Fixed-time vehicle cooperative control method capable of keeping connectivity

Abstract

The invention provides a fixed-time vehicle cooperative control method capable of keeping connectivity, and relates to the technical field of vehicle cooperative control. According to the method, a new dynamical model is constructed for vehicles in a motorcade, and an error dynamical model of the system is obtained according to the new dynamical model. A control optimization problem and a communication distance constraint function are defined according to a control target and demand, an upper-layer optimization controller is further designed, and a lower-layer tracking controller is further determined. Wherein the upper-layer design is a zero gradient and distributed optimization algorithm based on a sliding mode and is used for solving an optimization problem under communication distance constraint by combining a logarithmic barrier penalty function method, and the lower-layer design is used for combining a predefined time command filter in a vehicle controller so as to approximate a derivative of a control signal and prevent complexity explosion. The double-layer design jointly forms an improved double-layer fixed-time vehicle cooperative control strategy, so that a group of vehicles can keep communication connection and realize optimal consistency of zero-spacing errors at the same time.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle cooperative control, and specifically relates to a fixed-time vehicle cooperative control method for maintaining connectivity. Background Art

[0002] Cooperative control of autonomous vehicles is an important branch in intelligent transportation systems and has received extensive attention from all sectors of society. Currently, most research on vehicle cooperative control (e.g., [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 heterogenous vehicular platoons,” IEEE Trans. Intell. Transp. Syst., vol. 23, no. 7, pp. 7096-7111, Jul. 2022.]) only considers longitudinal control, that is, adjusting the distance between the host vehicle and the vehicle in front using the information of surrounding vehicles. However, in real-world scenarios, such as merging and lane-changing, the movement of vehicles occurs in a two-dimensional space, involving dual cooperative control in both the longitudinal and lateral directions. Existing longitudinal and lateral cooperative control of vehicles (e.g., [W.-D. Xu, X.-G. Guo, J.-L. Wang, et al., “Nonlinear disturbance observer-based fault-tolerant sliding-mode control for 2-D plane vehicular platoon with UTVFD and ANAS,” IEEE Transactions on Cybernetics, Apr. 2024. (DOI: 10.1109 / TCYB.2022.3222496)]) is a cooperative method defined by Euclidean distance and azimuth angle. However, due to the lack of a direct connection with the azimuth angle of the vehicle in front, the trajectory of the following vehicle is not unique. In addition, reliable vehicle-to-vehicle communication is the basis for achieving cooperative control. However, the transmission capacity of in-vehicle communication devices is limited by various factors, hindering the propagation of wireless signals.A large number of cooperative control strategies considering 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)]) ignore the influence of the Euclidean distance between vehicles. The vehicle cooperative control has relatively high requirements for the convergence speed of 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 mostly focuses on unrealistic longitudinal cooperation problems, and has not yet been able to achieve longitudinal and lateral cooperative control that meets the Euclidean distance constraint while ensuring the uniqueness of vehicle trajectories, and ignores the requirements of connected vehicle cooperative control for the convergence speed. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the purpose of the present invention is to propose a fixed-time vehicle cooperative control method for maintaining connectivity, including:

[0005] Step 1: Analyze the forces on each vehicle in the target vehicle fleet, construct the dynamic model of each vehicle, obtain the dynamic model of the leading vehicle and the dynamic models of other vehicles except the leading vehicle. The target vehicle fleet includes multiple vehicles, each vehicle is configured with a number, all vehicles are arranged according to the numbers, and the vehicle with the smallest number is used as the leading vehicle, and all vehicles are led by the leading vehicle according to the numbers and drive.

[0006] Step 2: Determine the pre-position p of the leading vehicle h,0 , according to the pre-position p of the leading vehicle h,0 , transform the dynamic model of the leading vehicle to obtain the transformed dynamic model of the leading vehicle, and determine the pre-position p of the i-th vehicle among other vehicles except the leading vehicle h,i, according to the leading position p of the i-th vehicle h,i , transform the dynamic model of the i-th vehicle among the vehicles other than the leading vehicle to obtain the transformed dynamic model of the i-th vehicle, and then obtain the transformed dynamic models of the vehicles other than the leading vehicle. Determine the spacing error between adjacent vehicles. According to the spacing error, the transformed dynamic model of the leading vehicle, and the transformed dynamic models of the vehicles other than the leading vehicle, construct an error dynamic model;

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

[0008] Step 4: Design an upper-layer optimization controller according to the error dynamic model, the optimization problem, and the communication distance constraint function

[0009] Step 5: Design a lower-layer tracking controller according to the error dynamic model and the upper-layer optimization controller The lower-layer tracking controller is used to achieve the control of the vehicle.

[0010] Optionally, the dynamic model of the leading vehicle in Step 1 is represented by the following formula:

[0011]

[0012] where

[0013] p c,0 =(x c,0 , y c,0 , θ 0 ) T ;

[0014] η c,0 =(v c,0 , w c,0 ) T ;

[0015] a c,0 =(a v,0 , a q,0 ) T ;

[0016] where is the time derivative of p c,0 , p c,0 represents the position and orientation of the leading vehicle in the inertial coordinate system, x c,0 represents the ordinate of the position of the leading vehicle in the inertial coordinate system, y c,0 represents the abscissa of the position of the leading vehicle in the inertial coordinate system, θ 0 represents the direction angle of the leading vehicle in the inertial coordinate system, η c,0Represents the speed of the leading vehicle in the moving coordinate system, v c,0 Represents the linear velocity of the leading vehicle in the moving coordinate system, w c,0 Represents the angular velocity of the leading vehicle in the moving coordinate system, is η c,0 The time derivative of, a c,0 Represents the acceleration of the leading vehicle in the moving coordinate system, a v,0 Represents the linear acceleration of the leading vehicle in the moving coordinate system, a w,0 Represents the angular acceleration of the leading vehicle in the moving coordinate system.

[0017] Optionally, the dynamic model of the vehicles other than the leading vehicle described in step 1 is specifically represented by the following formula:

[0018]

[0019] Wherein,

[0020] p c,i =(x c,i , y c,i , θ i ) T ;

[0021] η c,i =(v c,i , w c,i ) T ;

[0022] a c,i =(a v,i , a w,i ) T ;

[0023] u c,i =(u v,i , u w,i ) T ;

[0024]

[0025] D c,i =(F U,i 0) T ;

[0026]

[0027] Wherein, is the time derivative of p c,i p c,i Represents the position and orientation of the i-th vehicle among the vehicles other than the leading vehicle in the inertial coordinate system, i = 1, 2,..., N, and N represents the number of vehicles other than the leading vehicle, xc,i The ordinate of the position of the $i$-th vehicle in the inertial coordinate system, $y$ c,i The abscissa of the position of the $i$-th vehicle in the inertial coordinate system, $\theta$ i The direction angle of the $i$-th vehicle in the inertial coordinate system, $\eta$ c,i The speed of the $i$-th vehicle in the moving coordinate system, $v$ c,i The linear speed of the $i$-th vehicle in the moving coordinate system, $w$ c,i The angular speed of the $i$-th vehicle in the moving coordinate system, is the time derivative of $\eta$, $a$ c,i c,i The acceleration of the $i$-th vehicle in the moving coordinate system, $a$ v,i The linear acceleration of the $i$-th vehicle in the moving coordinate system, $a$ w,i The angular acceleration of the $i$-th vehicle in the moving coordinate system, is the time derivative of $a$, $u$ c,i c,i The input of the $i$-th vehicle, $u$ v,i is the throttle or brake input of the $i$-th vehicle, $u$ w,i is the steering wheel input of the $i$-th vehicle, $m$ i is the vehicle mass of the $i$-th vehicle, $\tau$ i is the engine time constant of the $i$-th vehicle, $h$ a,i is the air density of the $i$-th vehicle, $A$ i is the vehicle cross-sectional area of the $i$-th vehicle, $C$ d,i is the aerodynamic drag coefficient of the $i$-th vehicle, $r$ i is the tire rolling resistance coefficient of the $i$-th vehicle, $g$ is the gravitational constant, $\alpha$ slope,i is the road slope.

[0028] Optionally, the transformation dynamics model of the leading vehicle in step 2 is represented by the following formula:

[0029]

[0030] where,

[0031] $p$ h,0 $=(x$ h,0 , $y$ h,0 ) T ;

[0032] $\eta$ h,0 $=(v$ x,0 , $v$ y,0 ) T ;

[0033] $a$ h,0 $=(a$ x,0 , $a$ y,0 )​​T ;

[0034] Wherein, is the time derivative of p h,0 , p h,0 represents the front position of the converted leading vehicle, x h,0 represents the longitudinal position of the converted leading vehicle, y h,0 represents the lateral position of the converted leading vehicle; is the time derivative of η h,0 , η h,0 is the speed of the converted leading vehicle, v x,0 represents the longitudinal speed of the converted leading vehicle, v y,0 represents the lateral speed of the converted leading vehicle, a h,0 represents the acceleration of the converted leading vehicle, a x,0 represents the longitudinal acceleration of the converted leading vehicle, a y,0 represents the lateral acceleration of the converted leading vehicle.

[0035] Optionally, the front position p h,i of the i-th vehicle among other vehicles except the leading vehicle in step 2 is represented by the following formula:

[0036]

[0037] Wherein, x h,i represents the longitudinal position of the i-th vehicle after transformation, y h,i represents the lateral position of the i-th vehicle after transformation, L i represents the straight-line distance between the centroid position and the front position of the i-th vehicle;

[0038] Based on this, the transformation dynamics model of the i-th vehicle is represented by the following formula:

[0039]

[0040] Wherein,

[0041] η h,i =(v x,i , v u,i ) T ;

[0042] a h,i =(a x,i , a y,i ) T ;

[0043] u h,u =(u x,u , u y,i ) T ;

[0044]

[0045] u h,i = J -1 (θ i )A c,i u c,i ;

[0046] D h,i = J -1 (θ i )D c,i ;

[0047]

[0048] wherein, is the time derivative of p h,i , is the time derivative of η h,i , η h,i represents the speed of the i-th vehicle after transformation, v x,i represents the longitudinal speed of the i-th vehicle after transformation, v y,i represents the lateral speed of the i-th vehicle after transformation, is the time derivative of a h,i , a h,i represents the acceleration of the i-th vehicle after transformation, a x,i represents the longitudinal acceleration of the i-th vehicle after transformation, a y,i represents the lateral acceleration of the i-th vehicle after transformation, u x,i and u y,i represent the control input of the i-th vehicle after transformation, is the first-order time derivative of J(θ i ), is the second-order time derivative of J(θ i ), J -1 (θ i ) is the inverse matrix of J(θ i ).

[0049] Optionally, the spacing error between two adjacent vehicles in step 2 is expressed by the following formula:

[0050] e i = p h,i-1 - p h,i - Δ i,i-1 ;

[0051] wherein, e i = (e x,i , e y,i ) T e x,irepresents the longitudinal spacing error between the $i$-th vehicle and the $(i - 1)$-th vehicle in the two-dimensional plane; $e$ y,i represents the lateral spacing error between the $i$-th vehicle and the $(i - 1)$-th vehicle in the two-dimensional plane; $\Delta$ i,i-1 $=$ ($\Delta$ x,i,i-1 , $\Delta$ y,i,i-1 ) T is the expected constant distance between the $(i - 1)$-th vehicle and the $i$-th vehicle, $\Delta$ x,i,i-1 represents the expected constant longitudinal distance between the $i$-th vehicle and the $(i - 1)$-th vehicle in the two-dimensional plane; $\Delta$ y,i,i-1 represents the expected constant lateral distance between the $i$-th vehicle and the $(i - 1)$-th vehicle in the two-dimensional plane; $p$ h,i-1 represents the front position of the $(i - 1)$-th vehicle;

[0052] Based on this, the error dynamics model is expressed by the following formula:

[0053]

[0054] where, represents the first-order derivative of $e$ i with respect to time, $e$ v,i represents the speed error of the $i$-th vehicle, $e$ a,i represents the acceleration error of the $i$-th vehicle, is the first-order time derivative of $e$ v,i , is the first-order time derivative of $e$ a,i , is the third-order time derivative of $\Delta$ x,i,i-1 , is the third-order time derivative of $\Delta$ y,i,i-1 , represents the time derivative of the longitudinal acceleration of the $(i - 1)$-th vehicle, represents the time derivative of the lateral acceleration of the $(i - 1)$-th vehicle.

[0055] Optionally, the Euclidean distance $D$ between the $i$-th vehicle and the $(i - 1)$-th vehicle in the communication constraint condition described in step 3 i-1,i is less than the maximum effective communication distance $d$ com , and is specifically expressed by the following formula:

[0056]

[0057] where, $d$ com $> 0$, $t$ represents time, $D$ i-1,i is expressed by the following formula:

[0058]

[0059] where, $x$ h,i-1represents the longitudinal position of the (i - 1)-th vehicle after transformation, y h,i-1 represents the lateral position of the (i - 1)-th vehicle after transformation;

[0060] The control optimization problem is expressed by the following formula:

[0061]

[0062] where, f i (e i ) is the objective function of the i-th vehicle, e is the stack vector of all spacing errors e i , e j is the spacing error of the j-th vehicle, e * is the optimal solution of the control optimization problem, g i,com (e i ) is the communication distance constraint function, which is specifically expressed by the following formula:

[0063]

[0064] Optionally, the upper-layer optimization controller described in step 4 is specifically expressed by the following formula:

[0065]

[0066] where,

[0067]

[0068] L bf,i (e i ) = f i (e i ) - ρ bf,i log(-g i,com (e i ));

[0069] sig p (x) = (|x 1 |psign(x 1 ), |x 2 |psign(x 2 ),..., |x n |psign(x n ));

[0070] where, α 1 , α 2 and α 3 are constants and 0 < α 1 , α 2 < 1, T 1 , T 2All predefined time constants satisfy T 1 , T 2 > 0, and the two - dimensional column vector s i is a sliding - mode manifold, and L bf,i (e i ) is the constructed logarithmic barrier penalty function, {e i |g i , com(e i ) < 0}, is the derivative of the function L bf,i (e i ) with respect to its independent variable e i , is the second - derivative of the function L bf,i (e i ) with respect to its independent variable e i , is the inverse of the second - derivative matrix, is an auxiliary variable, k 1+ , k 1- and k are control parameters, ρ bf,i is a preset positive value, N represents the number of vehicles other than the leading vehicle, and N i represents the set of vehicles adjacent to the number of the i - th vehicle.

[0071] Optionally, the lower - layer tracking controller described in step 5 is specifically represented by the following formula:

[0072]

[0073] where

[0074] E v,i = e v,i - ε 1,1,i ;

[0075] E a,i = e a,i - ε 1,2,i ;

[0076]

[0077] where, u ε,i is the input signal of vehicle i, that is, the acceleration control signal, u h,i is the virtual speed control signal, the speed deviation error E v,i =(E v,x,i , E v,y,i ), E v,x,i represents the speed deviation error in the x - axis direction; E v,y,i represents the speed deviation error in the y - axis direction; the acceleration deviation error E a,i =(Ea,x,i , E a,y,i ), E a,x,i represents the acceleration deviation error in the x-axis direction; E a,y,i represents the acceleration deviation error in the y-axis direction; k Ev , k Ea and α 3 are preset parameters and satisfy 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 are preset parameters, T ε is a predefined time constant and T ε > 0; the subscript ι ∈ {1, 2}, ε 1,ι,i and ε 2,ι,i represent the filter output signal, is the time derivative of ε 1,ι,i , is the time derivative of ε 2,ι,i , e ε1,ι,i represents the filter error and satisfies 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 represents the magnitude of the filter error e corresponding to the virtual control signal ε1,1,i in the x-axis direction, e ε1,1,y,i represents the magnitude of the filter error e corresponding to the virtual control signal ε1,1,i in the y-axis direction; e ε1,2,x,i represents the magnitude of the filter error e ε,i corresponding to u ε1,2,i in the x-axis direction; e ε1,2,y,i represents the magnitude of the filter error e ε,i corresponding to u ε1,2,i in the y-axis direction.

[0078] The beneficial effects produced by adopting the above technical solution are as follows:

[0079] The present invention provides a fixed-time vehicle cooperative control method for maintaining connectivity. Specifically, a zero-gradient and distributed optimization algorithm based on sliding mode is designed, combined with the logarithmic barrier penalty function method, to solve the optimization problem under communication distance constraints and achieve the desired inter-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 and prevent complexity explosion. At the same time, an improved two-layer fixed-time vehicle cooperative control strategy is proposed, which can achieve optimal consensus with zero spacing error while maintaining communication connection. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a schematic flowchart of a fixed-time vehicle cooperative control method for maintaining connectivity in an embodiment of the present invention;

[0081] Figure 2 It is a schematic diagram of the front position in an embodiment of the present invention;

[0082] Figure 3 It is the motion trajectories of four vehicles under a hierarchical controller in an embodiment of the present invention;

[0083] Figure 4 It is a schematic diagram of the evolution of the speed deviation over time in an embodiment of the present invention. Among them, Figure (a) is a schematic diagram of the evolution of the speed deviation of vehicle 1 over time, Figure (b) is a schematic diagram of the evolution of the speed deviation of vehicle 2 over time, and Figure (c) is a schematic diagram of the evolution of the speed deviation of vehicle 3 over time;

[0084] Figure 5 It is a schematic diagram of the evolution of the spacing error over time in an embodiment of the present invention. Among them, Figure (a) is a schematic diagram of the evolution of the spacing error of vehicle 1 over time, Figure (b) is a schematic diagram of the evolution of the spacing error of vehicle 2 over time, and Figure (c) is a schematic diagram of the evolution of the spacing error of vehicle 3 over time;

[0085] Figure 6 It is the filtering error e ε1,1,i of the present invention over time in an embodiment. Among them, Figure (a) is a schematic diagram of the evolution of the filtering error e ε1,1,i of vehicle 1 over time, Figure (b) is a schematic diagram of the evolution of the filtering error e ε1,1,i of vehicle 2 over time, and Figure (c) is a schematic diagram of the evolution of the filtering error e ε1,1,i of vehicle 3 over time;

[0086] Figure 7 It is the filtering error e ε1,2,i of the present invention over time in an embodiment. Among them, Figure (a) is a schematic diagram of the evolution of the filtering error e ε1,2,iSchematic diagram of the evolution over time. Figure (b) shows the filtering error e of vehicle 2 ε1,2,i Schematic diagram of the evolution over time. Figure (c) shows the filtering error e of vehicle 3 ε1,2,i Schematic diagram of the evolution over time. Specific implementation manner

[0087] The following combines the accompanying drawings and embodiments to further describe in detail the specific implementation manner of the present invention. The following embodiments are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0088] Aiming at the problems existing in the prior art, the present invention is committed to solving the problem of fast cooperative control of connected vehicles with distance constraints, and proposes a new distributed two-layer fixed-time control strategy, which can achieve the desired cooperative relationship while maintaining the communication connection. Specifically, the present invention provides a fixed-time vehicle cooperative control method for maintaining connectivity, combined with Figure 1 , which may include the following steps:

[0089] Step 1: Analyze the forces acting on each vehicle in the target vehicle fleet, construct the dynamic model of each vehicle, obtain the dynamic model of the leading vehicle and the dynamic models of the other vehicles except the leading vehicle. The target vehicle fleet includes multiple vehicles, each vehicle is configured with a number, all vehicles are arranged according to the numbers, and the vehicle with the smallest number is used as the leading vehicle, and all vehicles are led by the leading vehicle according to the numbers;

[0090] The dynamic model of the leading vehicle in Step 1 is represented by the following formula:

[0091]

[0092] Where

[0093] p c,0 =(x c,0 , y c,0 , θ 0 ) T ;

[0094] η c,0 =(v c,0 , w c,0 ) T ;

[0095] a c,0 =(a v,0 , a q,0 ) T ;

[0096] Where is the time derivative of p c,0 , p c,0Denote the position and orientation of the leading vehicle in the inertial coordinate system, x c,0 Denote the ordinate of the position of the leading vehicle in the inertial coordinate system, y c,0 Denote the abscissa of the position of the leading vehicle in the inertial coordinate system, θ 0 Denote the direction angle of the leading vehicle in the inertial coordinate system, η c,0 Denote the speed of the leading vehicle in the moving coordinate system, v c,0 Denote the linear velocity of the leading vehicle in the moving coordinate system, w c,0 Denote the angular velocity of the leading vehicle in the moving coordinate system, is the time derivative of η, a c,0 Denote the acceleration of the leading vehicle in the moving coordinate system, a c,0 Denote the linear acceleration of the leading vehicle in the moving coordinate system, a v,0 Denote the angular acceleration of the leading vehicle in the moving coordinate system, a w,0 Denote the angular acceleration of the leading vehicle in the moving coordinate system.

[0097] The dynamic model of other vehicles except the leading vehicle described in step 1 is specifically represented by the following formula:

[0098]

[0099] Where,

[0100] p c,i =(x c,i ,y c,i ,θ i ) T ;

[0101] η c,i =(v c,i ,w c,i ) T ;

[0102] a c,i =(a v,i ,a w,i ) T ;

[0103] u c,i =(u v,i ,u w,i ) T ;

[0104]

[0105] D c,i =(F U,i 0) T ;

[0106]

[0107] wherein, is the time derivative of p c,i , p c,i represents the position and orientation of the i-th vehicle among other vehicles except the leading vehicle in the inertial coordinate system, i = 1, 2, …, N, N represents the number of other vehicles except the leading vehicle, x c,i represents the ordinate of the position of the i-th vehicle in the inertial coordinate system, y c,i represents the abscissa of the position of the i-th vehicle in the inertial coordinate system, θ i represents the direction angle of the i-th vehicle in the inertial coordinate system, η c,i represents the speed of the i-th vehicle in the moving coordinate system, v c,i represents the linear velocity of the i-th vehicle in the moving coordinate system, w c,i represents the angular velocity of the i-th vehicle in the moving coordinate system, is the time derivative of η c,i , a c,i represents the acceleration of the i-th vehicle in the moving coordinate system, a v,i represents the linear acceleration of the i-th vehicle in the moving coordinate system, a w,i represents the angular acceleration of the i-th vehicle in the moving coordinate system, is the derivative of a c,i with respect to time, u c,i represents the input of the i-th vehicle, u v,i is the throttle or brake input of the i-th vehicle, u w,i is the steering wheel input of the i-th vehicle, m i is the vehicle mass of the i-th vehicle, τ i is the engine time constant of the i-th vehicle, h a,i is the air density of the i-th vehicle, A i is the vehicle cross-sectional area of the i-th vehicle, C d,i is the aerodynamic drag coefficient of the i-th vehicle, r i is the tire rolling resistance coefficient of the i-th vehicle, g is the gravitational constant, α slope,i is the road slope.

[0108] Step 2: Determine the front position p h,0 of the leading vehicle. According to the front position p h,0 of the leading vehicle, transform the dynamic model of the leading vehicle to obtain the transformed dynamic model of the leading vehicle, and determine the front position p h,i of the i-th vehicle among other vehicles except the leading vehicle. According to the front position p h,i, the dynamic model of the $i$-th vehicle among the vehicles other than the leading vehicle is transformed to obtain the transformed dynamic model of the $i$-th vehicle, and then the transformed dynamic models of the vehicles other than the leading vehicle are obtained. The spacing error between two adjacent vehicles is determined, and an error dynamic model is constructed based on the spacing error, the transformed dynamic model of the leading vehicle, and the transformed dynamic models of the vehicles other than the leading vehicle;

[0109] The transformed dynamic model of the leading vehicle in step 2 is expressed by the following formula:

[0110]

[0111] where,

[0112] p h,0 =(x h,0 ,y h,0 ) T ;

[0113] η h,0 =(v x,0 ,v y,0 ) T ;

[0114] a h,0 =(a x,0 ,a y,0 ) T ;

[0115] where, is the time derivative of $p$ h,0 , $p$ h,0 represents the front position of the transformed leading vehicle, $x$ h,0 represents the longitudinal position of the transformed leading vehicle, $y$ h,0 represents the lateral position of the transformed leading vehicle; is the time derivative of $\eta$ h,0 , $\eta$ h,0 is the speed of the transformed leading vehicle, $v$ x,0 represents the longitudinal speed of the transformed leading vehicle, $v$ y,0 represents the lateral speed of the transformed leading vehicle, $a$ h,0 represents the acceleration of the transformed leading vehicle, $a$ x,0 represents the longitudinal acceleration of the transformed leading vehicle, $a$ y,0 represents the lateral acceleration of the transformed leading vehicle.

[0116] The front position $p$ h,i of the $i$-th vehicle among the vehicles other than the leading vehicle in step 2 is expressed by the following formula:

[0117]

[0118] where x h,i represents the longitudinal position of the i-th vehicle after transformation, and y h,i represents the lateral position of the i-th vehicle after transformation, and L i represents the straight-line distance between the centroid position and the front position of the i-th vehicle. Combining Figure 2 , where pointc i is the centroid position and pointh i is the front position;

[0119] Based on this, the transformation dynamics model of the i-th vehicle is expressed by the following formula:

[0120]

[0121] where

[0122] η h,i =(v x,i , v y,i ) T ;

[0123] a h,i =(a x,i , a y,i ) T ;

[0124] u h,i =(u x,i , u y,i ) T ;

[0125]

[0126] u h,i =J -1 (θ i )A c,i u c,i ;

[0127] D h,i =J -1 (θ i )D c,i ;

[0128]

[0129] where is the time derivative of p h,i , is the time derivative of η h,i , and η h,i represents the speed of the i-th vehicle after transformation, v x,i represents the longitudinal speed of the i-th vehicle after transformation, vy,i represents the lateral velocity of the \(i\)-th vehicle after transformation, is the h,i time derivative of \(a\), where \(a\) h,i represents the acceleration of the \(i\)-th vehicle after transformation, and \(a\) x,i represents the longitudinal acceleration of the \(i\)-th vehicle after transformation, y,i represents the lateral acceleration of the \(i\)-th vehicle after transformation, and \(u\) x,i and \(u\) y,i represent the control input of the \(i\)-th vehicle after transformation. is the first-order time derivative of \(J(\theta\) i ), and is the second-order time derivative of \(J(\theta\) i ). \(J\) -1 \((\theta\) i ) is the inverse matrix of \(J(\theta\) i ).

[0130] The spacing error between two adjacent vehicles in Step 2 is expressed by the following formula:

[0131] \(e\) i \(= p\) h,i-1 \(- p\) h,i \(- \Delta\) i,i-1 ;

[0132] where \(e\) i \(=(e\) x,i , \(e\) y,i ) T , \(e\) x,i represents the longitudinal spacing error between the \(i\)-th vehicle and the \((i - 1)\)-th vehicle in the two-dimensional plane; \(e\) y,i represents the lateral spacing error between the \(i\)-th vehicle and the \((i - 1)\)-th vehicle in the two-dimensional plane; \(\Delta\) i,i-1 \(=(\Delta\) x,i,i-1 , \(\Delta\) y,i,i-1 ) T is the desired constant distance between the \((i - 1)\)-th vehicle and the \(i\)-th vehicle. \(\Delta\) x,i,i-1 represents the desired constant longitudinal distance between the \(i\)-th vehicle and the \((i - 1)\)-th vehicle in the two-dimensional plane; \(\Delta\) y,i,i-1 represents the desired constant lateral distance between the \(i\)-th vehicle and the \((i - 1)\)-th vehicle in the two-dimensional plane; \(p\) h,i-1 represents the front position of the \((i - 1)\)-th vehicle.

[0133] Based on this, the error dynamics model is expressed by the following formula:

[0134]

[0135] where represents the first-order time derivative of \(e\) i with respect to time, and \(e\) v,iDenote the speed error of the \(i\)-th vehicle as \(e\). a,i Denote the acceleration error of the \(i\)-th vehicle as The first-order time derivative of \(e\) is v,i The first-order time derivative of \(e\) is The first-order time derivative of \(e\) is a,i The first-order time derivative of \(e\) is The third-order time derivative of \(\Delta\) is x,i,i-1 The third-order time derivative of \(\Delta\) is The third-order time derivative of \(\Delta\) is y,i,i-1 The third-order time derivative of \(\Delta\) is Denote the time derivative of the longitudinal acceleration of the \((i - 1)\)-th vehicle as Denote the time derivative of the lateral acceleration of the \((i - 1)\)-th vehicle as

[0136] Step 3: Define the communication constraint conditions in the Euclidean sense, and determine the control optimization problem and the communication distance constraint function;

[0137] The Euclidean distance \(D\) between the \(i\)-th vehicle and the \((i - 1)\)-th vehicle in the communication constraint conditions described in Step 3 i-1,i is less than the maximum effective communication distance \(d\) com and is specifically expressed by the following formula:

[0138]

[0139] where \(d\) com > 0, \(t\) represents time, and \(D\) i-1,i is expressed by the following formula:

[0140]

[0141] where \(x\) h,i-1 represents the longitudinal position of the \((i - 1)\)-th vehicle after transformation, and \(y\) h,i-1 represents the lateral position of the \((i - 1)\)-th vehicle after transformation;

[0142] The control optimization problem is expressed by the following formula:

[0143]

[0144] where \(f\) i (\(e\) i ) is the objective function of the \(i\)-th vehicle, \(e\) is the stack vector of all spacing errors \(e\) i where \(e\) j is the spacing error of the \(j\)-th vehicle, \(e\) * is the optimal solution of the control optimization problem, and \(g\) i,com (\(e\) i ) is the communication distance constraint function and is specifically expressed by the following formula:

[0145]

[0146] If the above optimization problem is solved, then the cooperative control of connected vehicles with communication preservation constraints is achieved.

[0147] Step 4: Design an upper-layer optimization controller according to the error dynamics model, the optimization problem, and the communication distance constraint function

[0148] The upper-layer optimization controller described in Step 4 is specifically represented by the following formula:

[0149]

[0150] where

[0151]

[0152] L bf,i (e i ) = f i (e i ) - ρ bf,i log(-g i,com (e i ));

[0153] sig p (x) = (|x 1 |psign(x 1 ), |x 2 |psign(x 2 ),..., |x n |psign(x n ));

[0154] where α 1 , α 2 and α 3 are constants and 0 < α 1 , α 2 < 1, T 1 , T 2 are all predefined time constants satisfying T 1 , T 2 > 0, the two-dimensional column vector s i is a sliding mode manifold, L bf,i (e i ) is the constructed logarithmic barrier penalty function, {e i |g i , com(e i ) < 0}, is the derivative of the function L bf,i (e i ) with respect to its independent variable e i , is the function L bf,i (e i ) with respect to its argument e i 's second derivative, is the inverse of the second derivative matrix, is the auxiliary variable, k 1+ , k 1- and k are control parameters, ρ bf,i is a preset positive value, N represents the number of vehicles other than the leading vehicle, N i represents the set of vehicles adjacent to the number of the i-th vehicle.

[0155] When determining the upper-layer optimal controller , for the platoon with error dynamics , the above upper-layer optimal controller is designed and the convergence of the upper-layer optimal controller is proved. The specific proof process includes:

[0156] Design the Lyapunov function: When t ≥ 0, its time derivative satisfies

[0157]

[0158] According to the preset time stability theory, it can be obtained that within T 1 time, the terminal sliding mode surface s of the i-th vehicle i converges to 0.

[0159] When t ≥ T 1 , design the Lyapunov function as Its time derivative satisfies

[0160]

[0161] where, is the minimum eigenvalue of the matrix , so the optimization problem will be solved within the fixed time T con time, and In summary, the proof of the convergence of the upper-layer optimal design is completed.

[0162] Step 5: Design a lower-layer tracking controller according to the error dynamics model and the upper-layer optimal controller The lower-layer tracking controller is used to achieve the control of the vehicle.

[0163] The lower-layer tracking controller described in Step 5 is specifically represented by the following formula:

[0164]

[0165] wherein

[0166] E v,i = e v,i - ε 1,1,i ;

[0167] E a,i = e a,i - ε 1,2,i ;

[0168]

[0169]

[0170] wherein, u ε,i is the input signal of vehicle i, i.e., the acceleration control signal, u h,i is the virtual speed control signal, and the speed deviation error E v,i = (E v,x,i , E v,y,i ), E v,x,i represents the speed deviation error in the x-axis direction; E v,y,i represents the speed deviation error in the y-axis direction; the acceleration deviation error E a,i = (E a,x,i , E a,y,i ), E a,x,i represents the acceleration deviation error in the x-axis direction; E a,y,i represents the acceleration deviation error in the y-axis direction; k Ev , k Ea and α 3 are preset parameters, and satisfy k Ev ≥ 1 / 2, k Ea ≥ 1 / 2, 0 < α 3 < 1; T 3 is the predefined time constant, and T 3 > 0; k ε1 and k ε2 are preset parameters, T ε is the predefined time constant, and T ε > 0; the subscript ι ∈ {1, 2}, ε 1,l,i and ε 2,l,i represent the filter output signals, is the time derivative of ε 1,l,i , is the time derivative of ε 2,ι,i , e ε1,ι,i represents the filter error, and satisfies e ε1,2,i = (e ε1,2,x,i , e ε1,2,y,i ) = u ε,i - ε 1,2,i , eε1,1,x,i represents the corresponding virtual control signal filter error e ε1,1,i in the x-axis direction, e ε1,1,y,i represents the corresponding virtual control signal filter error e ε1,1,i in the y-axis direction; e ε1,2,x,i represents the corresponding u ε,i filter error e ε1,2,i in the x-axis direction; e ε1,2,y,i represents the corresponding u ε,i filter error e ε1,2,i in the y-axis direction.

[0171] When determining the lower-layer tracking controller, the above-mentioned lower-layer tracking controller was first designed, and then the lower-layer tracking controller was proved. Specifically, it includes:

[0172] Design the Lyapunov function Its time derivative has the following results:

[0173]

[0174] Design Lyapunov It can be obtained that

[0175]

[0176] According to the predefined time theory, the velocity and acceleration deviation errors can be obtained within time T low = 2T ε + T 3 converge to 0, that is, the system is stable under the design of this controller. In summary, the system realizes vehicle coordination within a fixed time under the designed double-layer controller, and the upper bound of time is

[0177] For the above scheme, the present invention conducts simulation verification:

[0178] Consider a vehicle queue composed of one leading vehicle and three following vehicles, and each vehicle is equipped with a short-range (50 meters) communication device. Select the vehicle model parameters as: m i = 1607 kg, τ i = 0.25, h a,i = 1.2 kg / m3, A i = 10.7 m2, C d,i = 0.57, r i = 0.006, g = 9.8 m / s 2 , α slope,i = 30°. The communication topology is: Specify the initial state of the leading vehicle as: x c,0 (0) = 9.9 m, y c,0 (0) = 10 m, θ 0 (0) = 0 rad, v c,0 (0) = 0 m / s, w c,0 (0) = 0 rad / s, and the motion state is: a v,0 (t) = 5 (t < 5 s) - 2 (5 s ≤ t < 9 s) + 0.5t (9 s ≤ t < 11 s) + 0 (t ≥ 11 s), aw,0(t) = 0 rad / s 2 Specify the initial motion states of the other vehicles in the vehicle platoon as: v i (0) = 0 m / s, a i (0) = 0 m 2 / s, and their initial position errors are: e x,1 (0) = 2 m, e y,1 (0) = 4 m, e x,1 (0) = 3 m, e y,1 (0) = 3.5 m, e x,1 (0) = 1 m, e y,1 (0) = 4 m.

[0179] The desired inter-vehicle distance is △ x,i,i-1 = 10 m, △ y,i,i-1 = 0 m. Select the parameters of the formation controller as: 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.

[0180] The simulation results are as Figures 3 - 7 shown. Among them, Figure 3 Figure (a) to Figure (c) in it show the motion trajectories of four vehicles under the designed hierarchical controller. Figure 4 In Figures (a) to (c) in it, the evolution of the speed deviations of Vehicle 1, Vehicle 2, and Vehicle 3 over time is given, Figure 5 and in Figures (a) to (c) in it, the evolution of the spacing errors of Vehicle 1, Vehicle 2, and Vehicle 3 over time is given. From this, it can be seen that the vehicle group has achieved the cooperative control goal. Figure 6 In Figures (a) to (c) in it, the filtering error e of Vehicle 1, Vehicle 2, and Vehicle 3 is given ε1,1,iEvolution over time Figure 7 In FIGS. (a) to (c) in the middle, the filtering errors e of vehicle 1, vehicle 2, and vehicle 3 ε1,2,i are shown evolving over time, where i = 1, 2, 3. It can be clearly seen that these errors converge to zero within a predefined time.

[0181] The key technical points of the present invention are as follows:

[0182] 1. A new distributed two-layer fixed-time spacing strategy is designed.

[0183] 2. For a third-order longitudinal and lateral platoon system, based on the logarithmic barrier penalty function method, the problem of fast cooperative control of platoons with communication constraints always maintained under the Euclidean distance is achieved.

[0184] Compared with the existing technologies, the advantages of the present invention are as follows: A sliding-mode-based zero-gradient and distributed optimization algorithm is designed, combined with the logarithmic barrier penalty function method, to solve the optimization problem under communication distance constraints and reach the desired inter-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 and prevent complexity explosion. An improved two-layer fixed-time vehicle cooperative control strategy is proposed, which can achieve optimal consensus with zero spacing error while maintaining communication connections.

[0185] The above description is only for the preferred embodiments of the present disclosure and the explanation of the applied technical principles. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by the specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, technical solutions formed by mutually replacing the above features with (but not limited to) technical features with similar functions disclosed in the embodiments of the present 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 fleet, construct a dynamic model for each vehicle, and obtain a dynamic model of the leading vehicle and dynamic models of other vehicles except the leading vehicle. The target fleet includes multiple vehicles, each vehicle is configured with a number, and all vehicles are arranged according to the number. The vehicle with the smallest number is taken as the leading vehicle, and all vehicles are led by the leading vehicle according to the number. Step 2: Determine the leading vehicle's leading position p h,0 , according to the leading vehicle's leading position p h,0 , transform the dynamic model of the leading vehicle to obtain the transformed dynamic model of the leading vehicle, and determine the leading position p of the i-th vehicle among the vehicles other than the leading vehicle h,i , according to the leading position p of the i-th vehicle h,i , transforming the dynamic model of the i-th vehicle among the vehicles other than the leading vehicle to obtain the transformed dynamic model of the i-th vehicle, and then obtaining the transformed dynamic models of the vehicles other than the leading vehicle, determining the spacing error between two adjacent vehicles, and constructing an error dynamic model according to the spacing error, the transformed dynamic model of the leading vehicle and the transformed dynamic models of the vehicles other than the leading vehicle; Step 3: Define the communication constraints in the Euclidean sense and determine the control optimization problem and the communication distance constraint function; Step 4: Design the upper optimization controller based on the error dynamics model, optimization problem and communication distance constraint function Step 5: Optimize the controller based on the error dynamics model and the upper layer A lower-layer tracking controller is designed, wherein the lower-layer tracking controller is used to realize control of the vehicle.

2. A 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, p c,0 =(x c,0 ,y c,0 ,θ0) T ; or c,0 =(v c,0 ,w c,0 ) T ; a c,0 =(a v,0 ,a w,0 ) T ; in, Yes c,0 The time derivative of c,0 represents the position and orientation of the leading vehicle in the inertial coordinate system, x c,0 The ordinate of the lead vehicle's position in the inertial coordinate system, y c,0 represents the horizontal coordinate of the position of the leading vehicle in the inertial coordinate system, θ0 represents the direction angle of the leading vehicle in the inertial coordinate system, η c,0 represents the velocity of the leading vehicle in the moving coordinate system, v c,0 represents the linear velocity of the leading vehicle in the moving coordinate system, w c,0 represents the angular velocity of the leading vehicle in the moving coordinate system, is η c,0 The time derivative of c,0 represents the acceleration of the leading vehicle in the moving coordinate system, a v,0 represents the linear acceleration of the leading vehicle in the moving coordinate system, a w,0 represents the angular acceleration of the lead vehicle in the moving coordinate system.

3. A method for controlling fixed-time vehicles in a coordinated manner while maintaining connectivity according to claim 2, characterized in that: The dynamic model of the vehicles other than the leading vehicle described in step 1 is specifically expressed by the following formula: in, p c,i (x c,i ,y c,i ,θ i ) T 4 or c,i =(v c,i ,w c,i ) T ; a c,i =(a v,i ,a w,i ) T ; in c,i =(in v,i ,in w,i ) T ; D c,i =(F U,i 0) T ; in, Yes c,i The time derivative of c,i represents the position and direction of the i-th vehicle in the inertial coordinate system among the vehicles other than the leading vehicle, i = 1, 2, ..., N, N represents the number of vehicles other than the leading vehicle, x c,i The ordinate of the position of the i-th vehicle in the inertial coordinate system, y c,i The horizontal coordinate of the position of the i-th vehicle in the inertial coordinate system, θ i represents the direction angle of the i-th vehicle in the inertial coordinate system, η c,i represents the speed of the i-th vehicle in the moving coordinate system, v c,i represents the linear velocity of the i-th vehicle in the moving coordinate system, w c,i represents the angular velocity of the i-th vehicle in the moving coordinate system, is η c,i The time derivative of c,i represents the acceleration of the i-th vehicle in the moving coordinate system, a v,i represents the linear acceleration of the i-th vehicle in the moving coordinate system, a w,i represents the angular acceleration of the i-th vehicle in the moving coordinate system, is a c,i The time derivative, u c,i represents the input of the i-th vehicle, u v,i is the throttle or brake input of the i-th vehicle, u w,i is the steering wheel input of the i-th vehicle, m i is the vehicle mass of the i-th vehicle, τ i is the engine time constant of the ith vehicle, h a,i is the air density of the ith car, A i is the cross-sectional area of ​​the ith vehicle, C d,i is the aerodynamic drag coefficient of the ith vehicle, r i is the rolling resistance coefficient of the tire of the i-th vehicle, g is the gravity constant, α slope,i is the road slope.

4. A method for controlling fixed-time vehicles in a coordinated manner while maintaining connectivity according to claim 3, characterized in that: The transformation dynamics model of the leading vehicle in step 2 is expressed by the following formula: in, p h，0 =(x h，0 ,y h，0 ) T η h,0 =(v x,0 ,v y,0 ) T ; a h,0 =(a x,0 ,a y,0 ) T ; in, Yes h,0 The time derivative of h,0 represents the leading position of the converted leading vehicle, x h,0 represents the longitudinal position of the leading vehicle after transformation, y h,0 represents the lateral position of the leading vehicle after the conversion; is η h,0 The time derivative of h,0 is the converted speed of the leading vehicle, v x,0 represents the converted longitudinal velocity of the leading vehicle, v y,0 represents the converted lateral velocity of the leading vehicle, a h,0 represents the converted acceleration of the leading vehicle, a x,0 represents the converted longitudinal acceleration of the leading vehicle, a y,0 Represents the converted lateral acceleration of the leading vehicle.

5. A method for controlling fixed-time vehicles in a coordinated manner while maintaining connectivity according to claim 4, characterized in that: The leading position p of the i-th vehicle among all vehicles except the leading vehicle in step 2 h,i It is expressed by the following formula: Among them, x h,i represents the longitudinal position of the i-th vehicle after transformation, y h,i represents the lateral position of the i-th vehicle after transformation, L i represents the straight-line distance between the center of mass position and the front position of the i-th vehicle; Based on this, the transformation dynamics model of the i-th vehicle is expressed by the following formula: in, η h，i =(v x，i ,v y，i ) T a h,i =(a x,i ,a y,i ) T ; in h,u =(in x,u ,in y,i ) T ; u h,i =J -1 (θ i )A c,i u c,i ; D h,i =J -1 (θ i )D c,i ; in, Yes h,i The time derivative of is η h,i The time derivative of h,i represents the speed of the i-th vehicle after transformation, v x,i represents the longitudinal velocity of the i-th vehicle after transformation, v y,i represents the lateral velocity of the i-th vehicle after transformation, is a h,i The time derivative of h,i represents the acceleration of the i-th vehicle after transformation, a x,i represents the longitudinal acceleration of the i-th vehicle after transformation, a y,i represents the lateral acceleration of the i-th vehicle after transformation, u x,i and u y,i represents the control input of the i-th vehicle after transformation, is J(θ i ), is J(θ i ) is the second-order time derivative, J -1 (θ i ) is J(θ i ) is the inverse matrix of .

6. A method for controlling fixed-time vehicles in a coordinated manner while 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: e i =p h,i-1 -p h,i -D i,i-1 ; Among them, e i =(e x,i ,e y,i ) T , e x,i represents the longitudinal spacing error between the i-th vehicle and the i-1-th vehicle on the two-dimensional plane; e y,i represents the lateral spacing error between the i-th vehicle and the i-1-th vehicle on the two-dimensional plane; Δ i,i-1 =(Δ x,i,i-1 ,Δ y,i,i-1 ) T is the desired constant distance between the i-1th vehicle and the i-th vehicle, Δ x,i,i-1 represents the expected constant distance between the i-th vehicle and the i-1-th vehicle in the longitudinal direction on the two-dimensional plane; Δ y,i,i-1 represents the desired constant distance between the i-th vehicle and the i-1-th vehicle in the lateral direction on the two-dimensional plane; p h,i-1 represents the front position of the i-1th vehicle; Based on this, the error dynamics model is expressed by the following formula: in, Indicates e i The first derivative in time, e i,i represents the speed error of the i-th vehicle, e a,i represents the acceleration error of the i-th vehicle, for e v,i The first time derivative of for e a,i The first time derivative of is Δ x,i,i-1 The third-order time derivative of is Δ y,i,i-1 The third-order time derivative of represents the time derivative of the longitudinal acceleration of the i-1th vehicle, Represents the time derivative of the lateral acceleration of the i-1th vehicle.

7. A method for controlling fixed-time vehicles in a coordinated manner while maintaining connectivity according to claim 6, characterized in that: The communication constraint condition in step 3 is the Euclidean distance D between the i-th vehicle and the i-1-th vehicle. i-1,i Less than the maximum effective communication distance d com , which is specifically expressed by the following formula: Among them, d com >0, t represents time, D i-1,i It is expressed by the following formula: Among them, x h,i-1 represents the longitudinal position of the i-1th vehicle after transformation, y h,i-1 represents the lateral position of the i-1th vehicle after transformation; The control optimization problem is expressed as follows: in, f i (e i ) is the objective function of the i-th vehicle, and e is the total distance error e i The stack vector, e j is the distance error of the jth vehicle, e * is the optimal solution to the control optimization problem, g i,com (e i ) is the communication distance constraint function, which is specifically expressed by the following formula:

8. The method for controlling fixed-time vehicles in a coordinated manner while maintaining connectivity according to claim 7, characterized in that: The upper optimization controller described in step 4 It is specifically expressed by the following formula: in, L bf,i (e i )f i (e i )-ρ bf,i log ( -g i,com (e i )) sig p (x)=(|x1|psign(x1),|x2|psign(x2),...,|x n |psign(x n )); Among them, α1, α2 and α3 are constants with 0<α1, α2<1, T1, T2 are predefined time constants satisfying T1, T2>0, and the two-dimensional column vector s i It is a sliding mode flow type, L bf,i (e i ) is the constructed logarithmic barrier penalty function, {e i |g i ,com(e i )<0}, is the function L bf,i (e i ) for its independent variable e i The derivative of is the function L bf,i (e i ) for its independent variable e i The second-order derivative of is the inverse of the second-order derivative matrix, is an auxiliary variable, k 1+ ,k 1- and k are control parameters, ρ bf,i is a preset positive value, N represents the number of vehicles other than the leading vehicle, N i represents the set of vehicles adjacent to the number of the i-th vehicle.

9. A method for controlling fixed-time vehicles in a coordinated manner while maintaining connectivity according to claim 8, characterized in that: The lower layer tracking controller in step 5 is specifically expressed by the following formula: in AND v,i =and v,i -ε 1,1,i ; AND a,i =and a,i -ε 1,2,i ; Among them, u ε,i is the input signal of vehicle i, i.e., the acceleration control signal, u h,i is the virtual speed control signal, speed deviation error E v,i =(E v,x,i ,E v,y,i ), E v,x,i Indicates the speed deviation error in the x-axis direction; E v,y,i Indicates the velocity deviation error in the y-axis direction; acceleration deviation error E a,i =(E a,x,i ,E a,y,i ), E a,x,i Indicates the acceleration deviation error in the x-axis direction; E a,y,i Indicates the acceleration deviation error in the y-axis direction; k Ev ,k Ea and α3 are preset parameters and satisfy k Ev ≥1 / 2,k Ea ≥1 / 2,0<α3<1; T3 is a predefined time constant, and T3>0; k ε1 and k ε2 is the preset parameter, T ε is a predefined time constant, and T ε >0; subscript ι∈{1,2}, ε 1,ι,i and ε 2,ι,i represents the filter output signal, is 1,ι,i The time derivative of is 2,ι,i The time derivative of ε1,ι,i Represents the filter error, satisfying 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 The filter error e ε1,1,i The size in the x-axis direction, e ε1,1,y,i Indicates the corresponding virtual control signal The filter error e ε1,1,i The size in the y-axis direction; e ε1,2,x,i Indicates the corresponding u ε,i The filter error e ε1,2,i The size in the x-axis direction; e ε1,2,y,i Indicates the corresponding u ε,i The filter error e ε1,2,i The size in the y-axis direction.

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