Deep reinforcement learning formation control method considering vehicle heterogeneity

Abstract

The invention discloses a deep reinforcement learning formation control method considering vehicle heterogeneity. The method comprises the following steps: 1, establishing a three-order kinetic model capable of being used for identifying kinetic model parameters of heterogeneous vehicles; 2, when the motorcade moves, the vehicles collect motion state data of the vehicles through sensors, and the time parameter tau of the transmission system is identified online in real time by adopting a least square method according to the collected motion state; 3, designing a following controller of the following vehicle by adopting a PPO algorithm; 4, the following vehicle obtains motion state information of the adjacent front vehicle through V2V communication; and 5, by using the motion state information of the adjacent front vehicle, obtaining the expected acceleration by the following controller, and inhibiting acceleration oscillation by cooperating with the string stabilization and the first-order filter to obtain the real acceleration so as to control the vehicle to follow and realize the stable driving target of the motorcade. The method is suitable for various motion conditions and has a better optimization effect.

Description

Technical Field

[0001] The present invention belongs to the field of vehicle autonomous driving. Aiming at heterogeneous vehicle fleets with different-quality V2V communications, a formation control method based on deep reinforcement learning considering vehicle heterogeneity is provided, specifically involving an optimization technology for heterogeneous vehicle fleet formation control based on the deep reinforcement learning PPO algorithm. Background Art

[0002] As an important part of the intelligent transportation system, intelligent connected vehicles can obtain the status of surrounding vehicles and nearby road information in real time through advanced vehicle sensors and V2X (Vehicle To Everything) communication technology, realizing information interaction between vehicles and between vehicles and infrastructure. Cooperative Adaptive Cruise Control (CACC) based on V2V (Vehicle To Vehicle) communication can achieve fast and precise intelligent control, reduce traffic accidents caused by human factors, enhance vehicle active safety, and can also simplify traffic control and management, effectively alleviating road congestion.

[0003] On the basis of CACC, combining deep reinforcement learning formation control can improve the stability and safety of heterogeneous vehicle fleets. Although many researchers have conducted extensive research on CACC, there is still a problem when applying this technology in a networked autonomous vehicle queue. Most strategies do not consider the vehicle fleet dynamics parameters, making it difficult to apply to diverse heterogeneous vehicle fleets, and the scalability is also limited. Summary of the Invention

[0004] The object of the present invention is to propose a deep reinforcement learning formation control method considering vehicle heterogeneity in view of the deficiencies of the existing technology, which mainly includes three parts: vehicle fleet dynamics modeling, online identification of model parameters, and design of a deep reinforcement learning formation control model, to achieve the stability and safety of heterogeneous vehicle fleets. And under different working conditions of the leading vehicle's speed and acceleration changes, the following vehicle has good following stability and safety.

[0005] The specific design of the present invention is carried out according to the following steps:

[0006] Step 1: Establish a third-order dynamics model that can be used to identify the dynamics model parameters of heterogeneous vehicles:

[0007]

[0008] Since the true dynamics model is unknown and for vehicle fleet heterogeneity, the vehicle needs to obtain vehicle dynamics parameters, so we establish a third-order dynamics model to identify this important vehicle dynamics parameter.

[0009] where p n，t , v n，t , a n，t , are respectively the position, speed, acceleration, and control input of vehicle n at the t-th moment, Δt is the sampling interval, τ n，t and φ n，t are the powertrain time parameter and input time delay of vehicle n at the t-th moment, represents the control input after eliminating the input time delay.

[0010] In addition, adopting the CTH spacing strategy, the car-following error dynamic characteristics of vehicle n are proposed to be modeled as:

[0011]

[0012] where e n，p，t and e n，v，t , e n，a，t are the distance error, speed error, and acceleration error of vehicle n relative to vehicle n-1 at the t-th moment, D n，t is the total unknown disturbance of the car-following error dynamic model of vehicle n at the t-th moment, and its expression is as follows:

[0013]

[0014] After obtaining the car-following error dynamic model of a single vehicle, the platoon dynamic model is the car-following error dynamic model of all following vehicles in the platoon. In addition, the powertrain time constant input time delay φ n，t and external disturbance D n，t are the parameters of the platoon dynamic model, and D n，t cannot be obtained, and it is proposed to overcome it by the generalization ability of the reinforcement learning model.

[0015] Step 2: When the platoon is moving, the vehicle collects its own motion state data through sensors, and uses the least squares method to identify the powertrain time parameter τ in real time online according to the collected motion state. The specific operations are as follows:

[0016] In order to make the reinforcement learning formation control model applicable to different heterogeneous platoons, it is proposed to use the method of cache memory to uniformly set the input time delay of all vehicles to the maximum input time delay φ m of all vehicles in the platoon.

[0017] Since the powertrain time parameter is time-varying, we propose to use the least squares method with forgetting factor adaptation to identify the powertrain time parameter τ in the dynamic model of Step 1 in real time online n，t, the Laplace-transformed transfer function \(G(s)\) from the control input to the acceleration in the dynamic model is given as follows:

[0018]

[0019] where \(s\) is the complex variable after Laplace transformation.

[0020] Considering that the least squares method with forgetting factor adaptation is not applicable to the parameter identification of time-delay systems, the control input at time \(t - \varphi\) and the acceleration at time \(t\) are used as an input-output data pair, and the Laplace transformation is performed again. Then, the transfer function to be identified is transformed into: m At the moment, the control input and the acceleration at time \(t\) are used as an input-output data pair, and the Laplace transformation is performed again. Then, the transfer function to be identified is transformed into:

[0021]

[0022] The first-order backward difference method is used to obtain the parameter equation as follows:

[0023] y n，k =\(\varphi\) n，k \(\theta\) n，k

[0024] where \(y\) n，k = \(a\) n，k , Then, the identification parameters are obtained through the following recurrence formula

[0025]

[0026] where \(K\) k represents the intermediate parameter at time \(t\), \(P\) k-1 represents the intermediate parameter at time \(t - 1\), \(\lambda\) k-1 represents the forgetting factor at time \(t - 1\), and \(k\) represents the \(k\)-th moment.

[0027] To further improve the accuracy of parameter identification, the forgetting factor \(\lambda\) k is adaptively adjusted through the following formula:

[0028]

[0029] In the above formula, \(e\) base , \(round()\) and \(\delta\in[0, 1]\) are the reference error, the rounding function, and the sensitivity coefficient respectively. \(\lambda\) min represents the lower limit of the change of \(\lambda\) k , \(\in\) k is the intermediate parameter

[0030] Step 3: Design the following controller for the following vehicle using the PPO algorithm. Specifically as follows:

[0031] The state s of the following vehicle n at time t n，t is defined as follows:

[0032]

[0033] Among them, represents an intermediate variable, o_delay n，t represents the communication delay, represents the identification parameters of the adjacent leading vehicle, represents the control input data within the delay time window of the input time delay, τ n，t represents its own identification parameters

[0034] The reward function of the following controller is:

[0035]

[0036] Among them, α 1，t , α 2,t , α 3，t are time-varying weights to be designed to dynamically determine the relative importance of minimizing the following vehicle speed error, control input, and acceleration change rate. e n，p，max , e n，v，max , and jerk max are the maximum allowable values corresponding to the following distance error, following vehicle speed error, control input, and acceleration change rate, respectively. The acceleration change rate jerk n，t is defined as follows:

[0037]

[0038] Among them, represents the control input of the nth vehicle at time t, represents the identified parameter tau.

[0039] Step 4: The following vehicle obtains the motion state information of the adjacent leading vehicle through V2V communication. The motion state information includes the position p of the leading vehicle n - 1 n-1，t , speed v n-1，t , acceleration a n-1，t , and its identified own driveline time parameter Considering the communication delay, the following vehicle obtains the identified own driveline time parameter of the leading vehicle as

[0040] Step 5: Using the leading vehicle information in Step 4, the following controller in Step 3 obtains the desired acceleration, and then controls the vehicle to follow stably and achieve the steady state of the vehicle platoon;

[0041] Step 6: Continuously repeat Step 4 to Step 5 during driving, so that each vehicle in the vehicle fleet can maintain stable driving and achieve the adaptive control optimization of the heterogeneous vehicle fleet.

[0042] Compared with the prior art, the advantages of the present invention are as follows:

[0043] The present invention adopts a third-order dynamic model, which adds a vehicle inertia link and is closer to the real situation than the traditional second-order vehicle model. An acceleration first-order filter is adopted in the following controller, which alleviates the problem of acceleration oscillation to a certain extent. The present invention can be applied to a vehicle fleet of heterogeneous vehicles, greatly increasing the scope of application. The control method proposed by the present invention does not depend on the object model and environmental information, and can make up for the defects of the current model-based method to a certain extent. The present invention is applicable to various motion conditions, and can safely and comfortably achieve the goal of queue stability in various situations of rapid acceleration, deceleration and speed change, and has a better optimization effect than other current control algorithms. Description of the Drawings

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0045] Figure 1 is a flowchart of the control system described in the present invention;

[0046] Figure 2 is a schematic diagram of the communication mode of the vehicle fleet described in the present invention;

[0047] Figure 3 is a schematic diagram of the method for identifying parameters adopted by the present invention;

[0048] Figure 4 is a schematic diagram of the simulation scenario of the present invention; where (a) is the vehicle position curve during driving on the simulation road; (b) is the distance curve between each vehicle during driving on the simulation road; (c) is the distance error curve from the expected distance during driving on the simulation road; (d) is the speed curve of the vehicle during driving on the simulation road; (e) is the acceleration curve of the vehicle during driving on the simulation road. Detailed Embodiments

[0049] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0050] Step 1: Establish a third-order dynamic model that can be used to identify the dynamic model parameters of heterogeneous vehicles:

[0051]

[0052] Since the true dynamic model is unknown and vehicles need to obtain vehicle dynamic parameters for vehicle fleet heterogeneity, we establish a third-order dynamic model to identify this important vehicle dynamic parameter.

[0053] Among them, p n，t , v n，t , a n，t , are respectively the position, speed, acceleration, and control input of vehicle n at the t-th moment, Δt is the sampling interval, τ n，t and φ n，t are the driveline time parameter and input time delay of vehicle n at the t-th moment, represents the control input after eliminating the input time delay.

[0054] In addition, adopting the CTH spacing strategy, the following is the proposed modeling of the following-distance error dynamic characteristics of vehicle n:

[0055]

[0056] Among them, e n，p，t and e n，v，t , e n，a，t are the distance error, speed error, and acceleration error of vehicle n relative to vehicle n-1 at the t-th moment, D n，t is the total unknown disturbance of the following-distance error dynamic model of vehicle n at the t-th moment, and its expression is as follows:

[0057]

[0058] After obtaining the following-distance error dynamic model of a single vehicle, the vehicle fleet dynamic model is the following-distance error dynamic model of all following vehicles in the vehicle fleet. In addition, the driveline time constant input time delay φ n，t and external disturbance D n，t are the parameters of the vehicle fleet dynamic model, D n，tUnable to obtain, and it is intended to be overcome by strengthening the generalization ability of the reinforcement learning model.

[0059] Step 2: When the vehicle fleet is moving, the vehicle collects its own motion state data through sensors, and uses the least squares method to identify the transmission system time parameter τ in real time online according to the collected motion state. The specific operations are as follows:

[0060] In order to make the reinforcement learning formation control model applicable to different heterogeneous vehicle fleets, it is intended to use the cache memory method to uniformly set the input delay of all vehicles to the maximum input delay φ of all vehicles in the vehicle fleet m 。

[0061] Since the transmission system time parameter is time-varying, we intend to use the least squares method with forgetting factor adaptation to identify the transmission system time parameter τ in the dynamic model in real time online n，t Here, the transfer function G(s) from the control input to the acceleration in the dynamic model after Laplace transform is given as follows:

[0062]

[0063] where s is the complex variable after Laplace transform.

[0064] Considering that the least squares method with forgetting factor adaptation is not applicable to the parameter identification of time-delay systems, it is intended to use the control input at the (t - φ) m moment and the acceleration at the t moment as an input-output data pair, and perform Laplace transform again. Then, the transfer function to be identified is transformed into:

[0065]

[0066] It is intended to use the first-order backward difference method to obtain the parameter equation as follows:

[0067] y n，k =φ n，k θ n，k

[0068] where y n，k =a n，k ,

[0069] Then, it is intended to obtain the identification parameters through the following recurrence formula

[0070]

[0071] where K k represents the intermediate parameter at the t moment, P k-1 represents the intermediate parameter at the (t - 1) moment, and λ k-1The forgetting factor at time t-1 is denoted as, and k represents the k-th moment.

[0072] To further improve the accuracy of parameter identification, the forgetting factor λ k is adaptively adjusted through the following formula:

[0073]

[0074] In the above formula, e base , round(), and δ ∈ [0,1] are the reference error, rounding function, and sensitivity coefficient respectively. λ min represents the lower limit of the change of λ k , ∈ k is an intermediate parameter

[0075] Step 3: Design a following controller for the following vehicle using the PPO algorithm. Specifically as follows:

[0076] The state s of the following vehicle n at time t n，t is defined as follows:

[0077]

[0078] where, represents an intermediate variable, o_delay n，t represents the communication delay, represents the identified parameters of the adjacent leading vehicle, represents the control input data within the delay time window of the input time delay, τ n，t represents its own identified parameters

[0079] The reward function of the following controller is:

[0080]

[0081] where, α 1，t , α 2，t , α 3，t are time-varying weights to be designed to dynamically determine the relative importance of minimizing the following vehicle speed error, control input, and acceleration change rate. e n，p，max , e n，v，max , and jerk max are the maximum allowable values corresponding to the following vehicle distance error, following vehicle speed error, control input, and acceleration change rate respectively. The acceleration change rate jerk n，t is defined as follows:

[0082]

[0083] where, represents the control input of the nth vehicle at the t-th moment, represents the identified parameter tau.

[0084] Meanwhile, the desired acceleration of vehicle i is restricted as follows:

[0085]

[0086] where a min and a max are respectively the lower and upper limits of the allowable acceleration to avoid violating the physical limitations of the power and braking systems. a min and a max are respectively -5m / s 2 and 5m / s 2 .

[0087] Step 4: The following vehicle obtains the motion state information of the adjacent leading vehicle through V2V communication. The motion state information includes the position p n-1，t of the leading vehicle n - 1, the speed v n-1，t , the acceleration a n-1，t , and the identified time parameter of its own transmission system Considering the communication delay, the following vehicle obtains the identified time parameter of the leading vehicle's own transmission system as

[0088] Step 5: Using the information of the leading vehicle in Step 4, the following controller in Step 3 obtains the desired acceleration, and cooperates with the series stability and the first-order filter to suppress the acceleration oscillation, obtaining the true acceleration a i (n), and then controls the vehicle following and realizes the goal of stable platoon driving;

[0089] The series stability can be defined as:

[0090]

[0091] where H is the adjustment parameter, representing the size of the time window. If the condition in Equation (7) is satisfied, the stability of the BEV platoon can be ensured, and the safety of the vehicle can be improved.

[0092] The formula of the first-order acceleration filter can be expressed as:

[0093]

[0094] where filter and filter' are the filter coefficients, and bias is the deviation, expressed as:

[0095] bias = |a(n + 1) - a(n)|

[0096] To ensure driving safety, the distance d between adjacent vehicles n，t should be maintained within the following range:

[0097] d l，i ≤d n， t≤d u，i

[0098] where d l，i and d u，i are the lower and upper limits of the allowable distance between adjacent vehicles, and are obtained through the following formula according to the CTH distance strategy:

[0099]

[0100] where L n-1 is the vehicle length of the leading vehicle, r l，n and r u，n respectively represent the parameters for controlling the lower and upper limits of the distance range, and h n，g is the parameter set according to the distance strategy in the distance error modeling.

[0101] Step 6: Continuously repeat Step 4 to Step 5 during driving, so that each vehicle in the vehicle platoon can maintain stable driving and achieve adaptive control optimization of the heterogeneous vehicle platoon.

[0102] Figure 1 is the flowchart of the control system described in the present invention; Figure 2 is a schematic diagram of the communication mode of the vehicle platoon described in the present invention. It can be seen from the figure that the second vehicle can collect the motion state of the leading vehicle through sensors, and each following vehicle communicates with the adjacent leading vehicle in the same way; Figure 3 is a schematic diagram of the method for identifying parameters adopted by the present invention.

[0103] Example:

[0104] Figure 4 is a schematic diagram of the scenario for this simulation. In a simulation test, a heterogeneous vehicle row with one leading vehicle and 4 following vehicles was used; the sensor observation delay O_delay was set to 0.01 s, the input delay of the control input was set to 0.01 s, and the parameter initialization can be obtained through the following formula: s = [20, 11, 2, -7, -16] m, v = [2, 2, 2, 2, 2] m / s, a = [0, 0, 0, 0, 0] m / s2, tau =

[0105] [0.4, 0.35, 0.25, 0.3, 0.35], Δt = 0.01 s.

[0106] In this embodiment, the target vehicle fleet is controlled by the method described in steps 1 to 6. When the vehicle fleet controlled by the proposed heterogeneous vehicle fleet formation control method is in motion, the relationships between the spacing, speed, and acceleration of the vehicles and their positions are as Figure 4 shown. As Figure 4 shown in (d) thereof, the acceleration of the vehicle always varies within the acceleration range of the leading vehicle and does not amplify upstream along the vehicle fleet, thus ensuring passenger comfort and string stability. The control input of the leading vehicle varies within the specified range, which naturally limits the acceleration of the leading vehicle, as Figure 4 shown in (e) thereof. The spacing between each vehicle and the one in front of it always remains within [d l,i , d u,i , so driving safety can be achieved, as Figure 4 shown in (b) thereof. Therefore, the proposed heterogeneous vehicle fleet formation control method can achieve driving safety and passenger comfort while enabling the vehicle fleet to travel within the reference speed range. In addition, without violating the input saturation limit, the string stability of the vehicle fleet can be ensured.

[0107] The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, without departing from the principles and spirit of the present invention, various changes, modifications, substitutions, and variations made to these embodiments still fall within the protection scope of the present invention.

Claims

1. A deep reinforcement learning formation control method considering vehicle heterogeneity, characterized in that It includes the following steps: Step 1: Establish a third-order dynamic model that can be used to identify the dynamic model parameters of heterogeneous vehicles: Step 2: When the vehicle fleet is moving, the vehicle collects its own motion state data through sensors, and uses the least squares method to identify the transmission system time parameter τ in real time online according to the collected motion state; Step 3: Design a following controller for the following vehicle using the PPO algorithm; Step 4: The following vehicle obtains the motion state information of the adjacent leading vehicle through V2V communication. The motion state information includes the position, speed, acceleration of the leading vehicle, and the identified time parameter of its own transmission system. Considering the communication delay, the following vehicle obtains the identified time parameter of the leading vehicle's own transmission system with a delay; Step 5: Using the motion state information of the adjacent leading vehicle in Step 4, the following controller in Step 3 obtains the desired acceleration, cooperates with string stability and a first-order filter to suppress acceleration oscillation, obtains the real acceleration, and then controls the vehicle to follow and achieve the goal of stable driving of the vehicle fleet; Step 6: Continuously repeat Step 4 to Step 5 during driving, so that each vehicle in the vehicle fleet can maintain stable driving and achieve the adaptive control optimization of the heterogeneous vehicle fleet.

2. The deep reinforcement learning formation control method considering vehicle heterogeneity according to claim 1, characterized in that The specific implementation of Step 1 is as follows: Since the true dynamic model is unknown and for the heterogeneity of the vehicle fleet, the vehicle needs to obtain the vehicle dynamic parameters, so we establish a third-order dynamic model to identify this important vehicle dynamic parameter. where p n,t , v n,t , a n,t , are the position, velocity, acceleration, and control input of vehicle n at time t, respectively, Δt is the sampling interval, τ n,t and φ n,t are the powertrain time parameter and input time delay of vehicle n at time t, denotes the control input after eliminating the input time delay; Adopting the CTH spacing strategy, the following error dynamic characteristics of vehicle n are modeled as: where, e n,p,t and e n,v,t 、e n,a,t are the distance error, speed error, and acceleration error of vehicle n relative to vehicle n-1 at the t-th moment, and D n,t is the total unknown disturbance of the following-error dynamic model of vehicle n at the t-th moment, and its expression is as follows: After obtaining the single-vehicle car-following error dynamics model, the platoon dynamics model is the car-following error dynamics model of all following vehicles in the platoon, the transmission system time constant Input delay φ n,t and the external disturbance D n,t are the parameters of the platoon dynamics model. D n,t cannot be obtained and is intended to be overcome by enhancing the generalization ability of the reinforcement learning model.

3. The deep reinforcement learning formation control method considering vehicle heterogeneity according to claim 2, wherein The specific implementation of Step 2 is as follows: 2-1. Use the cache memory to uniformly set the input delay of all vehicles to the maximum input delay φ of all vehicles in the vehicle fleet m ; 2-2. Use the least squares method with forgetting factor adaptation to identify the time-varying transmission system time parameter τ in the dynamic model in real time online n,t , where the Laplace-transformed transfer function G(s) from the control input to the acceleration in the dynamic model is given as follows: where s is the complex variable after Laplace transform; 2-3. Adopt the control input at the (t - φ) m moment and the acceleration at the t moment as an input-output data pair, and perform the Laplace transform again. Then, the transfer function to be identified is transformed into: It is proposed to use the first-order backward difference method to obtain the parameter equation as follows: y n,k = φ n,k θ n,k where y n,k = a n,k , Then, the identification parameters are obtained by the following recurrence formula Among them, K k represents the intermediate parameter at time t, P k-1 represents the intermediate parameter at time t-1, λ k-1 represents the forgetting factor at time t-1, and k represents the k-th moment; Forgetting factor λ k It is adaptively adjusted by the following formula: Among them, e base , round(), and δ ∈ [0, 1] are the reference error, rounding function, and sensitivity coefficient respectively; λ min represents the lower limit of the change of λ k , and ∈ k is an intermediate parameter.

4. The deep reinforcement learning formation control method considering vehicle heterogeneity according to claim 3, characterized in that The specific implementation of Step 3 is as follows: The state s of the follower vehicle n at the t-th moment n,t is defined as follows: Among them, represents an intermediate variable, o_delay n,t represents the communication delay, represents the identification parameters of the adjacent leading vehicle, represents the control input data within the delay time window of the input time delay, τ n,t represents its own identification parameters; The reward function of the following controller is: where α 1,t , α 2,t , α 3,t is a time-varying weight to be designed to dynamically determine the relative importance of minimizing the car-following speed error, control input, and acceleration change rate; e n,p,max , e n,v,max , and jerk max are the maximum allowable values corresponding to the car-following distance error, car-following speed error, control input, and acceleration change rate, respectively; the acceleration change rate jerk n,t is defined as follows: Among them, represents the control input of vehicle n at the t-th moment, represents the identified parameter; At the same time, the desired acceleration of vehicle n is limited as follows: where a min and a max are the lower and upper limits of the allowable acceleration, respectively, to avoid violating the physical limitations of the power and braking systems.

5. A deep reinforcement learning formation control method considering vehicle heterogeneity according to claim 4, characterized in that, The specific implementation of Step 4 is as follows: The described motion state information includes the position p of the preceding vehicle n-1 n-1,t , speed v n-1,t , acceleration a n-1,t , and the time parameters of its identified own transmission system Considering the communication delay, the time parameters of the identified own transmission system of the preceding vehicle obtained by the following vehicle are 6. The formation control method based on deep reinforcement learning considering vehicle heterogeneity according to claim 4, characterized in that The specific implementation of Step 5 is as follows: The series stability equation is defined as: where H is the adjustment parameter, representing the size of the time window. If the conditions in the equation are met, the stability of the BEV vehicle fleet can be ensured; The formula of the first-order acceleration filter is expressed as: where filter and filter' are filter coefficients, and bias is the deviation, expressed as: bias = |a(n + 1) - a(n)| To ensure driving safety, the distance d between adjacent vehicles n,t should be maintained within the following range: d l,i ≤ d n,t ≤ d u,i where d l,i and d u,i are the lower and upper limits of the range of the allowable adjacent vehicle spacing, and are obtained by the following formula according to the CTH spacing strategy: Among them, L n-1 is the vehicle length of the vehicle in front, r l,n and r u,n respectively represent the parameters for the upper and lower limits of the control spacing range, h n,g is a parameter set according to the spacing strategy in the spacing error modeling.

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