optimization controller A lower-level tracking controller is designed to control the vehicle.

[0201] The lower-level tracking controller mentioned in step 5 is specifically represented by the following formula:

[0202] ;

[0203] ;

[0204] in

[0205] ;

[0206] ;

[0207] ;

[0208] ;

[0209] ;

[0210] ;

[0211] in, u ε,i For vehicles i The input signal, i.e., the acceleration control signal, u h,i For virtual speed control signals, speed deviation error E v,i = ( E v,x,i , E v,y,i ), E v,x,i express x Velocity deviation error in the axial direction; E v,y,i express y Velocity deviation error in the axial direction; acceleration deviation error E a,i = ( E a,x,i , E a,y,i ), E a,x,i express x Acceleration deviation error in the axial direction; E a,y,i express y Acceleration deviation error in the axial direction; k Ev , k Ea and α3 is a preset parameter, and it satisfies... k Ev ≥1 / 2, k Ea ≥1 / 2, 0< α 3 < 1; T 3 is a predefined time constant, and T 3>0; k ε1 and k ε2 These are preset parameters. T ε For a predefined time constant, and T ε >0; subscript , and This represents the filter output signal. for Time derivative, for Time derivative, Represents the filter error, satisfying e ε1,1,i =( e ε1,1,x,i , e ε1,1,y,i )= - ε 1,1,i , e 𝜀1,2,i =( e ε1,2,x,i , e ε1,2,y,i )= u ε,i - ε 1,2,i , e ε1,1,x,i Indicates the corresponding virtual control signal Filter error e ε1,1,i exist x Dimensions in the axial direction e ε1,1,y,i Indicates the corresponding virtual control signal Filter error e ε1,1,i exist y Dimensions along the axial direction; e ε1,2,x,i Indicates correspondence u ε,i Filter error e ε1,2,i exist x Dimensions along the axial direction; e ε1,2,y,iIndicates correspondence u ε,i Filter error e ε1,2,i exist y Dimensions along the axial direction.

[0212] When determining the lower-level tracking controller, the aforementioned lower-level tracking controller was designed first, and then the lower-level tracking controller was proven, specifically including:

[0213] Design a Lyapunov function. Its time derivative has the following result:

[0214] ;

[0215] Design by Lyapunov You can get

[0216] ;

[0217] The velocity and acceleration deviation errors can be obtained from the predefined time theory. The system converges to zero, indicating that it is stable under this controller design. In summary, the system, with its designed two-layer controller, achieves vehicle coordination within a fixed time interval, with an upper time bound of [value missing]. ;

[0218] Consider a vehicle convoy consisting of one lead vehicle and three follower vehicles, each equipped with a short-range (50-meter) communication device. The vehicle model parameters are selected as follows: m i =1607kg, =0.25, h a,i =1.2kg / m3, A i =10.7m2, C d,i =0.57, r i =0.006, g=9.8m / s 2 , The communication topology is as follows: Vehicle 0 Vehicle 1 Vehicle 2 Vehicle 3. The initial state of the lead vehicle is defined as follows: x c,0 (0) = 9.9m, y c,0 (0) = 10m, (0) = 0 rad, v c,0 (0) = 0 m / s, wc,0 (0) = 0 rad / s, the motion state is: a v,0 ( t )=5( t <5s)-2(5s≤ t <9s)+0.5 t (9s≤ t <11s)+0( t ≥11s), aw,0(t)=0rad / s 2 The initial motion states of the other vehicles in the convoy are defined as follows: , Their initial position errors are: e x,1 (0) = 2m, e y,1 (0) = 4m, e x,1 (0) = 3m, e y,1 (0) = 3.5m, e x,1 (0) = 1m, e y,1 (0) = 4m.

[0219] The desired workshop distance is △ x,i,i-1 =10m,△ y,i,i-1 =0m. The parameters selected for the formation controller are: k=1, α 1 = 0.5, α 2 = 0.5, α 3 = 0.5, ρ bf,i =0.001, T 1= T 2= T 3=3, k 𝜀1 =50, k 𝜀2 =50, T 𝜀 =2, k Ev =1, k Ea =1.

[0220] Simulation results are as follows Figure 3-7 As shown. Among them, Figure 3 The motion trajectories of the four vehicles under the designed hierarchical controller are shown. Figure 4 Figures (a) to (c) show the evolution of the speed deviations of vehicles 1, 2, and 3 over time. Figure 5Figures (a) to (c) show the evolution of the spacing error of vehicles 1, 2 and 3 over time, which shows that the vehicle group has achieved the goal of cooperative control. Figure 6 Figures (a) to (c) show the filtering errors for vehicles 1, 2, and 3. e ε1,1,i As time goes by, Figure 7 Figures (a) to (c) show the filtering errors for vehicles 1, 2, and 3. e ε1,2,i Over time, among other things... i =1,2,3, it is clear that these errors converge to zero within a predefined time.

[0221] The key technical point of this invention is:

[0222] 1. A new distributed two-layer fixed time interval strategy was designed.

[0223] 2. For a third-order longitudinal and transverse platoon system, a rapid platoon coordination control problem is solved by using the logarithmic obstacle penalty function method to ensure that communication constraints are always maintained under Euclidean distance.

[0224] Compared with existing technologies, the advantages of this invention are: It designs a sliding mode-based zero-gradient and distributed optimization algorithm, combined with the logarithmic obstacle penalty function method, to solve the optimization problem under communication distance constraints, achieving the desired vehicle spacing within a specified time. A predefined time command filter is incorporated into the vehicle controller to approximate the derivative of the control signal, preventing complexity explosion. An improved two-layer fixed-time vehicle cooperative control strategy is proposed, which can achieve optimal consistency with zero-spacing error while maintaining communication connectivity.

[0225] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A fixed-time vehicle cooperative control method for maintaining connectivity, characterized in that, include: Step 1: Perform force analysis on each vehicle in the target convoy, construct a dynamic model for each vehicle, obtain the dynamic model of the lead vehicle and the dynamic models of all other vehicles except the lead vehicle. The target convoy contains multiple vehicles, each vehicle is assigned a number, all vehicles are arranged according to their numbers, the vehicle with the smallest number is designated as the lead vehicle, and all vehicles are led by the lead vehicle according to their numbers. The dynamic model of the vehicles other than the lead vehicle is specifically represented by the following formula: ； ； ； in, ； ； ； ； ； ； ； ； ； in, yes Time derivative, This indicates the number of vehicles other than the lead vehicle. The position and orientation of the vehicle in the inertial coordinate system. , N This indicates the number of vehicles other than the lead vehicle. Indicates the first The ordinate of the vehicle's position in the inertial coordinate system. Indicates the first The x-coordinate of the vehicle's position in the inertial coordinate system. Indicates the first The vehicle's orientation angle in the inertial coordinate system. Indicates the first The speed of the vehicle in the moving coordinate system. Indicates the first The linear velocity of the vehicle in the moving coordinate system. Indicates the first The angular velocity of the vehicle in the moving coordinate system. yes Time derivative, Indicates the first The acceleration of the vehicle in the moving coordinate system. Indicates the first The linear acceleration of the vehicle in the moving coordinate system. Indicates the first The angular acceleration of the vehicle in the moving coordinate system. yes The time derivative, Indicates the first i Vehicle input, It is the first The vehicle's accelerator or brake input, It is the first The car's steering wheel input, It is the first The vehicle's quality, It is the first The engine time constant of a vehicle. It is the first Air density in a car It is the first The cross-sectional area of ​​a vehicle. It is the first The aerodynamic drag coefficient of a vehicle. It is the first The rolling resistance coefficient of a vehicle's tires. It is the gravitational constant. It refers to the road slope; Step 2: Determine the leading vehicle's forward position Based on the leading vehicle's forward position The dynamic model of the leading vehicle is transformed to obtain the transformed dynamic model of the leading vehicle, and the third dynamic model of the other vehicles is determined. i The front position of the vehicle According to the i The front position of the vehicle For the vehicles other than the lead vehicle, the first i The vehicle's dynamics model is transformed to obtain the first... i The transformation dynamics model of the vehicle is obtained, and then the transformation dynamics models of other vehicles except the lead vehicle are obtained. The distance error between adjacent vehicles is determined. Based on the distance error, the transformation dynamics model of the lead vehicle and the transformation dynamics models of other vehicles except the lead vehicle, an error dynamics model is constructed. Among them, the vehicles other than the lead vehicle are the first i The front position of the vehicle This can be expressed by the following formula: ； in, Represents the transformed th The longitudinal position of the vehicle Represents the transformed th The lateral position of the vehicle, Indicates the first The straight-line distance between the vehicle's center of gravity and its front end; Based on this, the first i The transformation dynamics model of a vehicle is expressed by the following formula: ； ； ； in, ； ； ； ； ； ； ； ； in, yes Time derivative, yes Time derivative, Represents the transformed th The speed of the car Represents the transformed th The longitudinal speed of the vehicle, Represents the transformed th The vehicle's lateral speed, yes Time derivative, Represents the transformed th The acceleration of the vehicle, Represents the transformed th The longitudinal acceleration of the vehicle, Represents the transformed th The vehicle's lateral acceleration, and Indicates the transformed th Vehicle control inputs, for The first time derivative, for The second time derivative, yes The inverse matrix; Step 3: Define the communication constraints in the Euclidean sense, and determine the control optimization problem and the communication distance constraint function; Step 4: Based on the error dynamics model, the optimization problem, and the communication distance constraint function, design the upper-level optimization controller. ; Step 5: Based on the error dynamics model and the upper-level optimization controller A lower-level tracking controller is designed to control the vehicle.

2. The fixed-time vehicle cooperative control method for maintaining connectivity according to claim 1, characterized in that, The dynamic model of the leading vehicle described in step 1 is expressed by the following formula: ; ； ； in, ； ； ； in, yes Time derivative, This indicates the position and orientation of the lead vehicle in the inertial coordinate system. The ordinate represents the position of the lead vehicle in the inertial coordinate system. The x-coordinate represents the position of the lead vehicle in the inertial coordinate system. This indicates the orientation angle of the lead vehicle in the inertial coordinate system. This indicates the speed of the lead vehicle in the moving coordinate system. This represents the linear velocity of the lead vehicle in the moving coordinate system. This represents the angular velocity of the lead vehicle in the moving coordinate system. yes Time derivative, This represents the acceleration of the lead vehicle in the moving coordinate system. This represents the linear acceleration of the lead vehicle in the moving coordinate system. This represents the angular acceleration of the lead vehicle in the moving coordinate system.

3. The fixed-time vehicle cooperative control method for maintaining connectivity according to claim 1, characterized in that, The transformation dynamics model of the leading vehicle in step 2 is expressed by the following formula: ； ； in, ； ； ； in, yes Time derivative, This indicates the forward position of the lead vehicle after the conversion. This indicates the longitudinal position of the lead vehicle after the conversion. Indicates the lateral position of the lead vehicle after the conversion; yes Time derivative, The speed of the leading vehicle after the conversion. This indicates the longitudinal speed of the leading vehicle after the conversion. This indicates the lateral speed of the leading vehicle after the conversion. This indicates the acceleration of the leading vehicle after the conversion. This represents the longitudinal acceleration of the lead vehicle after the conversion. This indicates the lateral acceleration of the leading vehicle after the conversion.

4. The fixed-time vehicle cooperative control method for maintaining connectivity according to claim 1, characterized in that, The communication constraints described in step 3 Vehicle and the Euclidean distance between -1 vehicles Less than the maximum effective communication distance Specifically, it is expressed by the following formula: ； in, t represents time. This can be expressed by the following formula: ； in, Represents the transformed th -1. The longitudinal position of the vehicle. Represents the transformed th The lateral position of the vehicle; The control optimization problem can be expressed by the following formula: ； ； in, , For the first The objective function of the vehicle, It is all spacing errors stack vector, For the first Vehicle spacing error, It is the optimal solution to the control optimization problem. It is the communication distance constraint function, specifically expressed by the following formula: 。 5. A fixed-time vehicle cooperative control method for maintaining connectivity according to claim 4, characterized in that, The upper-level optimization controller mentioned in step 4 Specifically, it is expressed by the following formula: ； in, ； ； ； ； ； The definition of the power sign function is: α1, α2, and α3 are constants and 0 < α1, α2 < 1. T1 and T2 are predefined time constants satisfying T1, T2 > 0. The two-dimensional column vector s... i It is a sliding flow pattern, L bf,i (e i ) is the constructed logarithmic barrier penalty function, {e i |g i ,com(e i )<0}, It is function L bf,i (e i ) on its independent variable e i The derivative of It is function L bf,i (e i ) on its independent variable e i The second derivative, It is the inverse of the second derivative matrix. It is an auxiliary variable, k 1+ , k 1- ρ and k are control parameters. bf,i As a preset positive value, N represents the number of vehicles other than the lead vehicle. i Let i represent the set of vehicles whose numbers are adjacent to the i-th vehicle.

6. The fixed-time vehicle cooperative control method for maintaining connectivity according to claim 5, characterized in that, The distance error between two adjacent vehicles in step 2 is expressed by the following formula: ； in, , Indicates the first Car and the i -1 longitudinal spacing error of vehicles on a two-dimensional plane; Indicates the first Car and the i -1 lateral spacing error of vehicles on a two-dimensional plane; It is the first Car and the The expected constant distance between vehicles Indicates the first Car and the i -1 The expected constant distance of a vehicle in the longitudinal direction on a two-dimensional plane; Indicates the first Car and the i -1 The expected constant distance that a vehicle travels laterally in a two-dimensional plane; Indicates the first i -1 vehicle's front position; Based on this, the error dynamics model is expressed by the following formula: ； ； ； ； ； in, express The first derivative in time, Indicates the first Vehicle speed error, Indicates the first The acceleration error of the vehicle, for The first time derivative, for The first time derivative, for Third-order time derivative for The third time derivative, Indicates the first i -1. Time derivative of the longitudinal acceleration of the vehicle. Indicates the first i -1 The time derivative of the lateral acceleration of the vehicle.

7. A fixed-time vehicle cooperative control method for maintaining connectivity according to claim 6, characterized in that, The lower-level tracking controller mentioned in step 5 is specifically represented by the following formula: ； ； in ； ； ； ； ； ； in, u ε,i For vehicles i The input signal, i.e., the acceleration control signal, u h,i For virtual speed control signals, speed deviation error E v,i = ( E v,x,i , E v,y,i ), E v,x,i express x Velocity deviation error in the axial direction; E v,y,i express y Velocity deviation error in the axial direction; acceleration deviation error E a,i = ( E a,x,i , E a,y,i ), E a,x,i express x Acceleration deviation error in the axial direction; E a,y,i express y Acceleration deviation error in the axial direction; k Ev , k Ea and α 3 is a preset parameter, and it satisfies... k Ev ≥1 / 2, k Ea ≥1 / 2, 0< α 3 < 1; T 3 is a predefined time constant, and T 3>0; k ε1 and k ε2 These are preset parameters. T ε For a predefined time constant, and T ε >0; subscript , and This represents the filter output signal. for Time derivative, for Time derivative, Represents the filter error, satisfying e ε1,1,i =( e ε1,1,x,i , e ε1,1,y,i )= - ε 1,1,i , e 𝜀1,2,i =( e ε1,2,x,i , e ε1,2,y,i )= u ε,i - ε 1,2,i , e ε1,1,x,i Indicates the corresponding virtual control signal Filter error e ε1,1,i exist x Dimensions in the axial direction e ε1,1,y,i Indicates the corresponding virtual control signal Filter error e ε1,1,i exist y Dimensions along the axial direction; e ε1,2,x,i Indicates correspondence u ε,i Filter error e ε1,2,i exist x Dimensions along the axial direction; e ε1,2,y,i Indicates correspondence u ε,i Filter error e ε1,2,i exist y Dimensions along the axial direction.

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