Multi-vehicle response networked autonomous vehicle hierarchical cooperative control method

Abstract

This invention discloses a hierarchical cooperative control method for multi-vehicle response connected autonomous vehicles, belonging to the field of intelligent connected vehicle cooperative control technology, and is used for longitudinal and lateral cooperative safety control of intelligent connected vehicle platoon merging at ramps. It includes: an upper layer based on PLF communication topology, combining second-order Taylor prediction feedforward and a variable headway model to generate desired acceleration, and using frequency domain constraints to ensure platoon chord stability; employing fifth-order polynomial programming to merge into a reference trajectory; a lower layer fusing control Lyapunov functions and higher-order barrier functions to construct a QP longitudinal controller, and designing a gain-scheduled LQR lateral tracking controller based on a two-degree-of-freedom vehicle model; quantifying the lateral encroachment range of the vehicle body and converting it into a longitudinal safety distance correction term, and achieving longitudinal and lateral coupled cooperative safety control through time-varying safety constraints. This method can effectively suppress platoon disturbance propagation, achieve high-precision trajectory tracking, and avoid lateral encroachment collision risks while ensuring stable operation of the vehicle platoon.

Description

Technical Field

[0001] This invention relates to the field of intelligent driving vehicle cooperative control technology, and discloses a hierarchical cooperative control method for connected autonomous vehicles with multi-vehicle response. Background Technology

[0002] With the rapid development of intelligent transportation and vehicle-to-everything (V2X) technologies, connected autonomous vehicles (CAVs) have become a key factor in improving road safety and driving efficiency by enabling real-time information sharing among multiple vehicles through vehicle-to-vehicle (V2V) and vehicle-to-everything (V2X) communication technologies. In vehicle platooning control, vehicles need to ensure smooth and safe traffic flow through real-time information sharing and strategy coordination. This relies on advanced communication technologies and intelligent algorithms to ensure that individual vehicles can effectively exchange information and make optimal decisions, thereby enhancing the overall system's efficiency and robustness. Currently, longitudinal control algorithms for vehicle platooning mainly adopt distributed control modes, with common control methods including cooperative adaptive cruise control, distributed robust control, distributed slippage control, and distributed model predictive control. Lateral vehicle movements include lane keeping, lane changing, and cornering; the accuracy of lateral control directly affects vehicle driving safety and lateral movement stability. Currently, the mainstream lateral control method mainly adopts path tracking strategies, which achieve lateral movement by controlling vehicles to travel along a pre-planned reference path. However, most current path tracking algorithms rely on the accuracy of trajectory planning, which limits the applicable scenarios for vehicle lateral movement control. Summary of the Invention

[0003] This invention discloses a hierarchical collaborative control method for connected autonomous vehicles with multi-vehicle response, in order to solve the technical problems of decoupling longitudinal and lateral control in the dynamic merging scenario of connected vehicle platoons, the inability of longitudinal safety constraints to adapt to lateral disturbances, and the difficulty in balancing platoon stability and driving safety.

[0004] A multi-vehicle response-based hierarchical cooperative control method for connected autonomous vehicles includes the following steps: S1. A leading vehicle-leading vehicle following PLF communication topology is adopted. The short-time domain motion state of the leading vehicle is predicted by the second-order Taylor formula and used as a feedforward quantity. The desired vehicle spacing is constructed by combining the variable headway model. The desired acceleration generation law is constructed based on the predicted state of the leading vehicle, the speed difference between the leading vehicle and the following vehicle and the spacing error. The stability of the queue is ensured by frequency domain constraints. S2. For vehicle merging scenarios, a continuous and smooth lateral reference path is generated by fitting a fifth-order polynomial. The path arc length is dynamically updated by combining the real-time vehicle speed and merging time to match the real-time motion state of the vehicle. S3. Based on the first-order inertial time-delay dynamics model of the vehicle, a quadratic programming QP controller is built that integrates the control Lyapunov function CLF and the control barrier function CBF. The stability of the queuing is guaranteed by the CLF constraint, and the longitudinal driving safety is guaranteed by the higher-order CBF constraint. S4. Based on the two-degree-of-freedom dynamic model of the vehicle, a lateral error state equation is constructed. A composite control strategy combining gain scheduling LQR state feedback and curvature feedforward compensation is adopted to output the front wheel steering angle and achieve high-precision tracking of the reference path. S5. Based on Lyapunov stability theory, it is proved that the lateral tracking error is bounded. Combining the lateral dynamic offset characteristics and physical motion boundary of the vehicle merging condition, the lateral trajectory tracking error effect is mapped to the longitudinal safety distance in real time. The time-varying control barrier function constraint of the condition-adaptive system is constructed to realize the safe and coordinated coupling control of the longitudinal and lateral motions during the vehicle merging process.

[0005] Furthermore, the adoption of a lead vehicle-lead vehicle following PLF communication topology, using a second-order Taylor formula to predict the short-time motion state of the lead vehicle and using it as a feedforward quantity, includes: The upper-level longitudinal speed guidance adopts a lead vehicle-lead vehicle following PLF communication topology. The following vehicle only obtains the status information of the lead vehicle and the lead vehicle in the prediction time domain. Inside, the second-order Taylor formula is used to predict the speed and acceleration of the navigator: ; In the formula, and These are the real-time longitudinal speed and acceleration of the lead vehicle, respectively. Let the rate of change of acceleration be... and These represent the predicted velocity and predicted acceleration of the navigator vehicle within the predicted time domain, respectively. For prediction in the time domain; The predicted value is used as a feedforward term for the expected acceleration of the following vehicle.

[0006] Furthermore, the construction of the desired vehicle spacing by combining the variable headway model includes: Connected vehicle platoons employ a variable headway strategy, dynamically adjusting the desired safe distance based on real-time vehicle speed. for: ; In the formula, For stationary safe distance, For the headway, Desired vehicle spacing; The following vehicle's following distance error is defined based on the actual vehicle distance and the expected vehicle distance. : ; In the formula, For the first The distance error between following vehicles. For the first The longitudinal position of the vehicle in front of the following vehicle. For the first The longitudinal position of the following vehicle. For the first The expected safe distance between vehicles.

[0007] Furthermore, the step of constructing the desired acceleration generation law based on the predicted state of the lead vehicle, the speed difference between the preceding and following vehicles, and the spacing error, and ensuring the chordal stability of the queue through frequency domain constraints, includes: By integrating the lead vehicle's feedforward, the speed difference between the two vehicles, and the spacing error, a longitudinal expected acceleration generation law is constructed: ; In the formula, and These are the predicted acceleration and predicted velocity of the navigator vehicle, respectively. , These are the speeds of the vehicle in front and the following vehicle, respectively. , , These are the navigation speed difference weighting coefficient, the preceding vehicle speed difference weighting coefficient, and the spacing error weighting coefficient, respectively. For vehicle spacing error, To determine the desired acceleration for the following vehicle; Integrate the desired acceleration to solve for the desired velocity and desired position of the following vehicle at the next moment: ; In the formula, To control the calculation cycle, For the first The longitudinal speed of the following vehicle, For the first The current longitudinal position of the following vehicle. In order to follow the car's expected speed at the next moment, To track the vehicle's desired position at the next moment, frequency domain analysis is performed on the desired acceleration generation law, and the transfer function of the distance error between adjacent vehicles is obtained through Laplace transform: ; In the formula, For the Laplace complex frequency operator, , , These are the feedback gain for vehicle spacing error, the feedback gain for the rate of change of vehicle spacing error, and the steady-state spacing error compensation gain, respectively. According to the stability condition of the queue string, when any angular frequency ,satisfy At that time, the propagation of queue errors is controllable, let , Substituting these values ​​into the adjacent vehicle spacing error transfer function, we obtain the sufficient conditions that the upper-level control parameters must satisfy: ; By selecting weight coefficients that satisfy the constraints , , This suppresses the propagation and amplification of spacing errors upstream along the vehicle convoy, ensuring the stable operation of the vehicle platoon.

[0008] Further, S2 includes: A 5th-order polynomial parameterized planning method is used to smoothly plan the lateral merging path, with arc length as the parameter. The horizontal offset of the independent variable : ; In the formula, This is the longitudinal arc length parameter of the path. , , , , , Let be the coefficients of the polynomial to be solved. The total path arc length and , , For each of the merging vehicles Speed ​​and expected acceleration Expected import time; The polynomial coefficients are solved using six sets of boundary conditions that are continuous throughout the entire path, including position, heading angle, and curvature, to ensure a smooth transition between the initial and final states of the planned path. The path start boundary conditions satisfy the continuity of lateral offset position, heading, and initial trajectory curvature, with the corresponding constraints being: , , , To incorporate the current trajectory curvature of the vehicle, , , These are the lateral offset, heading, and initial trajectory curvature of the starting point of the merging reference path, respectively. To compensate for the error between the merging vehicle's heading angle and the reference path's heading angle; the boundary conditions at the path endpoint satisfy lateral alignment, zeroing of heading and curvature, ensuring that the trajectory smoothly conforms to the target lane after merging, with the corresponding constraints being: , , , , , These are the lateral offset, heading, and curvature at the endpoint of the merged reference path, respectively. The lateral spacing between the center lines of adjacent lanes; Substitute the six boundary conditions into the lateral offset. In this process, by solving a system of linear equations, the polynomial coefficients are obtained, and an arc length update law is established: ; ; In the formula, for The arc length of the vehicle along the reference path at any given time. for The arc length of the vehicle along the reference path at any given time. for The first derivative of the arc length of the vehicle along the reference path at any given time with respect to time; The reference path shape and path length are dynamically and adaptively updated according to the real-time speed of the merging vehicles.

[0009] Furthermore, the vehicle-based first-order inertial time-delay dynamics model includes: A first-order inertial time-delay model is used as the longitudinal dynamics model of the vehicle: ; In the formula, For the first The real-time longitudinal position of the following vehicle with respect to time, first derivative. For the first The first derivative of the longitudinal velocity of the following vehicle with respect to time. For the first The actual longitudinal acceleration output of the following vehicle For the first derivative of acceleration with respect to time, The inertial time delay parameters of the vehicle engine. For the first The longitudinal control input for the following vehicle.

[0010] Furthermore, the construction of a quadratic programming QP controller that integrates the control Lyapunov function (CLF) and the control barrier function (CBF), ensuring queue following stability through CLF constraints and ensuring longitudinal driving safety through higher-order CBF constraints, includes: Based on the vehicle spacing error model and the expected vehicle spacing when the front end is variable The error is then differentiated in time using the first and second order derivatives. The first derivative yields the rate of change of the error. The second derivative yields the fundamental equation for the dynamic error. , For the first The first derivative of the longitudinal velocity of the following vehicle with respect to time; combining the longitudinal dynamics model of the vehicle, the expression for the rate of change of acceleration is obtained by deformation. ,Will Substituting into the second-order error dynamic equation and eliminating intermediate variables, we obtain the error dynamic equation that fully encompasses the vehicle's time-delay characteristics: ; In the formula, For the first The longitudinal acceleration of the following vehicle For the first Vehicle longitudinal control input, The time constant of the first-order inertial element of the vehicle's longitudinal actuator; Construct a combined error state quantity based on the error quantity and the error change rate. , , , For the constructed combined error state variables, Adjust the gain to the preset error state and Construct a positive definite control Lyapunov stability function based on the combined error state. : ; By taking the time derivative of the control Lyapunov function and introducing relaxation variables to construct a relaxable stability constraint, we can adapt to dynamic operating condition fluctuations. ; In the formula, The time derivative of the Lyapunov function. The attenuation rate and , The slack variables corresponding to the CLF stability constraints and ; Define system security set : ; In the formula, Let be the system state vector. For the first The following vehicle and the first The actual distance between the two vehicles in front. For the first The minimum safe following distance between vehicles; In the longitudinal dimension, the longitudinal distance between adjacent preceding and following vehicles shall not be less than the minimum safe vehicle spacing under the current operating conditions. : ; In the formula, This is the static minimum spacing. Minimum headway; Constructing a vertical security barrier function based on security sets : ; By sequentially taking the first and second time derivatives of the safety barrier function and simplifying the equations using the vehicle's first-order inertial time-delay longitudinal dynamics model, a result containing longitudinal control variables is obtained. The second-order dynamic expression of the barrier function is used to construct higher-order safety constraints; Since the system relative order corresponding to the longitudinal safety barrier function is 2, a two-level constraint chain is constructed based on the theory of higher-order control barrier functions; a linear K-function is selected. , , , For linear K-functions, , It is a positively adjustable gain parameter. For the independent variable of a linear class K function, construct auxiliary constraint variables in sequence and establish constraint inequalities. , These are first-order auxiliary constraint variables constructed based on the safety barrier function. Auxiliary constraint variables The first derivative with respect to time; Introducing a second-order extended K-function constraint chain to implement safety constraints for higher-order systems: ; In the formula, For the original security barrier variables, for The first derivative with respect to time, , It is a positively adjustable gain parameter; By establishing a time-delay dynamics model of the vehicle with constraint chains, eliminating intermediate variables, and deriving the model containing longitudinal control variables, the desired result can be obtained. Explicit CBF safety inequality constraints; Construct a QP solution framework, with the QP cost function as follows: ; In the formula, , , These are preset weighting coefficients, corresponding to control quantity tracking accuracy, control quantity smoothness, and slack variable penalty weight, respectively. For the first The longitudinal control input of the vehicle at the current moment needs to be solved. The desired control quantity at the current moment. For the first The longitudinal control input of the vehicle at the current moment needs to be solved. For the first The longitudinal control input of the vehicle at a given moment. For the first The slack variables corresponding to the CLF stability constraints of the vehicle; longitudinal control quantity With stability slack variables Together, they serve as the optimization variables in a quadratic programming problem. The cost function is used as the optimization objective. The optimization problem is constructed by combining the CLF stability constraint, the higher-order CBF safety constraint, and the longitudinal control magnitude constraint. By solving this quadratic programming optimization problem, the optimal longitudinal control input that simultaneously satisfies the system stability and driving safety constraints is obtained.

[0011] Further, S4 includes: A two-degree-of-freedom bicycle dynamics model is constructed based on the geodetic coordinate system and the vehicle's local coordinate system. Force and torque decompositions are performed on the entire vehicle, and the differential equations of lateral motion are obtained: ; In the formula, and These represent the longitudinal and lateral forces acting on the front wheels of the vehicle, respectively. For the overall vehicle quality, Let the vehicle's yaw moment of inertia be... For the longitudinal speed of the vehicle, For the vehicle's lateral acceleration, The yaw rate of the vehicle body. The yaw acceleration of the vehicle body. , These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. For the rear wheel to bear lateral force, The steering angle of the vehicle's front wheels; By rearranging and simplifying the equations of motion, we obtain the lateral dynamics state equations of the vehicle: ; In the formula, For the vehicle's lateral speed, , These are the combined lateral stiffness of the front and rear wheels, respectively. A lateral tracking error dynamic model is constructed. Based on the differential relationship of small-angle errors, the lateral dynamic state equations of the vehicle are solved simultaneously to obtain the lateral error state-space equations containing disturbances: ; In the formula, This is the first derivative of the lateral tracking error state vector with respect to time. This is the lateral tracking error state vector. For the system matrix, For the input matrix, The curvature perturbation vector; Design a gain-scheduled LQR optimal state feedback controller, ignoring curvature disturbance vectors, with the control objectives of minimizing trajectory tracking error in the infinite time domain and smoothing the front wheel steering angle control input, and construct a quadratic optimal control objective integral function: ; In the formula, It is a symmetric positive semidefinite state weighting matrix. To control the input weighting coefficients; The positive definite symmetric matrix is ​​obtained by solving the algebraic Riccati equation. Based on matrix Calculate the optimal feedback gain matrix Obtain the optimal feedback angle : ; Based on the steady-state circular motion characteristics of the vehicle, the feedforward compensation steering angle adapted to the variable curvature trajectory is derived. : ; In the formula, The curvature of the reference trajectory; Integrating LQR dynamic state feedback corner Curvature feedforward compensation angle The final front wheel steering angle control value is obtained. : .

[0012] Furthermore, the proof that the lateral tracking error is bounded based on Lyapunov stability theory includes: A lateral closed-loop perturbation system model is constructed. Based on the optimal feedback gain matrix of the fourth-order lateral error state space equation and the curvature feedforward compensation rotation angle, the lateral trajectory tracking closed-loop dynamic equation is obtained simultaneously. Integrating the reference trajectory curvature perturbation and the feedforward compensation residual error, a closed-loop dynamic model containing lumped bounded perturbations is constructed. ; In the formula, For a horizontal closed-loop system matrix, The disturbance term includes feedforward compensation residuals and curvature perturbations and satisfies , The maximum norm of the disturbance term; The boundedness of lateral tracking error is proved based on Lyapunov theory; a positive definite symmetric matrix is ​​obtained by solving the algebraic Riccati equation. Construct the positive definite Lyapunov energy function : ; By taking the time derivative of the Lyapunov energy function and substituting it into the transverse closed-loop perturbation dynamics equation, and combining this with solving the algebraic Riccati equation, the minimum eigenvalue property of positive definite matrices, and the Cauchy-Schwarz inequality, a scaling derivation is obtained to derive the upper bound constraint relationship of the energy function derivative. , For matrix The smallest eigenvalue; When the derivative of the energy function is less than 0, the global upper bound of the transverse state vector error is obtained: ; In the formula, This is the upper bound of the error; Define the maximum norm of the perturbation term as Determine the global upper bound of the lateral tracking error and prove that the error is bounded throughout the entire process: .

[0013] Furthermore, by combining the lateral dynamic offset characteristics and physical motion boundaries of the vehicle merging condition, the lateral trajectory tracking error effect is mapped to the longitudinal safety clearance in real time, and a time-varying control barrier function constraint that is adaptive to the operating condition is constructed to achieve safe and coordinated coupling control of the longitudinal and lateral motions during the vehicle merging process, including: Based on the vehicle's geometric dimensions, establish the following formulas for calculating the lateral offset of the four corner points of the vehicle body relative to the center of the reference trajectory: ; In the formula, The horizontal positions of the four corner points of the vehicle body. As a reference, the center position of the trajectory For the centroid lateral position tracking error, For vehicle width, The front overhang is the vehicle's wheelbase. The heading angle error is the tangential angle between the vehicle body axis and the reference trajectory. The derivation is based on the global error upper bound obtained from the lateral state vector. , By applying inequality scaling to the lateral offset using the small-angle approximation characteristic, the upper bound of the maximum lateral offset at the vehicle body corner is obtained: ; Based on the upper limit of the maximum lateral offset of the vehicle body, an additional safety margin is introduced, defining a universally applicable lateral safety envelope radius. : ; In the formula, To add a safety margin; A dynamic correction term for longitudinal safety distance is constructed, and a time-varying longitudinal safety margin correction term is designed to adapt to the merging conditions, taking into account the vehicle's longitudinal length, body width, and lateral safety envelope radius. ; In the formula, This is the dynamic correction amount for the longitudinal safety distance. This refers to the longitudinal length of the vehicle body. Preset safety ratio coefficient; By combining dynamic safety correction terms, time-varying high-order control barrier function constraints of the merging vehicle relative to the preceding and following vehicles are constructed to adapt to the longitudinal safety protection requirements under lateral dynamic disturbances. The longitudinal safety constraint barrier function for the vehicle merging into the target clearance ahead: ; In the formula, To account for the lateral inflow effect, for the first The time-varying safety barrier function constructed by the preceding vehicle. To merge the longitudinal position of the vehicle, To incorporate the real-time vehicle speed, The safety distance correction term is introduced to account for the merging effect, and the lateral position error is... Heading angle error longitudinal speed of vehicles Front wheel steering angle The function; The longitudinal safety constraint barrier function of the vehicle after merging the relative clearance between the vehicle and the target: ; In the formula, For the first The longitudinal position of the following vehicle; This achieves deep coupling between lateral trajectory tracking and longitudinal safety protection, ultimately ensuring a safe, stable, and collision-free process for vehicles merging into the convoy.

[0014] Compared with the prior art, the present invention has the following beneficial effects: This invention constructs a hierarchical collaborative control architecture, relying on the PLF communication topology combined with predictive feedforward and frequency domain constraints to ensure platoon chord stability. Simultaneously, it integrates a CLF and a higher-order CBF to construct a longitudinal QP controller and employs gain-scheduled LQR to achieve high-precision lateral trajectory tracking. By proving the boundedness of lateral tracking error through Lyapunov theory, it transforms the lateral vehicle encroachment effect into a time-varying longitudinal safety constraint, achieving deep coupling between longitudinal and lateral control. Compared to traditional decoupled control schemes, this invention can suppress the step-by-step transmission of disturbances between platoons, effectively avoiding the collision risk caused by lateral encroachment during merging, and improving driving safety in dynamic ramp merging scenarios while ensuring stable platoon following. Attached Figure Description

[0015] Figure 1 This is a flowchart of the technology of the present invention; Figure 2 The curve showing the change in the speed of the CAV convoy; Figure 3 The acceleration variation curve of the CAV convoy; Figure 4 This is a curve showing the change in the distance between the following vehicle and the front vehicle. Figure 5 The curve showing the change in distance deviation between the following vehicle and the vehicle in front during following; Figure 6 A three-dimensional motion trajectory diagram for dynamic integration of CAV queues under high-speed operating conditions; Figure 7 The curve shows the change in the distance between the front of the vehicles during the merging process of the CAV queue under high-speed conditions. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0017] Example 1 Multi-vehicle response hierarchical cooperative control method for connected autonomous vehicles, such as Figure 1 As shown, it includes the following steps: S1. A leading vehicle-leading vehicle following PLF communication topology is adopted. The short-time domain motion state of the leading vehicle is predicted by the second-order Taylor formula and used as a feedforward quantity. The desired vehicle spacing is constructed by combining the variable headway model. The desired acceleration generation law is constructed based on the predicted state of the leading vehicle, the speed difference between the leading vehicle and the following vehicle and the spacing error. The stability of the queue is ensured by frequency domain constraints. Considering that while V2V communication technology can acquire information about all vehicles in a platoon during platooning operations, using all this information for overall platoon control calculations would significantly increase the difficulty of subsequent model solving. Therefore, a lead-leader vehicle (PLF) communication topology is adopted, where following vehicles adjust their own operating status solely based on the status information of the lead and levitation vehicles. During platooning operations, the levitation vehicle follows a pre-defined strategy, while the following vehicles use the operating status information of the lead and levitation vehicles as input to control their following speed and acceleration, maintaining a suitable distance between vehicles at all times.

[0018] The upper-level longitudinal speed guidance adopts a lead vehicle-lead vehicle following PLF communication topology. The following vehicle only obtains the status information of the lead vehicle and the lead vehicle in the prediction time domain. Inside, the second-order Taylor formula is used to predict the speed and acceleration of the navigator vehicle: ; In the formula, and These are the real-time longitudinal speed and acceleration of the lead vehicle, respectively. Let the rate of change of acceleration be... and These represent the predicted velocity and predicted acceleration of the navigator vehicle within the predicted time domain, respectively. For prediction in the time domain; The predicted value is used as a feedforward to the expected acceleration of the following vehicle, ensuring that the queue can respond in advance when the speed changes; The connected vehicle platoon spacing strategy uses variable headway to determine the desired vehicle spacing. for: ; In the formula, For stationary safe distance, For the headway, Desired vehicle spacing; The difference between the actual distance between the following vehicle and the vehicle in front and the expected distance is defined as the spacing error. : ; In the formula, For the first The distance error between following vehicles. For the first The longitudinal position of the vehicle in front of the following vehicle. For the first The longitudinal position of the following vehicle. For the first The expected safe distance between vehicles; To ensure rapid convergence of spacing errors and maintain queue stability, the upper layer does not directly send absolute velocity values ​​to the lower layer; instead, it sends expected acceleration. The expected acceleration is a linear superposition of the lead vehicle's feedforward term, the velocity feedback term relative to the lead vehicle, the velocity feedback term relative to the preceding vehicle, and the spacing error feedback term, forming the longitudinal expected acceleration generation law: ; In the formula, and These are the predicted acceleration and predicted velocity of the navigator vehicle, respectively. , These are the speeds of the vehicle in front and the following vehicle, respectively. , , These are the navigation speed difference weighting coefficient, the preceding vehicle speed difference weighting coefficient, and the spacing error weighting coefficient, respectively. For vehicle spacing error, To determine the desired acceleration for the following vehicle; By performing a first-order integral on the desired acceleration, we obtain the desired velocity and desired position of the following vehicle at the next moment: ; In the formula, To control the calculation cycle, For the first The platform follows the actual speed of the vehicle at the current moment. For the first The platform follows the vehicle's current longitudinal position. In order to follow the car's expected speed at the next moment, To follow the vehicle to its expected position at the next moment; To ensure that the upper-level guiding law does not cause the error to amplify upstream along the queue, a frequency domain analysis is performed on the acceleration generation law. Ignoring the feedforward disturbance of the lead vehicle and considering error propagation, the Laplace transform and simplification of the desired vehicle spacing, spacing error, and longitudinal desired acceleration generation law yield the transfer function of the adjacent vehicle spacing error: ; In the formula, For the Laplace complex frequency operator, , , These are the feedback gain for vehicle spacing error, the feedback gain for the rate of change of vehicle spacing error, and the steady-state spacing error compensation gain, respectively. According to the definition of string stability, when for any angular frequency... ,when At that time, the propagation of queue errors is controllable, let , Substituting these values ​​into the adjacent vehicle spacing error transfer function, we obtain the sufficient conditions that the upper-level control parameters must satisfy: ; By selecting weight coefficients that satisfy the constraints , , This suppresses the propagation and amplification of spacing errors upstream along the vehicle convoy, ensuring the stable operation of the vehicle platoon.

[0019] S2. For vehicle merging scenarios, a continuous and smooth lateral reference path is generated by fitting a fifth-order polynomial. The path arc length is dynamically updated by combining the real-time vehicle speed and merging time to match the real-time motion state of the vehicle. A smooth and continuous lateral inflow reference path is constructed using a fifth-order polynomial parameterization method, with the path arc length in the Frenet coordinate system as the reference. Construct the horizontal offset as the independent variable. : ; In the formula, This is the longitudinal arc length parameter of the path. , , , , , Let be the coefficients of the polynomial to be solved. The total path arc length and , , For each of the merging vehicles Speed ​​and expected acceleration Expected import time; The boundary conditions for the polynomials are shown in Table 1. In Table 1, To incorporate the error between the vehicle's heading angle and the reference path's heading angle, The curvature of the vehicle's current trajectory. Distance from the center line of the lane; Table 1 Polynomial Boundary Conditions .

[0020] Substitute the six boundary conditions given in Table 1 into the lateral offset. In this process, the polynomial coefficients are obtained. It is also considered that the above-mentioned planned path depends only on the arc length. To ensure that the lateral planning path matches the real-time vehicle speed, an arc length update law is established: ; ; In the formula, in the formula, for The arc length of the vehicle along the reference path at any given time. for The arc length of the vehicle along the reference path at any given time. for The first derivative of the arc length of the vehicle along the reference path at any given time with respect to time; Combined lateral offset Using the arc length update law, the reference path for the current cycle is solved. The upper layer sends the reference path sequence to the lower layer for lateral control to ensure that vehicles merge smoothly.

[0021] S3. Based on the first-order inertial time-delay dynamics model of the vehicle, a quadratic programming QP controller is built that integrates the control Lyapunov function CLF and the control barrier function CBF. The stability of the queuing is guaranteed by the CLF constraint, and the longitudinal driving safety is guaranteed by the higher-order CBF constraint. The upper-level longitudinal collaborative planner is primarily responsible for determining the vehicle speed and acceleration control strategies, and using the lower-level longitudinal controller to maintain appropriate vehicle spacing within the connected vehicle platoon, balancing safety and road utilization. A connected vehicle platoon spacing control scheme is adopted, dynamically adjusting the platoon spacing through the CLF-CBF-QP controller to ensure the stability and safety of longitudinal following within the platoon.

[0022] A first-order inertial time-delay model is used as the longitudinal dynamics model of the vehicle: ; In the formula, For the first The real-time longitudinal position of the following vehicle with respect to time, first derivative. For the first The first derivative of the longitudinal velocity of the following vehicle with respect to time. For the first The actual longitudinal acceleration output of the following vehicle For the first derivative of acceleration with respect to time, The inertial time delay parameters of the vehicle engine. The desired longitudinal control acceleration output by the lower-level controller; Under ideal conditions, when a convoy of connected vehicles is in steady-state operation, if the speed of the lead vehicle remains constant, the following control objectives must be met between any two adjacent vehicles: ; In the formula, For the first The longitudinal speed of the following vehicle For the first Longitudinal acceleration of the following vehicle; Based on the vehicle spacing error model and the expected vehicle spacing when the front end is variable The error is then differentiated in time using the first and second order derivatives. The first derivative yields the rate of change of the error. ; The second derivative yields the fundamental equation for the error dynamics. By combining the longitudinal dynamics model of the vehicle and deforming it, the expression for the rate of change of acceleration can be obtained. ,Will Substituting into the second-order error dynamic equation and eliminating intermediate variables, we obtain the error dynamic equation that fully encompasses the vehicle's time-delay characteristics: ; In the formula, For the first Vehicle longitudinal control input, The time constant of the first-order inertial element of the vehicle's longitudinal actuator; To achieve error convergence control in stages, the first-level error state variables are defined. The rate of change of spacing error Set as a virtual control variable, construct a virtual control convergence relationship to ensure rapid convergence of the basic spacing error: ; In the formula, The expected rate of change of error, For the constructed combined error state variables, Adjust the gain to the preset error state and ; Define a second-level error state variable to characterize the deviation between the actual rate of change of error and the expected rate of change of error in the virtual control: ; In the formula, For the constructed combined error state variables; From the above formula, it can be seen that when the second layer error When it approaches 0, the first layer spacing error It can achieve exponential convergence, satisfying the steady-state car-following requirements of the queue. By simultaneously establishing the vehicle time-delay dynamics model, the second-order dynamic equation of the error, and the two-layer error state relation, the dynamic differential equation of the second-layer error state is obtained: ; Based on the two-level error state variables, a globally positive definite control Lyapunov function is constructed to determine the stability of the closed-loop system. ; Lyapunov functions with respect to time Differentiating the equation, substituting it into the error state dynamic equation, and rearranging, we obtain the stability criterion: ; To ensure that the vehicle spacing error continues to converge exponentially, the derivative of the Lyapunov function is constrained to satisfy... , where is the attenuation rate and ; By rearranging and transforming inequalities, the result containing the longitudinal control input is derived. Linear CLF stability constraints: ; Considering extreme conditions such as vehicle dynamic merging and emergency speed adjustment, where the spacing error approaches zero or the CLF stability constraint and CBF safety constraint are prone to conflict and optimization failure, a non-negative stability relaxation variable is introduced. The constraints are relaxed flexibly to prevent controller failure. The relaxed Lyapunov stability constraints are: ; In the formula, The slack variables corresponding to the CLF stability constraints and ; Finally, the following CLF explicit constraint conditions are obtained, which are adaptable to dynamic working conditions and compatible with safety constraint solutions: ; In the formula, For the first Slack variables for vehicle CLF stability constraints; By combining this stability constraint with the higher-order CBF safety constraint and embedding it into a quadratic programming QP solution framework, constraint conflict problems can be avoided while ensuring the stability of vehicle platoon following, thus achieving precise control of longitudinal stability and safety during the merging process of connected vehicle platoons. In connected vehicle platooning mode, to ensure no collisions occur when the platoon adjusts its longitudinal spacing, a safety set is defined. : ; In the formula, Let be the system state vector. For the first The following vehicle and the first The actual distance between the two vehicles in front. For the first The minimum safe following distance between vehicles; In the longitudinal dimension, the longitudinal distance between adjacent preceding and following vehicles shall not be less than the minimum safe distance under the current operating conditions. : ; In the formula, The minimum safe distance between two adjacent vehicles. This is the static minimum spacing. Minimum headway; Constructing a vertical security barrier function based on security sets : ; To explicitly introduce longitudinal control input into the constraint equations Take the first derivative of the barrier function with respect to time: ; After taking the first derivative of the barrier function with respect to time and then differentiating it again, the following can be obtained by combining the longitudinal dynamics model of the vehicle: ; A safety barrier function is employed, and auxiliary state variables are constructed in a hierarchical manner to transform the underlying safety conditions into linear control constraints that can be adapted to quadratic programming, ensuring that the safety set remains unchanged throughout the forward propagation. First, the first layer of auxiliary state variables is constructed, directly mapping the vehicle's original collision avoidance safety conditions: ; Since a single-layer barrier function cannot constrain the dynamics of a second-order system, a linear K-function is introduced. Construct a second layer of auxiliary state variables. The controller's self-designed adjustment function is used to integrate the value and rate of change of the safety barrier function, correct low-level safety state deviations, and achieve the first level of stabilization of safety constraints. ; In the formula, These are first-order auxiliary constraint variables constructed based on the safety barrier function. For the original security barrier variables, for The first derivative with respect to time; To completely lock the system's safe state and prevent dynamic instability of the second-level auxiliary variables from causing safety out-of-bounds errors, a linear K-function is further introduced. Dynamic constraints are applied to the second-level auxiliary variables to ensure, in principle, that the system always remains within a preset safe set. ; In the formula, Auxiliary constraint variables The first derivative with respect to time; To simplify online computation and adapt to the real-time solution requirements of onboard controllers, linear forms are selected as the two types of K functions. (Setting...) and , and , , It is a positively adjustable gain parameter. The independent variable is a linear K-function, used to adjust the response speed and relaxation margin of the collision avoidance constraint.

[0023] linear K-function Substituting into the formula for calculating the second-level auxiliary variables, and combining it with the expression for the first derivative of the barrier function, we can expand and simplify to obtain: ; right By performing time differentiation and simultaneously establishing the vehicle time-delay dynamics model, substituting the control variables and rearranging, we obtain the dynamic differential equations for the second layer of auxiliary variables: ; linear K-function Substitution In this process, we obtain the simplified solvable constraint form: ; United Equations of state Dynamic equations and top-level safety constraints, combined with like terms, will control the input. Placing it alone on the left side of the inequality, we ultimately obtain a higher-order CBF explicit safety constraint adapted to quadratic programming, which can achieve safe management of dynamic platoon following while ensuring vehicles travel without collisions. ; To enable the controller to respond promptly to upper-level inputs and quickly calculate the corresponding control quantities, a quadratic programming (QP) scheme is used to solve the model. That is, for each following vehicle in the connected vehicle fleet, the QP is solved in each control cycle.

[0024] For the following vehicle, the QP decision variables are defined as: ; In the formula, To control the quantity, For the first The slack variables corresponding to the CLF stability constraints of the vehicle; The QP cost function is constructed as follows: ; In the formula, , , These are preset weighting coefficients, corresponding to control quantity tracking accuracy, control quantity smoothness, and slack variable penalty weight, respectively. For the first The longitudinal control input of the vehicle at the current moment needs to be solved. The desired control quantity at the current moment. For the first The longitudinal control input of the vehicle at a given moment; The QP cost function is rearranged into quadratic programming canonical form, and the positive definite matrix is ​​derived. With gradient vector : ; ; In the formula, It is a positive definite matrix. For the first The longitudinal control input of the vehicle at a given moment; This ensures that there is a unique optimal solution to the QP optimization problem, guaranteeing the stability and uniqueness of the control output.

[0025] To simplify constraint expression and adapt to the standard QP solution framework, the CLF stability constraints and higher-order CBF safety constraints derived earlier are unified into linear inequality forms. Specifically, the CLF stability constraint is simplified to... , P is the optimized variable vector, and CLF stability constraints are the equivalent thresholds after adjustment. The advanced CBF collision avoidance safety constraints are simplified as follows: ; In the formula, The equivalent threshold after adjusting for higher-order CBF safety constraints; Obtain the complete QP constraints: ; In the formula, The constraint coefficient matrix and , For the constraint threshold vector and , , These are the upper and lower limits of the output of the vehicle's longitudinal actuator, corresponding to the vehicle's physical limits for acceleration and deceleration. Finally, a complete quadratic programming optimization model that balances stability, security, and physical constraints is constructed: ; ; By solving the QP model, the optimal longitudinal control quantity can be output in each control cycle, which not only ensures stable convergence of vehicle platoon spacing error and collision-free safe driving, but also avoids multi-constraint conflict problems, while satisfying the physical limitations of vehicle actuators, and realizes smooth, safe and high-precision dynamic car-following control of connected vehicle platoons.

[0026] S4. Based on the two-degree-of-freedom dynamic model of the vehicle, a lateral error state equation is constructed. A composite control strategy combining gain scheduling LQR state feedback and curvature feedforward compensation is adopted to output the front wheel steering angle and achieve high-precision tracking of the reference path. A two-degree-of-freedom bicycle dynamics model is constructed based on the geodetic coordinate system and the vehicle's local coordinate system. Force and torque decompositions are performed on the entire vehicle, and the differential equations of lateral motion are obtained: ; In the formula, and These represent the longitudinal and lateral forces acting on the front wheels of the vehicle, respectively. For the overall vehicle quality, Let the vehicle's yaw moment of inertia be... For the longitudinal speed of the vehicle, For the vehicle's lateral acceleration, The yaw rate of the vehicle body. The yaw acceleration of the vehicle body. , These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. For the rear wheel to bear lateral force, The steering angle of the vehicle's front wheels; By rearranging and simplifying the equations of motion, we obtain the lateral dynamics state equations of the vehicle: ; In the formula, For the vehicle's lateral speed, , These are the combined lateral stiffness of the front and rear wheels, respectively. A lateral tracking error dynamic model is constructed. Based on the differential relationship of small-angle errors, the lateral dynamic state equations of the vehicle are solved simultaneously to obtain the lateral error state-space equations containing disturbances: ; In the formula, Let be the lateral tracking error state vector and , Given an input matrix and , Let be the curvature perturbation vector and , The system matrix and , This is the lateral position error. This represents the rate of change of the lateral error. For heading angle error, The rate of change of heading angle error. For reference trajectory curvature, For the overall vehicle weight, This refers to the vehicle's real-time longitudinal speed. The rate of change of curvature of the reference trajectory; To achieve rapid convergence of lateral path tracking error while suppressing frequent fluctuations in front wheel steering angle control, and to balance tracking accuracy and ride comfort, an infinite-time domain LQR optimal controller is designed based on simplified state equations. A quadratic optimal objective function is constructed, using the cumulative state deviation and cumulative control input during the tracking process as the optimization weighting objectives: ; In the formula, It is a symmetric positive semi-definite state weighting matrix, taken as a diagonal matrix. To control the input weighting coefficients, used to limit the front wheel steering angle amplitude; The vehicle lateral control problem is treated as a quadratic optimal control problem, and the optimal input is solved. Make the objective function Minimize by solving the algebraic Riccati equation This yields a positive definite symmetric matrix. Based on matrix Calculate the optimal feedback gain matrix The optimal feedback turning angle is obtained: ; Pure LQR state feedback control can achieve asymptotic stability of a disturbance-free homogeneous error system and effectively eliminate dynamic tracking deviations, but it cannot offset the inherent steady-state disturbances caused by path curvature, resulting in steady-state tracking errors and making it difficult to meet the requirements for high-precision path merging. To eliminate steady-state errors caused by curvature and further improve trajectory tracking accuracy, a feedforward steering angle compensation is introduced, constructing a composite lateral control architecture of state feedback + feedforward compensation. Based on the vehicle's steady-state circular driving mechanics characteristics, the feedforward compensation steering angle adapted to variable curvature trajectories is derived. : ; Integrating LQR dynamic state feedback corner Curvature feedforward compensation angle The final front wheel steering angle control value is obtained. : ; Substituting the total control law into the transverse error state-space equations, we can simultaneously derive the dynamic equations of the closed-loop system: ; The optimal feedback gain is obtained by solving the algebraic Riccati equation. This allows the closed-loop system matrix to be... Satisfying the Hurwitz stability condition ensures the global asymptotic stability of the closed-loop lateral control system. When the system reaches steady state, the dynamic rate of change of the tracking error is zero, i.e. To make the steady-state tracking error approach zero and completely offset the effects of curvature disturbances, the steady-state compensation condition must be met: ; The designed LQR feedback + feedforward compensation composite lateral controller balances dynamic correction capability and steady-state error compensation capability, and the final front wheel steering angle control value is: ; This composite control strategy can effectively adapt to complex merging conditions such as time-varying vehicle speed and curved paths. It not only ensures the dynamic stability of the lateral system, but also completely eliminates the steady-state tracking error caused by curvature disturbances. Combined with the longitudinal queue safety constraint control mentioned above, it enables efficient, safe and high-precision collaborative merging of connected vehicle queues.

[0027] S5. Based on Lyapunov stability theory, it is proved that the lateral tracking error is bounded. Combining the lateral dynamic offset characteristics and physical motion boundary of the vehicle merging condition, the lateral trajectory tracking error effect is mapped to the longitudinal safety distance in real time. The time-varying control barrier function constraint of the condition-adaptive system is constructed to realize the safe and coordinated coupling control of the longitudinal and lateral motions during the vehicle merging process.

[0028] A lateral closed-loop perturbation system model is constructed. Based on the optimal feedback gain matrix of the fourth-order lateral error state space equation and the curvature feedforward compensation rotation angle, the lateral trajectory tracking closed-loop dynamic equation is obtained simultaneously. Integrating the reference trajectory curvature perturbation and the feedforward compensation residual error, a closed-loop dynamic model containing lumped bounded perturbations is constructed. ; In the formula, For a horizontal closed-loop system matrix, The disturbance term includes feedforward compensation residuals and curvature perturbations and satisfies , The maximum norm of the disturbance term; Positive definite symmetric matrices obtained by solving the algebraic Riccati equations Construct a positive definite Lyapunov energy function to determine the error convergence characteristics of the closed-loop system: ; By taking the time derivative of the Lyapunov energy function and substituting it into the transverse closed-loop perturbation dynamics equation, and combining the solution of the algebraic Riccati equation, the minimum eigenvalue property of the positive definite matrix, and the Cauchy-Schwarz inequality, a scaling derivation is obtained, yielding the upper bound constraint relationship of the energy function derivative: ; In the formula, For matrix The smallest eigenvalue and ; When the derivative of the energy function is less than zero, the system energy continues to decay, the tracking error converges steadily, and the global upper bound of the transverse state vector is obtained: ; In the formula, The upper bound of the error limits the extreme offset range of the vehicle's center of gravity lateral displacement error and heading angle error.

[0029] Define the maximum norm of the perturbation term as By using global scaling of inequalities, the global upper bound of the lateral tracking error can be determined, proving that the error is bounded throughout the entire process: ; Simply constraining the lateral error of the vehicle's center of gravity cannot completely eliminate the risk of merging collisions. As a rigid body structure, lateral displacement and yaw deflection will cause the four corners of the vehicle to shift, expanding the vehicle's longitudinal footprint and making it highly susceptible to encroaching on the safe zone of the target merging gap. Therefore, this invention, based on the conclusion of the boundedness of lateral error, quantifies the maximum lateral offset of the vehicle body, constructs a lateral safety envelope, and further realizes dynamic correction of the longitudinal CBF safety distance, achieving coordinated lateral and longitudinal safety control.

[0030] Based on the vehicle's geometric dimensions, establish the following formulas for calculating the lateral offset of the four corner points of the vehicle body relative to the center of the reference trajectory: ; In the formula, The horizontal positions of the four corner points of the vehicle body As a reference, the center position of the trajectory This refers to the lateral position tracking error of the centroid. For vehicle width, The front overhang is the vehicle's wheelbase. The heading angle error is the tangential angle between the vehicle body axis and the reference trajectory. The derivation is based on the global error upper bound obtained from the lateral state vector. , By applying inequality scaling to the lateral offset using the small-angle approximation characteristic, the upper bound of the maximum lateral offset at the vehicle body corner is obtained: ; To uniformly characterize the maximum safe lateral offset range of a vehicle, a safety margin is introduced to construct a lateral safety envelope radius, covering all extreme lateral offset conditions, and a universally applicable lateral safety envelope radius is defined. : ; In the formula, The lateral safety envelope radius of the vehicle. To add a safety margin; A dynamic correction term for longitudinal safety distance is constructed, and a time-varying longitudinal safety margin correction term is designed to adapt to the merging conditions, taking into account the vehicle's longitudinal length, body width, and lateral safety envelope radius. ; In the formula, This is the dynamic correction amount for the longitudinal safety distance. This refers to the longitudinal length of the vehicle body. To preset the safety ratio coefficient, This is the lateral position error. For heading angle error, For the longitudinal speed of the vehicle, The steering angle of the vehicle's front wheels; To address the bidirectional collision risk between the merging vehicle and the target vehicle, and in conjunction with dynamic safety correction terms, time-varying high-order control barrier function constraints are constructed for the merging vehicle relative to the preceding and following vehicles, respectively, to adapt to the longitudinal safety protection requirements under lateral dynamic disturbances. The longitudinal safety constraint barrier function for the vehicle ahead of the target clearance entering the vehicle: ; In the formula, To account for the lateral inflow effect, for the first The time-varying safety barrier function constructed by the preceding vehicle. For the first The longitudinal position of the vehicle in front of the following vehicle. To merge the longitudinal position of the vehicle, To incorporate the real-time vehicle speed, The safety distance correction term is introduced to account for the merging effect, and the lateral position error is... Heading angle error longitudinal speed of vehicles Front wheel steering angle The function; The longitudinal safety constraint barrier function of the vehicle after merging the relative clearance between the vehicle and the target: ; In the formula, For the first The longitudinal position of the following vehicle; This achieves deep coupling between lateral trajectory tracking and longitudinal safety protection, ultimately ensuring a safe, stable, and collision-free process for vehicles merging into the convoy. Example

[0031] Simulation experiments were conducted using the built-in D-Level Sedan vehicle model in Carsim, with the experimental scenario set as a highway. The experiments verified the CAV merging performance of the connected vehicle platoon under different speed conditions under the cooperative controller. Furthermore, the feasibility of the proposed cooperative control framework in traffic scenarios was verified by analyzing the operating parameters of all vehicles in the scenario. The experiment consisted of two verification phases: Phase 1 verified the driving effect of the connected vehicle platoon under the CLF-CBF-QP controller; Phase 2 verified the impact of external CAV merging on the connected vehicle platoon under feedforward LQR and time-varying CBF cooperative control.

[0032] In the first phase of the experiment, a highway scenario was set up with 7 CAVs traveling in a convoy. The initial speed of the lead car was set to 60 km / h, and the simulation duration was set to 150 seconds. The speed of the lead car changed continuously during the driving process to verify the stability of the vehicle convoy following the longitudinal controller.

[0033] The longitudinal simulation results of the CAV platoon show that, at a speed of 60 km / h, the platoon maintains a stable spacing. Even when the lead vehicle's speed changes, the following vehicles maintain good following performance. Figure 2 and Figure 3 The speed and acceleration information of the platoon shows that when the speed of the lead vehicle changes, the following vehicles can quickly respond to the changes in the state of the lead vehicle and maintain the same control objective as the lead vehicle as possible, and the platoon operation satisfies chord stability. Figure 4 and Figure 5 The system provides information on the headway and following distance deviation of the connected platoon. When the speed of the lead vehicle changes, the platoon can quickly adjust the platoon spacing and maintain a consistent target spacing after the speed stabilizes. During the entire platoon's operation, the absolute value of the following distance deviation between the following vehicle and the vehicle in front is less than 0.025s.

[0034] In the first phase of the experiment, the changes in the operating status of the lead vehicle had the greatest impact on the following vehicle V1 and the V0-V1 distance. The following distance deviation of the subsequent platoon did not change significantly. This indicates that in the highway scenario, the longitudinal controller based on the CLF-CBF-QP design has good control performance and can meet the requirements of the stability of the connected platoon following.

[0035] In the second phase of the experiment, two operating conditions were set: a low initial speed of 60 km / h and a high initial speed of 90 km / h for the connected queue, to verify the feasibility of the hierarchical collaborative control scheme during the merging of external CAVs. The LQR controller was applied to the lateral control of the connected queue merging scenario. It fits a fifth-order polynomial lateral merging trajectory through upper-level lateral path planning and tracks this path. Simultaneously, the longitudinal time-varying CBF control queue reserves a safe merging distance, achieving longitudinal and lateral collaborative control of the merging scenario.

[0036] Under low-speed conditions, the control results of CAV lateral motion and the vehicle motion state process show that the feedforward LQR can track the upper-level path planning very well. During the merging process, the lateral displacement error of the vehicle is less than 0.1m, the maximum heading angle error is 0.17°, and the maximum tracking error of the output front wheel steering angle is 0.23°, indicating that the lateral controller has good control accuracy.

[0037] Under low-speed conditions, when a CAV merges into a connected vehicle queue, the longitudinal and lateral movements of vehicles within the queue are affected by the merging of external vehicles. The proposed hierarchical collaborative control method allows these disturbances to recover and stabilize relatively quickly. An external CAV accelerates from behind towards the connected queue, gradually approaching the target gap V3-V4. Through longitudinal and lateral collaborative control, it interacts with the queue, which adjusts its speed to create a suitable vehicle spacing, enabling the CAV to successfully merge. The nearly identical changes in the headway V3H and H-V4 during the vehicle H merging process demonstrate that time-varying CBF control can dynamically adjust the appropriate headway, ensuring safety during the interaction between merging vehicles and the queue.

[0038] Table 2 shows the control performance of fixed CBF and time-varying CBF under low-speed conditions. As can be seen from Table 2, during CAV merging, the vehicle spacing constraint using time-varying CBF is 2.56m higher in the minimum longitudinal spacing than that using fixed CBF, indicating that time-varying CBF control has a higher safety margin in the longitudinal direction. The average lane-changing speed of time-varying CBF is higher than that of fixed CBF, and the lane-changing time is reduced by 0.85s, indicating that time-varying CBF has higher lane-changing efficiency. In terms of peak longitudinal and lateral acceleration, compared to fixed CBF, the peak longitudinal and lateral acceleration of time-varying CBF is lower. and This indicates that the speed change of the time-varying CBF is more gradual, resulting in greater comfort.

[0039] Table 2 Performance Evaluation Table for CAV Import under Low-Speed ​​Conditions .

[0040] Simulation results demonstrate that under low-speed conditions, the longitudinal and transverse controllers can ensure the effectiveness of longitudinal and transverse control of the CAV queue and can complete the task of merging external CAVs.

[0041] The effectiveness and safety of the longitudinal and lateral controllers under high-speed driving conditions were verified in a high-speed scenario.

[0042] Under high-speed conditions, with the coordinated control of the longitudinal and lateral controllers, the lateral displacement error of the CAV during the merging process remains less than 0.1m, the maximum heading angle error is 0.22°, and the maximum tracking error of the output front wheel steering angle is 0.55°. The control results demonstrate that the coordinated controller still meets the CAV control requirements under high-speed conditions.

[0043] The three-dimensional trajectory and headway of the CAV platoon under high-speed conditions are as follows: Figure 6 and Figure 7 As shown, by Figure 6 and Figure 7It can be seen that during the process of external CAV merging, it interacts with the vehicle queue through the longitudinal and lateral collaborative controller. The queue creates a suitable merging gap for it, so that the CAV can successfully merge into the target gap. After the CAV merges in, it forms a new connected vehicle queue with the original queue. The headway quickly converges to a stable state, eliminating the disturbance caused by the merging of external CAV.

[0044] Table 3 shows the control performance of fixed and time-varying CBFs under high-speed conditions. As can be seen from Table 3, the minimum longitudinal spacing of the time-varying CBF is 3.25m higher than that of the fixed CBF, indicating a higher safety margin. The average lane-changing speed of the time-varying CBF is still higher than that of the fixed CBF, and the lane-changing time is reduced by 0.87s, resulting in higher merging efficiency. The peak longitudinal and lateral accelerations of the time-varying CBF are lower than those of the fixed CBF. and It offers greater comfort during the merging process.

[0045] Table 3 Performance Evaluation Table for CAV Import under High-Speed ​​Operating Conditions .

[0046] Simulation results demonstrate the effectiveness of the proposed hierarchical cooperative control framework in longitudinal queuing control and longitudinal-lateral cooperative control under low-speed and high-speed road conditions. In particular, it exhibits excellent control performance in scenarios where external CAVs merge into the connected queuing, ensuring the safety and efficiency of both external CAVs and the connected queuing.

[0047] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A hierarchical cooperative control method for connected autonomous vehicles with multi-vehicle response, characterized in that, Includes the following steps: S1. A leading vehicle-leading vehicle following PLF communication topology is adopted. The short-time domain motion state of the leading vehicle is predicted by the second-order Taylor formula and used as a feedforward quantity. The desired vehicle spacing is constructed by combining the variable headway model. The desired acceleration generation law is constructed based on the predicted state of the leading vehicle, the speed difference between the leading vehicle and the following vehicle and the spacing error. The stability of the queue is ensured by frequency domain constraints. S2. For vehicle merging scenarios, a continuous and smooth lateral reference path is generated by fitting a fifth-order polynomial. The path arc length is dynamically updated by combining the real-time vehicle speed and merging time to match the real-time motion state of the vehicle. S3. Based on the first-order inertial time-delay dynamics model of the vehicle, a quadratic programming QP controller is built that integrates the control Lyapunov function CLF and the control barrier function CBF. The stability of the queuing is guaranteed by the CLF constraint, and the longitudinal driving safety is guaranteed by the higher-order CBF constraint. S4. Based on the two-degree-of-freedom dynamic model of the vehicle, a lateral error state equation is constructed. A composite control strategy combining gain scheduling LQR state feedback and curvature feedforward compensation is adopted to output the front wheel steering angle and achieve high-precision tracking of the reference path. S5. Based on Lyapunov stability theory, it is proved that the lateral tracking error is bounded. Combining the lateral dynamic offset characteristics and physical motion boundary of the vehicle merging condition, the lateral trajectory tracking error effect is mapped to the longitudinal safety distance in real time. The time-varying control barrier function constraint of the condition-adaptive system is constructed to realize the safe and coordinated coupling control of the longitudinal and lateral motions during the vehicle merging process.

2. The multi-vehicle response-based hierarchical cooperative control method for connected autonomous vehicles according to claim 1, characterized in that, The method employs a lead vehicle-lead vehicle following PLF communication topology, utilizing a second-order Taylor formula to predict the short-time motion state of the lead vehicle and using it as a feedforward quantity, including: The upper-level longitudinal speed guidance adopts a lead vehicle-lead vehicle following PLF communication topology. The following vehicle only obtains the status information of the lead vehicle and the lead vehicle in the prediction time domain. Inside, the second-order Taylor formula is used to predict the speed and acceleration of the navigator vehicle: ； In the formula, and These are the real-time longitudinal speed and acceleration of the lead vehicle, respectively. Let the rate of change of acceleration be... and These represent the predicted velocity and predicted acceleration of the navigator vehicle within the predicted time domain, respectively. For prediction in the time domain; The predicted value is used as a feedforward term for the expected acceleration of the following vehicle.

3. The multi-vehicle response-based hierarchical cooperative control method for connected autonomous vehicles according to claim 2, characterized in that, The construction of the desired vehicle spacing by combining the variable headway model includes: Connected vehicle platoons employ a variable headway strategy, dynamically adjusting the desired safe distance based on real-time vehicle speed. for: ； In the formula, For stationary safe distance, The headway is the distance between the front and rear of the train. Desired vehicle spacing; The following vehicle's following distance error is defined based on the actual vehicle distance and the expected vehicle distance. : ； In the formula, For the first The distance error between following vehicles. For the first The longitudinal position of the vehicle in front of the following vehicle. For the first The longitudinal position of the following vehicle. For the first The expected safe distance between vehicles.

4. The multi-vehicle response-based hierarchical cooperative control method for connected autonomous vehicles according to claim 3, characterized in that, The process of constructing a desired acceleration generation law based on the predicted state of the lead vehicle, the speed difference between the preceding and following vehicles, and the spacing error, and ensuring the stability of the queuing chord through frequency domain constraints, includes: By integrating the lead vehicle's feedforward, the speed difference between the two vehicles, and the spacing error, a longitudinal expected acceleration generation law is constructed: ； In the formula, and These are the predicted acceleration and predicted velocity of the navigator vehicle, respectively. , These are the speeds of the vehicle in front and the following vehicle, respectively. , , These are the navigation speed difference weighting coefficient, the preceding vehicle speed difference weighting coefficient, and the spacing error weighting coefficient, respectively. For vehicle spacing error, To determine the desired acceleration for the following vehicle; Integrate the desired acceleration to solve for the desired velocity and desired position of the following vehicle at the next moment: ； In the formula, To control the calculation cycle, For the first The longitudinal speed of the following vehicle, For the first The current longitudinal position of the following vehicle. In order to follow the car's expected speed at the next moment, To follow the vehicle to its desired position at the next moment; Frequency domain analysis was performed on the expected acceleration generation law, and the transfer function of the distance error between adjacent vehicles was obtained by Laplace transform: ； In the formula, For the Laplace complex frequency operator, , , These are the feedback gain for vehicle spacing error, the feedback gain for the rate of change of vehicle spacing error, and the steady-state spacing error compensation gain, respectively. According to the stability condition of the queue string, when any angular frequency ,satisfy At that time, the propagation of queue errors is controllable, let , Substituting these values ​​into the adjacent vehicle spacing error transfer function, we obtain the sufficient conditions that the upper-level control parameters must satisfy: ； By selecting weight coefficients that satisfy the constraints , , This suppresses the propagation and amplification of spacing errors upstream along the vehicle convoy, ensuring the stable operation of the vehicle platoon.

5. The multi-vehicle response-based hierarchical cooperative control method for connected autonomous vehicles according to claim 4, characterized in that, S2 includes: A 5th-order polynomial parameterized planning method is used to smoothly plan the lateral merging path, with arc length as the parameter. The horizontal offset of the independent variable : ； In the formula, This is the longitudinal arc length parameter of the path. , , , , , Let be the coefficients of the polynomial to be solved. The total path arc length and , , For each of the merging vehicles Speed ​​and expected acceleration Expected import time; The polynomial coefficients are solved using six sets of boundary conditions that are continuous throughout the entire path, including position, heading angle, and curvature, to ensure a smooth transition between the initial and final states of the planned path. The path start boundary conditions satisfy the continuity of lateral offset position, heading, and initial trajectory curvature, with the corresponding constraints being: , , , To incorporate the current trajectory curvature of the vehicle, , , These are the lateral offset, heading, and initial trajectory curvature of the starting point of the merging reference path, respectively. To compensate for the error between the merging vehicle's heading angle and the reference path's heading angle; the boundary conditions at the path endpoint satisfy lateral alignment, zeroing of heading and curvature, ensuring that the trajectory smoothly conforms to the target lane after merging, with the corresponding constraints being: , , , , , These are the lateral offset, heading, and curvature at the endpoint of the merged reference path, respectively. The lateral spacing between the center lines of adjacent lanes; Substitute the six boundary conditions into the lateral offset. In this process, by solving a system of linear equations, the polynomial coefficients are obtained, and an arc length update law is established: ； ； In the formula, for The arc length of the vehicle along the reference path at any given time. for The arc length of the vehicle along the reference path at any given time. for The first derivative of the arc length of the vehicle along the reference path at any given time with respect to time; The reference path shape and path length are dynamically and adaptively updated according to the real-time speed of the merging vehicles.

6. The multi-vehicle response-based hierarchical cooperative control method for connected autonomous vehicles according to claim 5, characterized in that, The vehicle-based first-order inertial time-delay dynamics model includes: A first-order inertial time-delay model is used as the longitudinal dynamics model of the vehicle: ； In the formula, For the first The real-time longitudinal position of the following vehicle with respect to time, first derivative. For the first The first derivative of the longitudinal velocity of the following vehicle with respect to time. For the first The actual longitudinal acceleration output of the following vehicle For the first derivative of acceleration with respect to time, The inertial time delay parameters of the vehicle engine. For the first The longitudinal control input for the following vehicle.

7. The multi-vehicle response-based hierarchical cooperative control method for connected autonomous vehicles according to claim 6, characterized in that, The construction of a quadratic programming QP controller that integrates the control Lyapunov function (CLF) and the control barrier function (CBF) ensures queue following stability through CLF constraints and longitudinal driving safety through higher-order CBF constraints, including: Based on the vehicle spacing error model and the expected vehicle spacing when the front end is variable The error is then differentiated in time using the first and second order derivatives. The first derivative yields the rate of change of the error. The second derivative yields the fundamental equation for the dynamic error. , For the first The first derivative of the longitudinal velocity of the following vehicle with respect to time; combining the longitudinal dynamics model of the vehicle, the expression for the rate of change of acceleration is obtained by deformation. ,Will Substituting into the second-order error dynamic equation and eliminating intermediate variables, we obtain the error dynamic equation that fully encompasses the vehicle's time-delay characteristics: ； In the formula, For the first The longitudinal acceleration of the following vehicle For the first Vehicle longitudinal control input, The time constant of the first-order inertial element of the vehicle's longitudinal actuator; Construct a combined error state quantity based on the error quantity and the error change rate. , , , For the constructed combined error state variables, Adjust the gain to the preset error state and Construct a positive definite control Lyapunov stability function based on the combined error state. : ； By taking the time derivative of the control Lyapunov function and introducing relaxation variables to construct a relaxable stability constraint, we can adapt to dynamic operating condition fluctuations. ； In the formula, The time derivative of the Lyapunov function. The attenuation rate and , The slack variables corresponding to the CLF stability constraints and ; Define system security set : ； In the formula, Let be the system state vector. For the first The following vehicle and the first The actual distance between the two vehicles in front. For the first The minimum safe following distance between vehicles; In the longitudinal dimension, the longitudinal distance between adjacent preceding and following vehicles shall not be less than the minimum safe vehicle spacing under the current operating conditions. : ； In the formula, This is the static minimum spacing. Minimum headway; Constructing a vertical security barrier function based on security sets : ； By sequentially taking the first and second time derivatives of the safety barrier function and simplifying the equations using the vehicle's first-order inertial time-delay longitudinal dynamics model, a result containing longitudinal control variables is obtained. The second-order dynamic expression of the barrier function is used to construct higher-order safety constraints; Since the system relative order corresponding to the longitudinal safety barrier function is 2, a two-level constraint chain is constructed based on the theory of higher-order control barrier functions; a linear K-function is selected. , , , For linear K-functions, , It is a positively adjustable gain parameter. For the independent variable of a linear class K function, construct auxiliary constraint variables in sequence and establish constraint inequalities. , These are first-order auxiliary constraint variables constructed based on the safety barrier function. Auxiliary constraint variables The first derivative with respect to time; Introducing a second-order extended K-function constraint chain to implement safety constraints for higher-order systems: ； In the formula, For the original security barrier variables, for The first derivative with respect to time, , It is a positively adjustable gain parameter; By establishing a time-delay dynamics model of the vehicle with constraint chains, eliminating intermediate variables, and deriving the model containing longitudinal control variables, the desired result can be obtained. Explicit CBF safety inequality constraints; Construct a QP solution framework, with the QP cost function as follows: ； In the formula, , , These are preset weighting coefficients, corresponding to control quantity tracking accuracy, control quantity smoothness, and slack variable penalty weight, respectively. For the first The longitudinal control input of the vehicle at the current moment needs to be solved. The desired control quantity at the current moment. For the first The longitudinal control input of the vehicle at the current moment needs to be solved. For the first The longitudinal control input of the vehicle at a given moment. For the first The slack variables corresponding to the CLF stability constraints of the vehicle; longitudinal control quantity With stability slack variables Together, they serve as the optimization variables in a quadratic programming problem. The cost function is used as the optimization objective. The optimization problem is constructed by combining the CLF stability constraint, the higher-order CBF safety constraint, and the longitudinal control magnitude constraint. By solving this quadratic programming optimization problem, the optimal longitudinal control input that simultaneously satisfies the system stability and driving safety constraints is obtained.

8. The multi-vehicle response-based hierarchical cooperative control method for connected autonomous vehicles according to claim 7, characterized in that, S4 includes: A two-degree-of-freedom bicycle dynamics model is constructed based on the geodetic coordinate system and the vehicle's local coordinate system. Force and torque decompositions are performed on the entire vehicle, and the differential equations of lateral motion are obtained: ； In the formula, and These represent the longitudinal and lateral forces acting on the front wheels of the vehicle, respectively. For the overall vehicle quality, Let the vehicle's yaw moment of inertia be... For the longitudinal speed of the vehicle, For the lateral acceleration of the vehicle, The yaw rate of the vehicle body. The yaw acceleration of the vehicle body. , These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. For the rear wheel to bear lateral force, The steering angle of the vehicle's front wheels; By rearranging and simplifying the equations of motion, we obtain the lateral dynamics state equations of the vehicle: ； In the formula, For the vehicle's lateral speed, , These are the combined lateral stiffness of the front and rear wheels, respectively. A lateral tracking error dynamic model is constructed. Based on the differential relationship of small-angle error, the lateral dynamic state equations of the vehicle are solved simultaneously to obtain the lateral error state-space equations containing disturbances: ； In the formula, This is the first derivative of the lateral tracking error state vector with respect to time. This is the lateral tracking error state vector. For the system matrix, For the input matrix, The curvature perturbation vector; Design a gain-scheduled LQR optimal state feedback controller, ignoring curvature disturbance vectors, with the control objectives of minimizing trajectory tracking error in the infinite time domain and smoothing the front wheel steering angle control input, and construct a quadratic optimal control objective integral function: ； In the formula, It is a symmetric positive semidefinite state weighting matrix. To control the input weighting coefficients; The positive definite symmetric matrix is ​​obtained by solving the algebraic Riccati equation. Based on matrix Calculate the optimal feedback gain matrix Obtain the optimal feedback angle : ； Based on the steady-state circular motion characteristics of the vehicle, the feedforward compensation steering angle adapted to the variable curvature trajectory is derived. : ； In the formula, The curvature of the reference trajectory; Integrating LQR dynamic state feedback corner Curvature feedforward compensation angle The final front wheel steering angle control value is obtained. : 。 9. The multi-vehicle response-based hierarchical cooperative control method for connected autonomous vehicles according to claim 8, characterized in that, The proof that the lateral tracking error is bounded based on Lyapunov stability theory includes: A lateral closed-loop perturbation system model is constructed. Based on the optimal feedback gain matrix of the fourth-order lateral error state space equation and the curvature feedforward compensation rotation angle, the lateral trajectory tracking closed-loop dynamic equation is obtained simultaneously. Integrating the reference trajectory curvature perturbation and the feedforward compensation residual error, a closed-loop dynamic model containing lumped bounded perturbations is constructed. ； In the formula, For a horizontal closed-loop system matrix, The disturbance term includes feedforward compensation residuals and curvature perturbations and satisfies , The maximum norm of the disturbance term; The boundedness of lateral tracking error is proved based on Lyapunov theory; a positive definite symmetric matrix is ​​obtained by solving the algebraic Riccati equation. Construct the positive definite Lyapunov energy function : ； By taking the time derivative of the Lyapunov energy function and substituting it into the transverse closed-loop perturbation dynamics equation, and combining this with solving the algebraic Riccati equation, the minimum eigenvalue property of positive definite matrices, and the Cauchy-Schwarz inequality, a scaling derivation is obtained to derive the upper bound constraint relationship of the energy function derivative. , For matrix The smallest eigenvalue; When the derivative of the energy function is less than 0, the global upper bound of the transverse state vector error is obtained: ； In the formula, This is the upper bound of the error; Define the maximum norm of the perturbation term as Determine the global upper bound of the lateral tracking error and prove that the error is bounded throughout the entire process: 。 10. The multi-vehicle response hierarchical cooperative control method for connected autonomous vehicles according to claim 9, characterized in that, The method combines the lateral dynamic offset characteristics and physical motion boundaries of the vehicle merging condition, maps the lateral trajectory tracking error effect to the longitudinal safety clearance in real time, constructs a time-varying control barrier function constraint that is adaptive to the operating condition, and realizes safe and coordinated coupling control of the longitudinal and lateral motions during the vehicle merging process, including: Based on the vehicle's geometric dimensions, establish the following formulas for calculating the lateral offset of the four corner points of the vehicle body relative to the center of the reference trajectory: ； In the formula, The horizontal positions of the four corner points of the vehicle body. As a reference, the center position of the trajectory For the centroid lateral position tracking error, For vehicle width, The front overhang is the vehicle's wheelbase. The heading angle error is the tangential angle between the vehicle body axis and the reference trajectory. The derivation is based on the global error upper bound obtained from the lateral state vector. , By applying inequality scaling to the lateral offset using the small-angle approximation characteristic, the upper bound of the maximum lateral offset at the vehicle body corner is obtained: ； Based on the upper limit of the maximum lateral offset of the vehicle body, an additional safety margin is introduced, defining a universally applicable lateral safety envelope radius. : ； In the formula, To add a safety margin; A dynamic correction term for longitudinal safety distance is constructed, and a time-varying longitudinal safety margin correction term is designed to adapt to the merging conditions, taking into account the vehicle's longitudinal length, body width, and lateral safety envelope radius. ； In the formula, This is the dynamic correction amount for the longitudinal safety distance. This refers to the longitudinal length of the vehicle body. Preset safety ratio coefficient; By combining dynamic safety correction terms, time-varying high-order control barrier function constraints of the merging vehicle relative to the preceding and following vehicles are constructed to adapt to the longitudinal safety protection requirements under lateral dynamic disturbances. The longitudinal safety constraint barrier function for the vehicle merging into the target clearance ahead: ； In the formula, To account for the lateral inflow effect, for the first The time-varying safety barrier function constructed by the preceding vehicle. To merge the longitudinal position of the vehicle, To incorporate the real-time vehicle speed, The safety distance correction term is introduced to account for the merging effect, and the lateral position error is... Heading angle error longitudinal speed of vehicles Front wheel steering angle The function; The longitudinal safety constraint barrier function of the vehicle after merging the relative clearance between the vehicle and the target: ； In the formula, For the first The longitudinal position of the following vehicle; This achieves deep coupling between lateral trajectory tracking and longitudinal safety protection, ultimately ensuring a safe, stable, and collision-free process for vehicles merging into the convoy.

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