Vehicle following model considering lateral deviation effect of front vehicle in Internet of Vehicles environment and acceleration optimization method

Abstract

The invention discloses a vehicle following model and acceleration optimization method considering a front vehicle lateral offset effect in an Internet of Vehicles environment, and belongs to the field of intelligent traffic, and the method comprises the steps: introducing a rearview effect, the front vehicle lateral offset effect and multi-front vehicle speed information on the basis of a full-speed-difference following model, establishing a car-following model considering the lateral deviation effect of the front car in an Internet of Vehicles environment; performing linear stability analysis and nonlinear analysis on the car-following model to obtain a neutral stability condition and a coexistence condition; the simulation verification can describe the car following behavior considering the lateral deviation in the car networking environment, and reveal the operation mechanism of the networked vehicle in the traffic system. Besides, whether a driving safety gain factor and a motion synchronization gain factor are introduced to update the car-following model or not is judged based on driving safety identification and motion state synchronization identification conditions of the car-following vehicle, the acceleration of the car-following vehicle at the next moment is optimized, and the car-following vehicle can run in a safer and more efficient car-following mode on the road.

Description

Technical Field

[0001] The present invention relates to the field of intelligent transportation technology, and in particular to a vehicle following model and an acceleration optimization method that take into account the lateral offset effect of a leading vehicle in a connected vehicle environment. Background Art

[0002] Car-following behavior is one of the driving behaviors. By analyzing the car-following behavior of vehicles and building a car-following model to simulate the car-following behavior of vehicles on the road, traffic fluidity can be improved and traffic congestion can be reduced. According to the real traffic conditions, establishing a suitable car-following model can reveal the dynamic change law of traffic flow and understand the operation mechanism of the traffic system, which plays an important role in alleviating traffic congestion and improving traffic flow stability.

[0003] With the development of intelligent transportation systems, information sharing between connected vehicles has been realized by using vehicle networking technology. As the number of intelligent connected vehicles on the road increases, the interaction between vehicles becomes more and more complex. Traditional following models are difficult to adapt to the following behavior requirements in the connected environment. In the vehicle networking environment, scholars have established following models that integrate various types of information from different perspectives. Most of the existing vehicle following models focus on the longitudinal motion state information such as the speed and spacing of the leading vehicle or multiple leading vehicles. However, the leading vehicle may produce lateral deviation behavior during driving due to avoiding obstacles, changing lanes or responding to other traffic conditions. This deviation not only affects the driving trajectory of the following vehicle, but may also lead to potential collision risks. The existing following models lack consideration or fail to describe the following situation with multiple leading vehicles having lateral deviations. When dealing with acceleration control, the influence of the lateral deviation of the leading vehicle is often ignored, resulting in inaccurate acceleration adjustment of the following vehicle, which is prone to driving safety risks and low traffic efficiency. Summary of the invention

[0004] The purpose of the present invention is to provide a vehicle following model and acceleration optimization method considering the lateral offset effect of the leading vehicle in a vehicle networking environment. The model is improved on the basis of the full speed difference following model, and the rear view effect, lateral offset effect and multiple leading vehicle speed information are introduced to construct a new following model. The established following model is subjected to linear stability analysis to obtain a neutral stability condition, and then the established following model is subjected to nonlinear analysis to obtain a coexistence condition. Simulation analysis is performed based on the neutral stability condition and the coexistence condition to reveal the influence of the established following model on the stability of traffic flow. Vehicle following trajectory data is extracted based on measured traffic state information, and a simplified following model considering the lateral offset effect of the leading vehicle is constructed. The following model is calibrated based on a genetic algorithm, and a driving time distance index is selected as a driving safety identification condition to determine whether to introduce a driving safety gain factor to update the following model. The speed relationship between the following vehicle and the leading vehicle is selected as a motion state synchronization identification condition to determine whether to introduce a motion state synchronization gain factor to update the following model. Finally, the output following model is an optimized acceleration to achieve safe and efficient following driving of networked vehicles on the road.

[0005] To achieve the above object, the present invention provides a vehicle following model that takes into account the lateral deviation effect of the leading vehicle in a connected vehicle environment, comprising the following steps:

[0006] Step S1, based on the full speed difference following model, the rear view effect, the lateral offset effect of the preceding vehicle and the speed information of multiple preceding vehicles are introduced to establish a following model that takes into account the lateral offset effect of the preceding vehicle in a connected vehicle environment;

[0007] Step S2, performing a linear stability analysis on the car-following model established in step S1, assuming an initial steady-state traffic flow, introducing a small disturbance equation, linearizing the equation to obtain a linear differential equation, and solving the equation to obtain a neutral stability condition;

[0008] Step S3, performing nonlinear analysis on the car-following model established in step S1, performing model differentiation to obtain a differential equation, defining a slow variable and introducing the differential equation, obtaining a nonlinear partial differential equation according to Taylor expansion, and sorting out the coexistence conditions.

[0009] Preferably, in step S1, in the following model, the rearview effect is characterized as the degree of attention of the leading vehicle, and the optimal speed function of the following vehicle is divided into the rearward observation optimization speed and the forward observation optimization speed; the lateral offset effect of the leading vehicle is characterized as the rate of change of the offset angle of the leading vehicle, which is characterized as the relationship between the lateral offset distance, the headway and the body length, and different leading vehicles have different lateral offset sensitivity coefficients; the speed information of multiple leading vehicles is introduced into the number of communicating vehicles, and the speed difference information of multiple leading vehicles is considered. Different leading vehicles have different speed difference sensitivity coefficients, and a following model considering the lateral offset effect of the leading vehicle in the Internet of Vehicles environment is established.

[0010] Preferably, the established car-following model considering the lateral deviation effect of the leading vehicle in the connected vehicle environment is as shown in the following formula:

[0011]

[0012] Where a is the driver's reaction sensitivity coefficient; p is the driver's attention coefficient to the vehicle ahead; V F (·) represents the optimal speed function for forward observation, V B (·) represents the optimal speed function for backward observation; x n (t) is the position of the nth vehicle at time t, Δx n (t) = x n+1 (t)-x n (t) is the headway distance, v n (t) is the speed of the nth vehicle at time t, w is the influence coefficient of the vehicle in front, q is the influence coefficient of the lateral deviation of the vehicle in front, K is the number of vehicles in front of the vehicle, j is the jth vehicle in front of the following vehicle, is the offset angle between the nth vehicle and its jth preceding vehicle at time t, Δv n+j-1 (t) is the speed difference between the n+jth vehicle and the n+j-1th vehicle at time t, γ j is the deviation angle between the following vehicle n and the vehicle in front Sensitivity coefficient of rate of change, λ j is the sensitivity coefficient of the speed difference between the n+j-1th vehicle and the vehicle in front;

[0013] The optimal speed function used for forward observation optimization speed and backward observation optimization speed is as follows:

[0014]

[0015] In the formula, α′ and α″ are V F 、V B The coefficient of the optimal speed function, tanh(·) is the hyperbolic tangent function, h c The safe distance between the front of the following vehicle and the vehicle ahead;

[0016] Combined with the following behavior in the real following scenario, the following characteristics of the vehicle are analyzed. The deviation angle of the vehicle in front of the following vehicle is related to the lateral deviation distance, the head distance between the front and rear vehicles, and the body length, which can be expressed as shown in the following formula:

[0017]

[0018] In the formula, Δx n+j-1 (t) is the headway between the n+j-1th vehicle and the preceding vehicle at time t, l j is the length of the n+jth vehicle, b jis the lateral offset distance between the longitudinal centerline of the following vehicle n and the longitudinal centerline of the vehicle ahead of it;

[0019] The sensitivity coefficient of the impact of the front vehicle on the following vehicle is related to the distance of the position. The sensitivity coefficient γ j and λ j As the distance increases from far to near, the coefficient is assumed to be as follows:

[0020]

[0021] In the formula, K represents the number of vehicles communicating with the vehicle ahead;

[0022] The established car-following model taking into account the lateral deviation effect of the leading vehicle in the connected vehicle environment provides a car-following model for solving the neutral stability condition of the car-following model based on the linear theory stability analysis in step S2.

[0023] Preferably, in step S2, assuming the initial steady-state traffic flow, let y n (t) is uniform flow By introducing a small disturbance and linearizing it, we can get the linear differential equation related to the disturbance. Let y n (t) = e ikn+zt Perform Fourier series expansion, parameter z is z=z1(ik)+z2(ik) 2 +...Expand; where e is an exponential function, i is an imaginary unit, n is a spatial variable, k is a spatial variable deviation value, t is a time variable, z is a time variable deviation value, z1 and z2 are the first-order term and second-order term coefficients of z, respectively, which are used to solve the stability range; according to traffic flow theory, if z2>0, the traffic system traffic flow maintains a stable state and runs smoothly; if z2<0, the traffic system traffic flow is in an unstable state and cannot guarantee smooth driving; when z2=0, the neutral stability condition of the traffic system traffic flow is as shown in the following formula:

[0024]

[0025] When the lateral offset influence coefficient is 0 and the number of communicating vehicles ahead is 1, the lateral offset effect and the speed information of multiple preceding vehicles are not considered, and the model degenerates into the BLVD model. On this basis, when the preceding vehicle attention coefficient is 1, the model degenerates into the FVD model. On this basis, when the preceding vehicle influence coefficient is 0, the model degenerates into the OV model. The neutral stability condition obtained by solving the problem is consistent with the existing following models.

[0026] Preferably, in step S3, the following model considering the lateral offset effect of the leading vehicle in the connected vehicle environment is differentiated to obtain a nonlinear partial differential equation. After integration, the headway represented by the kink-antikink wave is calculated as shown in the following formula:

[0027]

[0028] In the formula, c is the propagation velocity, A1 is the vibration amplitude, m1 = pV' F +(1-p)V′ B , a c =(1+ε 2 )a, a1 and a2 are the coefficients of the second and third terms of the mKdV equation before linear transformation; the kink-antikink solution represents the coexistence phase formed by the free phase and the congestion phase in the traffic flow, and the coexistence condition is used to describe the traffic flow condition;

[0029] In order to further illustrate the influence of the following model considering the lateral deviation effect of the leading vehicle on the stability of traffic flow in the connected vehicle environment, a simulation analysis was carried out based on the neutral stability condition and the coexistence condition.

[0030] The present invention provides an acceleration optimization method for a vehicle following model taking into account the lateral offset effect of a leading vehicle in a connected vehicle environment, comprising the following steps:

[0031] Step 1: extract vehicle following trajectory data. According to the measured traffic data, extract the applicable following trajectory data and perform denoising to obtain smooth data as the data input for calibration of the following model parameters.

[0032] Step 2: construct a following model for the following vehicle at the next moment. Based on the vehicle following model that considers the lateral offset effect of the leading vehicle in the vehicle networking environment, a simplified following model that considers the offset effect of the first leading vehicle is selected as the model basis of the acceleration optimization method.

[0033] Step 3: Calibrate the basic parameters of the vehicle following model. The data from step 1 is used as the input data in the calibration process. The following model constructed in step 2 is the model to be calibrated. The calibration parameter value results are obtained based on the genetic algorithm optimization iteration.

[0034] Step 4: Identify the driving safety of the following vehicle. Select the driving time distance index as the driving safety identification condition. If the driving time distance is less than or equal to the driving time safety distance threshold, introduce the driving safety gain value based on the following model calibrated in step 3 and update the following model. If the driving time distance is greater than the driving time safety distance threshold, further identify the synchronization of the motion states of the following vehicle and the leading vehicle.

[0035] Step 5: Identify the motion state synchronization between the following vehicle and the leading vehicle. Select the speed relationship between the following vehicle and the leading vehicle as the motion state synchronization identification condition. If the speed of the following vehicle is greater than that of the leading vehicle, the following vehicle keeps the following model calibrated in step 3 unchanged. If the speed of the following vehicle is less than or equal to the speed of the leading vehicle, introduce the motion state synchronization gain value based on the following model calibrated in step 3 to update the following model.

[0036] Step six, outputting the optimized acceleration of the following vehicle at the next moment, selecting one of the following models obtained by the following vehicle driving safety identification in step four and the two following models obtained by the motion state synchronization identification in step five to output, and obtaining the optimized acceleration of the following vehicle at the next moment.

[0037] Preferably, in step 2, the forward observation optimization speed and the backward observation optimization speed adopt the optimal speed function in step S1, and the following model of the following vehicle at the next moment is simplified as shown in the following formula:

[0038]

[0039] Where ACC is the simulated following car model at the next moment, l1 is the body length of the first front car, b1 is the lateral offset distance of the first front car, Δv n (t) is the speed difference between the n+1th car and the nth car at time t.

[0040] Preferably, in step 4, the influence of the following vehicle speed, the front vehicle speed and the vehicle-to-vehicle distance is considered, a driving safety gain factor is introduced, a driving safety identification and judgment condition for the following vehicle is designed, and a driving safety index t based on time distance is introduced. TTC Determine whether it is necessary to increase the safety gain item to ensure driving safety; TTC Considering the relative speed and vehicle distance between vehicles, is the driving time safety distance threshold. The larger the driving time distance value, the safer the following car is. The driving safety gain value is introduced into the following car model ACC to update the following car model, reducing the acceleration of the following car at the next moment to avoid collision between the following car and the front car; if It is necessary to identify the synchronization of the movement states of the following vehicle and the leading vehicle to obtain the optimized acceleration result at the next moment.

[0041] Preferably, in step 5, the influence of the following vehicle speed, the leading vehicle speed and the average speed of the two is taken into consideration, a motion state synchronization gain factor between the following vehicle and the leading vehicle is introduced, and the speed relationship between the following vehicle and the leading vehicle is designed as a motion state synchronization identification judgment condition; n (t) is the speed of the nth vehicle at time t, v n+1(t) is the speed of the n+1th vehicle at time t, if v n+1 (t)<v n (t), the following car keeps the following model ACC unchanged, and the following car uses the calibrated following model as the optimized acceleration result of the following car at the next moment; if v n (t)≤v n+1 (t), under the condition that the following vehicle and the leading vehicle have a safe driving time distance, the motion state synchronization gain value is introduced into the following model ACC to update the following model, and the acceleration of the following vehicle at the next moment is increased to improve the motion state synchronization between the following vehicle and the leading vehicle.

[0042] Therefore, the present invention adopts the vehicle following model and acceleration optimization method considering the lateral deviation effect of the leading vehicle in the above-mentioned vehicle networking environment, which has the following beneficial effects:

[0043] (1) The present invention introduces the rearview effect, the lateral offset effect of the leading vehicle and the speed information of multiple leading vehicles to construct a new vehicle following model. Compared with the existing following model, the model considers the lateral offset behavior of the leading vehicle as the rate of change of the offset angle of the leading vehicle, which is characterized by the relationship between the lateral offset distance, the headway and the body length. The number of communicating vehicles is introduced into the rate of change of the lateral offset angle and the speed difference of the leading vehicle to characterize the perception and communication capabilities of the networked vehicle, thereby revealing the operation mechanism of the networked vehicle in the traffic system. In the case of congested flow, the following model can also characterize the changing law of traffic flow stability. The newly established following model has stronger adaptability.

[0044] (2) The present invention proposes an acceleration optimization method based on the driving safety identification and motion state synchronization identification of the following vehicle. By dynamically modeling the lateral deviation of the leading vehicle, a driving safety gain factor and a motion state synchronization gain factor are introduced to optimize the acceleration adjustment process of the following vehicle, and the acceleration of the following vehicle at the next moment is output, so that the following vehicle can control the acceleration and deceleration more scientifically during the following driving process, allowing the following vehicle to drive more safely and efficiently on the road.

[0045] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a diagram of the overall execution steps of an embodiment of the present invention;

[0047] Figure 2 A diagram of the execution steps of modeling the vehicle following behavior considering the lateral offset effect of the leading vehicle in a connected vehicle environment according to an embodiment of the present invention;

[0048] Figure 3 A combined graph of a neutral stability curve and a coexistence curve for changes in the number of vehicles in front vehicle communication according to an embodiment of the present invention;

[0049] Figure 4 A combined graph of a neutral stability curve and a coexistence curve for changes in the lateral offset distance of a leading vehicle according to an embodiment of the present invention;

[0050] Figure 5 This is a diagram of execution steps of an acceleration optimization method for a vehicle following model that takes into account the lateral offset effect of a leading vehicle in a connected vehicle environment according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical scheme and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention are further described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not intended to limit the embodiments of the present invention. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions.

[0052] It should be noted that the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or server that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units that are not explicitly listed or inherent to these processes, methods, products or devices.

[0053] Like reference numerals and letters denote similar items in the following drawings, and thus, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0054] Example

[0055] like Figure 1 , Figure 2 As shown, a vehicle following model considering the lateral deviation effect of the leading vehicle in a connected vehicle environment according to the present invention comprises the following steps:

[0056] Step S1: Based on the full speed difference following model, the rear view effect, the lateral offset effect of the leading vehicle and the speed information of multiple leading vehicles are introduced to establish a following model that takes into account the lateral offset effect of the leading vehicle in the connected vehicle environment.

[0057] In the following model, the rearview effect is characterized as the attention degree of the vehicle in front, and the optimal speed function of the following vehicle is divided into the rearward observation optimization speed and the forward observation optimization speed. The lateral offset effect of the leading vehicle is characterized as the rate of change of the offset angle of the leading vehicle, which is characterized as the relationship between the lateral offset distance, the headway and the body length. Different leading vehicles have different lateral offset sensitivity coefficients. The speed information of multiple leading vehicles is introduced into the number of communicating vehicles, and the speed difference information of multiple leading vehicles is considered. Different leading vehicles have different speed difference sensitivity coefficients. A following model considering the lateral offset effect of the leading vehicle in the Internet of Vehicles environment is established.

[0058] Specifically, as shown in formula (1):

[0059]

[0060] Where a is the driver's reaction sensitivity coefficient; p is the driver's attention coefficient to the vehicle ahead; V F (·) represents the optimal speed function for forward observation, V B (·) represents the optimal speed function for backward observation; x n (t) is the position of the nth vehicle at time t, Δx n (t) = x n+1 (t)-x n (t) is the headway distance, v n (t) is the speed of the nth vehicle at time t, w is the influence coefficient of the vehicle in front, q is the influence coefficient of the lateral deviation of the vehicle in front, K is the number of vehicles in front of the vehicle, j is the jth vehicle in front of the following vehicle, is the offset angle between the nth vehicle and its jth preceding vehicle at time t, Δv n+j-1 (t) is the speed difference between the n+jth vehicle and the n+j-1th vehicle at time t, γ j is the deviation angle between the following vehicle n and the vehicle in front Sensitivity coefficient of rate of change, λ j is the sensitivity coefficient of the speed difference between the (n+j-1)th vehicle and the vehicle in front of it.

[0061] The optimal speed function used for the forward observation optimization speed and the backward observation optimization speed is shown in formula (2):

[0062]

[0063] In the formula, α′ and α″ are V F 、V B The coefficient of the optimal speed function, tanh(·) is the hyperbolic tangent function, h c It is the safe distance between the front of the following vehicle and the vehicle in front.

[0064] Combined with the following behavior in the real following scenario, the following characteristics of the vehicle are analyzed. The deviation angle of the vehicle in front of the following vehicle is related to the lateral deviation distance, the head distance between the front and rear vehicles, and the body length, which can be further expressed as shown in formula (3):

[0065]

[0066] In the formula, Δx n+j-1 (t) is the headway between the n+j-1th vehicle and the preceding vehicle at time t, l j is the length of the n+jth vehicle, b j It is the lateral offset distance between the longitudinal centerline of the following vehicle n and the longitudinal centerline of the vehicle ahead of it.

[0067] The sensitivity coefficient of the impact of the front vehicle on the following vehicle is related to the distance of the position. The sensitivity coefficient γ j and λ j As the distance increases from far to near, it is assumed that the coefficient value is as shown in formula (4):

[0068]

[0069] Where K represents the number of vehicles communicating with the front vehicle.

[0070] The established car-following model taking into account the lateral deviation effect of the leading vehicle in the connected vehicle environment provides a car-following model for solving the neutral stability condition of the car-following model based on the linear theory stability analysis in step S2.

[0071] Step S2: Perform a linear stability analysis on the car-following model established in step S1, assume an initial steady-state traffic flow, introduce a small disturbance equation, linearize it to obtain a linear differential equation, and solve it to obtain a neutral stability condition.

[0072] Assume that the initial state of the traffic flow is stable, all vehicles have a uniform headway h and an optimal speed pV F (h)+(1-p)V B (h), then the initial positions of all vehicles in steady state are as shown in (5):

[0073]

[0074] Among them, L is the length of the road section and N is the total number of vehicles.

[0075] Let y n (t) is uniform flow The initial small disturbance of the vehicle, the initial position of each vehicle is shown in (6):

[0076]

[0077] By introducing a small perturbation, rewriting equation (3) we can obtain:

[0078]

[0079] In the formula, Δy n+j-1 (t) = y n+j (t)-y n+j-1 (t), y n+j (t) is the disturbance of the n+jth vehicle at time t, y n+j-1 (t) is the disturbance of the n+j-1th vehicle at time t, and Δy in equation (7) is n+j-1 The high-order terms of (t) are removed and the time derivative is taken to obtain the rate of change of the lateral deviation angle as shown in formula (8):

[0080]

[0081] According to Taylor expansion, substituting equations (6) and (8) into equation (1) and linearizing them, we can obtain the linear differential equation related to the disturbance as shown in equation (9):

[0082]

[0083] In the formula,

[0084] Let y n (t) = e ikn+zt Perform Fourier series expansion, where e is the exponential function, i is the imaginary and real unit, n is the spatial variable, k is the deviation value of the spatial variable, t is the time variable, z is the deviation value of the time variable, and the parameter z is z=z1(ik)+z2(ik) 2 +... Expand, where z1 and z2 are the first-order and second-order coefficients of z respectively. ik Taylor expansion, ignoring the higher-order terms, is as shown in formula (10):

[0085]

[0086] Further simplification yields the coefficients of the first-order and second-order expansion terms of z as shown in equations (11)-(12):

[0087] z1=pV F ′(h)+(1-p)V B '(h)(11);

[0088]

[0089] According to traffic flow theory, if z2>0, the traffic system traffic flow maintains a stable state and runs smoothly; if z2<0, the traffic system traffic flow is in an unstable state and cannot guarantee smooth running. When z2=0, the neutral stability condition of the traffic system traffic flow is shown in formula (13):

[0090]

[0091] Obviously, when the lateral offset influence coefficient is 0 and the number of communicating vehicles ahead is 1, that is, the lateral offset effect and the speed information of multiple preceding vehicles are not considered, it degenerates into the BLVD model. On this basis, when the preceding vehicle attention coefficient is 1, it degenerates into the FVD model. On this basis, when the preceding vehicle influence coefficient is 0, it degenerates into the OV model. The neutral stability condition obtained by solving is consistent with the existing following models.

[0092] In the derivation of linear stability analysis, the effects of second-order and higher-order terms are ignored. The ignored higher-order terms have a smaller effect than the first-order terms, but it is necessary to perform nonlinear analysis near the critical point to reveal the impact of higher-order terms on traffic flow stability.

[0093] Step S3: Perform nonlinear analysis on the car-following model established in step S1, perform model differentiation to obtain a differential equation, define a slow variable and introduce the differential equation, obtain a nonlinear partial differential equation according to Taylor expansion, and organize to obtain the coexistence conditions.

[0094] In step S3, a nonlinear analysis is performed on the car-following model established in step 1. The model is differentiated to obtain a differential equation. A critical point is assumed, a slow variable is defined and the differential equation is introduced. A nonlinear partial differential equation is obtained according to Taylor expansion, and the coexistence conditions are obtained.

[0095] The following model established by formula (1) in a connected vehicle environment taking into account the lateral offset effect of the leading vehicle is differentiated and obtained as shown in formula (14):

[0096]

[0097] Assume (h c ,a c ) is the critical point, and the slow variables X and T of the spatial variable n and the time variable t are introduced near it as shown in formula (15):

[0098] X=ε(n+b0t),T=ε 3 t,ε(0<ε<<1) (15);

[0099] Among them, b0 is an undetermined constant, ε is a minimum value, and the headway is assumed to be as shown in formula (16):

[0100] Δx n(t) = h c +εR(X,T)(16);

[0101] Where R(X,T) is a function of the spatial slow variable X and the temporal slow variable T. Substitute equation (16) into equation (3), and refer to equation (8) to obtain equation (17):

[0102]

[0103] For the convenience of calculation, it is assumed that the body length and vehicle offset distance of all vehicles are uniformly constant, and the coefficient of the lateral offset change rate term is set to A, as shown in formula (18):

[0104]

[0105] Substituting equations (15)-(18) into equation (14), Taylor expands to ε 5 The order of magnitude is obtained, and the nonlinear partial differential equation is shown in formula (19):

[0106]

[0107]

[0108] In the formula, and They are respectively expressed as partial derivatives of X and T under the function R(X,T),

[0109]

[0110] Let m1 = pV′ F +(1-p)V′ B , m2=pV′ F -(1-p)V′ B ,m3=pV″′ F +(1-p)V″′ B ,m4=pV″′ F -(1-p)V″′ B At the critical point (h c ,a c ), let b0 = m1, a c =(1+ε 2 )a, eliminate ε 2 and ε 3 The term is simplified as shown in formula (20):

[0111]

[0112] The coefficients are as shown in formulas (21)-(25):

[0113]

[0114]

[0115] Perform a linear transformation on equation (20): The mKdV equation is shown in equation (26):

[0116]

[0117] In the formula, Ignoring the correction term O(ε), we get the standard mKdV equation. Its kink-antikink wave solution is shown in equation (27):

[0118]

[0119] In order to obtain the propagation velocity c in equation (27), The solvability condition (28) must be satisfied:

[0120]

[0121] After integration and sorting, the propagation velocity c of the kink-antikink density wave is obtained as shown in equation (29):

[0122]

[0123] Substituting back the original variables, the solution of the mKdV equation can be obtained as shown in equation (30):

[0124]

[0125] Substituting formula (30) into formula (16), the headway expressed by the kink-antikink wave can be obtained as shown in formula (31):

[0126]

[0127] Among them, the vibration amplitude A1 of the kink-antikink wave is shown in formula (32):

[0128]

[0129] The kink-antikink solution represents the coexistence phase formed by the free phase and the congested phase in the traffic flow. The coexistence curve can be used to describe the traffic flow conditions. According to equations (31) and (32), the coexistence condition can be obtained as shown in equation (33):

[0130] a=a c / [1+a2(Δx n (t)-h c ) 2 / a1c](33);

[0131] In order to further illustrate the impact of the following model considering the lateral deviation effect of the leading vehicle on traffic flow stability in the connected vehicle environment, a simulation analysis is conducted based on the neutral stability condition and the coexistence condition, and the above-mentioned following behavior modeling process is supplemented. Figure 3 to Figure 4 As shown in the figure, the established car-following model verified by simulation can describe the changing law of traffic flow stability.

[0132] Figure 3 to Figure 4 The horizontal axis represents the headway h, in meters, and the vertical axis represents the driver's reaction sensitivity coefficient a, in seconds. -1 The solid line is the neutral stability curve, the dashed line is the coexistence curve, the stable region is above the solid curve, the metastable region is between the solid and dashed lines, and the unstable region is below the solid curve.

[0133] Figure 3 , when p=0.9,w=0.2,q=0.1,K=4,b1=b2=b3=b4=1,l1=l2=l3=l4=5, as the number of communicating vehicles in front increases, the neutral stability curve and the coexistence curve decrease, and when the number of communicating vehicles is 3, the downward trend slows down, and the stability of traffic flow is enhanced, indicating that communicating with multiple leading vehicles and sharing traffic status information has a positive impact on the stability of the traffic system.

[0134] Figure 4 , when p = 0.9, w = 0.2, q = 0.1, K = 3, l1 = l2 = l3 = 5, as the lateral offset distance increases, the neutral stability curve and the coexistence curve are rising, and the stability of the traffic flow is weakened, indicating that the increase of the lateral offset distance has a negative impact on the stability of the traffic system.

[0135] like Figure 1 , Figure 5 As shown, the acceleration optimization method of the vehicle following model considering the lateral deviation effect of the leading vehicle in the vehicle networking environment described in the present invention is an acceleration optimization method based on driving safety identification and motion state synchronization identification, and includes the following steps:

[0136] Step 1: Extract vehicle following trajectory data. According to the measured traffic data, extract the applicable following trajectory data and perform denoising to obtain smooth data as the data input for calibration of the following model parameters.

[0137] In step 1, the vehicle following trajectory data is extracted. The vehicle trajectory aerial photography dataset CQSkyEyeX from a certain highway is selected, which contains more than 20,000 vehicle trajectory data. The traffic data of the following vehicle, the vehicle behind the following vehicle, and the vehicle in front of the following vehicle are extracted from the data of the first section of the ring road of a certain city, providing a data basis for building the following model. The key parameters of the vehicle trajectory output of the first section of the ring road of a certain city are explained in Table 1:

[0138] Table 1 CQSkyEyeX vehicle trajectory output parameter description

[0139]

[0140]

[0141] The main process of extracting vehicle following trajectory data is: (1) select trajectory data with driving direction 2 and vehicle trajectory position in lane 5; (2) eliminate trajectory data with lane change behavior in lane 5; (3) extract trajectory data of following vehicles, vehicles behind following vehicles, and vehicles in front of following vehicles in lane 5; (4) perform denoising on the trajectory data and select Kalman filter as the filter to obtain smooth trajectory data; (5) construct 303 sets of data including following duration, head distance between following vehicle and vehicle behind, head distance between following vehicle and vehicle in front, speed difference between following vehicle and vehicle in front, speed of following vehicle, body length of leading vehicle, and lateral offset distance of leading vehicle. The above data are used as data input for parameter calibration of following model, where body length of leading vehicle is constant and is not affected by motion characteristics, and lateral offset distance of leading vehicle is taken as average.

[0142] Step 2: Construct a following model for the following vehicle at the next moment. Based on the vehicle following model that considers the lateral offset effect of the leading vehicle in the Internet of Vehicles environment, a simplified following model that only considers the offset effect of the first leading vehicle is selected as the model basis for the acceleration optimization method.

[0143] In step 2, the forward observation optimization speed and the backward observation optimization speed adopt the optimal speed function of formula (2), and only consider the offset effect of the first leading vehicle to simplify the following model of the following vehicle at the next moment as shown in formula (34):

[0144]

[0145] Where ACC is the simulated following car model at the next moment. l1 is the body length of the first front car, and b1 is the lateral offset distance of the first front car.

[0146] Step 3: Calibration of basic parameters of vehicle following model. The data from step 1 is used as input data in the calibration process. The following model constructed in step 2 is the model that needs to be calibrated. The calibration parameter value results are obtained based on genetic algorithm optimization iteration.

[0147] In step three, the basic parameters of the car-following model based on genetic algorithm are calibrated. The vehicle following trajectory data constructed in step one is used as data input, and the car-following model in step two is used as the model to be calibrated. The genetic algorithm toolbox (ga) of Matlab is used to solve the parameters. The population size is set to 100, the crossover probability is 0.8, the mutation probability is 0.05, and the number of iterations is 300. The average error of the fitted acceleration and the measured acceleration is selected as the optimization fitness function. The calibration results in Table 2 are obtained by running the calibration program. The calibration results of the basic parameters are substituted into the car-following model in step two, which is the simulated acceleration value of the car-following vehicle at the next moment.

[0148] Table 2 Calibration results of basic parameters of ACC of car-following model

[0149] parameter Calibration value (unit) parameter Calibration value (unit) α′ 23.09 w 0.01 α″ 42.04 q 0.99 <![CDATA[h c ]]> 9.68(m) <![CDATA[b1]]> 1(m) a <![CDATA[0.80(s -1 )]]> <![CDATA[l1]]> 5(m) p 0.98

[0150] Step 4: Identify the driving safety of the following vehicle. Select the driving time distance index as the driving safety identification condition. If the driving time distance is less than or equal to the driving time safety distance threshold, introduce the driving safety gain value based on the following model calibrated in step 3 and update the following model. If the driving time distance is greater than the driving time safety distance threshold, it is necessary to further identify the synchronization of the motion states of the following vehicle and the preceding vehicle.

[0151] Considering the speed difference between the following vehicle and the leading vehicle and the relationship between the vehicle-to-vehicle distance, a driving safety gain factor is designed, and the driving time distance indicator is selected as the driving safety identification condition. The driving safety gain value is introduced into the following model after parameter calibration, and the following model is updated to ensure that there is a driving time safety distance between the following vehicle and the leading vehicle.

[0152] In step 4, in order to ensure that the following vehicle and its leading vehicle have sufficient driving safety and avoid collision between vehicles, the influence of the following vehicle speed, the leading vehicle speed and the inter-vehicle distance is considered, and the driving safety gain factor is introduced as shown in formula (35):

[0153]

[0154] Among them, d1 is the driving safety gain factor of the following vehicle, which takes into account the relationship between the speed difference and the distance between vehicles.

[0155] Design the following car driving safety identification judgment condition, introduce the driving safety index based on time distance to judge whether it is necessary to increase the safety gain item to ensure sufficient driving safety. Design the driving time distance index as shown in formula (36):

[0156]

[0157] Among them, t TTC Taking into account the relative speed and vehicle distance between vehicles, is the driving time safety distance threshold. According to existing literature, it is generally taken as 2.4s. The larger the driving time distance value, the safer the following car is. If it is less than the driving time safety distance threshold, it is necessary to take measures to reduce acceleration to avoid collision between the following car and the front car.

[0158] like In an emergency, if the following car does not have the deceleration required to avoid collision with the preceding car, it is necessary to introduce a driving safety gain value based on the following model (34) to ensure that there is a driving time safety distance between the following car and the preceding car. At this time, the updated following model is shown in (37):

[0159]

[0160] Among them, ACC1 is the updated following car model of the next moment, that is, the acceleration of the following car at the next moment, and f1 is the safety gain reaction coefficient, which is a negative number. The value is determined by the coupling relationship between the following car acceleration, the speed difference between the following car and the front car, and the distance between the cars. By reducing the acceleration of the following car, the speed of the following car is reduced. The updated following model ACC1 is directly output as the optimized acceleration result of the following car at the next moment.

[0161] like There is enough driving time safety distance between the following car and the leading car. The optimized acceleration result of the following car at the next moment can only be obtained after the synchronous identification of the motion states of the following car and the leading car.

[0162] Step 5: Identification of the motion state synchronization between the following vehicle and the leading vehicle. The speed relationship between the following vehicle and the leading vehicle is selected as the motion state synchronization identification condition. If the speed of the following vehicle is greater than that of the leading vehicle, the following vehicle keeps the following model after the parameter calibration in step 3 unchanged and maintains the following model; if the speed of the following vehicle is less than or equal to the speed of the leading vehicle, the motion state synchronization gain value is introduced based on the following model calibrated in step 3 to update the following model.

[0163] Considering the relationship between the speed of the following vehicle, the speed of the leading vehicle and their average speeds, the motion state synchronization gain factor is designed, and the speed relationship between the following vehicle and the leading vehicle is selected as the motion state synchronization identification condition. The motion state synchronization gain value is introduced into the following model after parameter calibration, and the following model is updated to ensure the safe and efficient driving of the following vehicle.

[0164] In step 5, under the condition of sufficient driving time and safe distance, in order to ensure that the following vehicle and the leading vehicle maintain synchronization of motion states, the influence of the following vehicle speed, the leading vehicle speed and the average speed of the two are considered, and the motion state synchronization gain factor between the following vehicle and the leading vehicle is introduced as shown in formula (38):

[0165]

[0166] Where d2 is the motion state synchronization gain factor between the following vehicle and the preceding vehicle, is the average speed of the vehicles in the following convoy, θ is an infinitesimal positive number, ensuring that the denominator is not zero.

[0167] If v n+1 (t)<v n (t), the following vehicle keeps the following model ACC unchanged, and the following vehicle uses the following model after parameter calibration as the optimized acceleration result of the following vehicle at the next moment, as shown in formula (39):

[0168]

[0169] If v n (t)≤v n+1 (t), under the condition that the following car and the leading car have enough driving time and distance to ensure safety, the motion state synchronization gain value is introduced based on the following model formula (34) to ensure that the following car and the leading car maintain motion state synchronization. At this time, the updated following model is shown in formula (40):

[0170]

[0171] Among them, ACC2 is the updated following car model of the next moment, that is, the acceleration of the following car at the next moment, and f2 is the motion synchronization gain reaction coefficient, which is a positive number, and the value is determined by the coupling relationship between the following car acceleration and the speed of each vehicle. Under the condition of meeting the driving time safety distance, by increasing the following car acceleration, the speed of the following car can be increased faster, and the following car and the leading car can maintain the synchronization of the motion state while reducing the distance between the following car and the leading car, thereby improving the traffic efficiency of vehicles on the road.

[0172] Step 6: Output the optimized acceleration of the following vehicle at the next moment. Select one of the updated following model ACC1 obtained by the following vehicle driving safety identification in step 4 and the maintaining following model ACC and the updated following model ACC2 obtained by the synchronization identification of the motion state of the following vehicle and the preceding vehicle in step 5 to output the optimized acceleration of the following vehicle at the next moment. This enables the following vehicle to drive more safely and efficiently on the road.

[0173] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A vehicle following model considering the lateral deviation effect of the leading vehicle in a connected vehicle environment, characterized by: The following steps are involved: Step S1, based on the full speed difference following model, the rear view effect, the lateral offset effect of the preceding vehicle and the speed information of multiple preceding vehicles are introduced to establish a following model that takes into account the lateral offset effect of the preceding vehicle in a connected vehicle environment; Step S2, performing a linear stability analysis on the car-following model established in step S1, assuming an initial steady-state traffic flow, introducing a small disturbance equation, linearizing the equation to obtain a linear differential equation, and solving the equation to obtain a neutral stability condition; Step S3, performing nonlinear analysis on the car-following model established in step S1, performing model differentiation to obtain a differential equation, defining a slow variable and introducing the differential equation, obtaining a nonlinear partial differential equation according to Taylor expansion, and sorting out the coexistence conditions.

2. The vehicle following model considering the lateral deviation effect of the leading vehicle in the connected vehicle environment according to claim 1 is characterized by: In step S1, in the following model, the rearview effect is characterized as the degree of attention of the vehicle in front, and the optimal speed function of the following vehicle is divided into the rearward observation optimization speed and the forward observation optimization speed; the lateral offset effect of the leading vehicle is characterized as the rate of change of the offset angle of the leading vehicle, which is characterized as the relationship between the lateral offset distance, the headway and the body length, and different leading vehicles have different lateral offset sensitivity coefficients; the speed information of multiple leading vehicles is introduced into the number of communicating vehicles, and the speed difference information of multiple leading vehicles is considered. Different leading vehicles have different speed difference sensitivity coefficients, and a following model considering the lateral offset effect of the leading vehicle in the Internet of Vehicles environment is established.

3. The vehicle following model considering the lateral deviation effect of the leading vehicle in the connected vehicle environment according to claim 2 is characterized by: The established car-following model considering the lateral deviation effect of the leading vehicle in the connected vehicle environment is shown in the following formula: Where a is the driver's reaction sensitivity coefficient; p is the driver's attention coefficient to the vehicle ahead; V F (·) represents the optimal speed function for forward observation, V B (·) represents the optimal speed function for backward observation; x n (t) is the position of the nth vehicle at time t, Δx n (t) = x n+1 (t)-x n (t) is the headway distance, v n (t) is the speed of the nth vehicle at time t, w is the influence coefficient of the vehicle in front, q is the influence coefficient of the lateral deviation of the vehicle in front, K is the number of vehicles in front of the vehicle, j is the jth vehicle in front of the following vehicle, is the offset angle between the nth vehicle and its jth preceding vehicle at time t, Δv n+j-1 (t) is the speed difference between the n+jth vehicle and the n+j-1th vehicle at time t, γ j is the deviation angle between the following vehicle n and the vehicle in front Sensitivity coefficient of rate of change, λ j is the sensitivity coefficient of the speed difference between the n+j-1th vehicle and the vehicle in front; The optimal speed function used for forward observation optimization speed and backward observation optimization speed is as follows: In the formula, α′ and α″ are V F 、V B The coefficient of the optimal speed function, tanh(·) is the hyperbolic tangent function, h c The safe distance between the front of the following vehicle and the vehicle ahead; Combined with the following behavior in the real following scenario, the following characteristics of the vehicle are analyzed. The deviation angle of the vehicle in front of the following vehicle is related to the lateral deviation distance, the head distance between the front and rear vehicles, and the body length, which can be expressed as shown in the following formula: In the formula, Δx n+j-1 (t) is the headway between the n+j-1th vehicle and the preceding vehicle at time t, l j is the length of the n+jth vehicle, b j is the lateral offset distance between the longitudinal centerline of the following vehicle n and the longitudinal centerline of the vehicle ahead of it; The sensitivity coefficient of the impact of the front vehicle on the following vehicle is related to the distance of the position. The sensitivity coefficient γ j and λ j As the distance increases from far to near, the coefficient is assumed to be as follows: In the formula, K represents the number of vehicles communicating with the vehicle ahead; The established car-following model taking into account the lateral deviation effect of the leading vehicle in the connected vehicle environment provides a car-following model for solving the neutral stability condition of the car-following model based on the linear theory stability analysis in step S2.

4. The vehicle following model considering the lateral deviation effect of the leading vehicle in the connected vehicle environment according to claim 3 is characterized by: In step S2, assuming the initial steady-state traffic flow, let y n (t) is uniform flow By introducing a small disturbance and linearizing it, we can get the linear differential equation related to the disturbance. Let y n (t) = e ikn+zt Perform Fourier series expansion, parameter z is z=z1(ik)+z2(ik) 2 +...Expand; where e is an exponential function, i is an imaginary unit, n is a spatial variable, k is a spatial variable deviation value, t is a time variable, z is a time variable deviation value, z1 and z2 are the first-order term and second-order term coefficients of z, respectively, which are used to solve the stability range; according to traffic flow theory, if z2>0, the traffic system traffic flow maintains a stable state and runs smoothly; if z2<0, the traffic system traffic flow is in an unstable state and cannot guarantee smooth driving; when z2=0, the neutral stability condition of the traffic system traffic flow is as shown in the following formula: When the lateral offset influence coefficient is 0 and the number of communicating vehicles ahead is 1, the lateral offset effect and the speed information of multiple leading vehicles are not considered, and the model degenerates into the BLVD model. On this basis, when the leading vehicle attention coefficient is 1, the model degenerates into the FVD model. On this basis, when the leading vehicle influence coefficient is 0, the model degenerates into the OV model. The neutral stability condition obtained by solving the problem is consistent with the existing following models.

5. The vehicle following model considering the lateral deviation effect of the leading vehicle in the connected vehicle environment according to claim 4 is characterized by: In step S3, the following car model considering the lateral offset effect of the leading vehicle in the connected vehicle environment is differentiated to obtain a nonlinear partial differential equation. After integration, the headway represented by the kink-antikink wave is calculated as shown in the following formula: In the formula, c is the propagation velocity, A1 is the vibration amplitude, m1 = pV' F +(1-p)V′ B , a c =(1+ε 2 )a, a1 and a2 are the coefficients of the second and third terms of the mKdV equation before linear transformation; the kink-antikink solution represents the coexistence phase formed by the free phase and the congestion phase in the traffic flow, and the coexistence condition is used to describe the traffic flow condition; In order to further illustrate the influence of the following model considering the lateral deviation effect of the leading vehicle on the stability of traffic flow in the connected vehicle environment, a simulation analysis was carried out based on the neutral stability condition and the coexistence condition.

6. The acceleration optimization method of a vehicle following model considering the lateral deviation effect of a leading vehicle in a connected vehicle environment according to any one of claims 1 to 5, characterized in that: The following steps are involved: Step 1: extract vehicle following trajectory data. According to the measured traffic data, extract the applicable following trajectory data and perform denoising to obtain smooth data as the data input for calibration of the following model parameters. Step 2: construct a following model for the following vehicle at the next moment. Based on the vehicle following model that considers the lateral offset effect of the leading vehicle in the vehicle networking environment, a simplified following model that considers the offset effect of the first leading vehicle is selected as the model basis of the acceleration optimization method. Step 3: Calibrate the basic parameters of the vehicle following model. The data from step 1 is used as the input data in the calibration process. The following model constructed in step 2 is the model to be calibrated. The calibration parameter value results are obtained based on the genetic algorithm optimization iteration. Step 4: Identify the driving safety of the following vehicle. Select the driving time distance index as the driving safety identification condition. If the driving time distance is less than or equal to the driving time safety distance threshold, introduce the driving safety gain value based on the following model calibrated in step 3 and update the following model. If the driving time distance is greater than the driving time safety distance threshold, further identify the synchronization of the motion states of the following vehicle and the leading vehicle. Step 5: Identify the motion state synchronization between the following vehicle and the leading vehicle. Select the speed relationship between the following vehicle and the leading vehicle as the motion state synchronization identification condition. If the speed of the following vehicle is greater than that of the leading vehicle, the following vehicle keeps the following model calibrated in step 3 unchanged. If the speed of the following vehicle is less than or equal to the speed of the leading vehicle, introduce the motion state synchronization gain value based on the following model calibrated in step 3 to update the following model. Step six, outputting the optimized acceleration of the following vehicle at the next moment, selecting one of the following models obtained by the following vehicle driving safety identification in step four and the following model obtained by the synchronization identification of the motion states of the following vehicle and the leading vehicle in step five to output, and obtaining the optimized acceleration of the following vehicle at the next moment.

7. The acceleration optimization method of the vehicle following model considering the lateral deviation effect of the leading vehicle in the vehicle networking environment according to claim 6 is characterized by: In step 2, the forward observation optimization speed and the backward observation optimization speed adopt the optimal speed function in step S1, and the following model of the following vehicle at the next moment is simplified as shown in the following formula: Where ACC is the simulated following car model at the next moment, l1 is the body length of the first car in front, b1 is the lateral offset distance of the first car in front, Δv n (t) is the speed difference between the n+1th car and the nth car at time t.

8. The acceleration optimization method of the vehicle following model considering the lateral deviation effect of the leading vehicle in the vehicle networking environment according to claim 7, characterized in that: In step 4, the influence of the following vehicle speed, the front vehicle speed and the distance between vehicles is considered, the driving safety gain factor is introduced, the driving safety identification and judgment conditions of the following vehicle are designed, and the driving safety index t based on time distance is introduced. TTC Determine whether it is necessary to increase the safety gain item to ensure driving safety; TTC Considering the relative speed and vehicle distance between vehicles, is the driving time safety distance threshold. The larger the driving time distance value, the safer the following car is. The driving safety gain value is introduced into the following car model ACC to update the following car model, reducing the acceleration of the following car at the next moment to avoid collision between the following car and the front car; if t TTC >t 0 TTC , it is necessary to identify the synchronization of the motion states of the following vehicle and the leading vehicle and obtain the optimized acceleration result of the following vehicle at the next moment.

9. The acceleration optimization method of the vehicle following model considering the lateral deviation effect of the leading vehicle in the vehicle networking environment according to claim 8, characterized in that: In step 5, considering the influence of the following car speed, the leading car speed and the average speed of the two, the motion state synchronization gain factor between the following car and the leading car is introduced, and the speed relationship between the following car and the leading car is designed as the motion state synchronization identification judgment condition; n (t) is the speed of the nth vehicle at time t, v n+1 (t) is the speed of the n+1th vehicle at time t, if v n+1 (t)<v n (t), the following car keeps the following model ACC unchanged, and the following vehicle uses the calibrated following model as the optimized acceleration result of the following car at the next moment; if v n (t)≤v n+1 (t), under the condition that the following vehicle and the leading vehicle have a safe driving time distance, the motion state synchronization gain value is introduced into the following model ACC to update the following model, and the acceleration of the following vehicle at the next moment is increased to improve the motion state synchronization between the following vehicle and the leading vehicle.

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