Stability control method for intelligent convoy during high-speed steering

Abstract

The present invention proposes a control method for the operational stability of a high-speed steering intelligent fleet. The present invention selects any adjacent front and rear vehicles in the intelligent fleet, connects the front and rear vehicles into a system through a virtual articulated model constructed by a virtual structure method, and uses the second-kind Lagrange equation theory to establish a ten-degree-of-freedom intelligent fleet system model that takes into account nonlinear tires and steering systems. The system damping ratio is defined by the characteristic equation analysis method, and the dynamic critical speed of the system is analyzed through the relationship between the system damping ratio and the motion stability of the intelligent fleet, and is used as an indicator of the stability of the intelligent fleet system. The sensitivity analysis method, the control variable analysis method, and the time domain analysis method are used to analyze the influence of the intelligent fleet structure characteristics and system parameters on the system dynamic critical speed and the system motion stability under lateral disturbances, thereby proving the correctness of the proposed control strategy and its easy promotion and use.

Description

Technical Field

[0001] The invention belongs to the field of intelligent transportation, and in particular relates to a high-speed steering intelligent vehicle fleet stability control method. Background Art

[0002] In recent years, with the rapid growth of the number of cars, problems such as resource consumption, environmental pollution and traffic congestion have become increasingly prominent. In order to cope with these problems, the field of intelligent transportation has begun to focus on more energy-saving, environmentally friendly and efficient travel methods. Among them, intelligent vehicle platooning (IVP) has attracted much attention due to its significant advantages. Studies have shown that vehicles in intelligent platoons use communication technology to achieve instant acceleration and deceleration control of the vehicle in front, ensuring that the distance and speed between vehicles are kept stable, forming a tight driving queue, improving driving safety, helping to reduce traffic congestion and reduce fuel consumption. Therefore, intelligent platooning has important application value and research significance.

[0003] Compared with a single vehicle, vehicle platooning involves interactions between vehicles, and the motion stability control of intelligent platoons has always been a difficult point in research. At present, the relevant research on the motion stability of intelligent platoons mainly focuses on the analysis of the longitudinal platoon stability (string stability) of intelligent platoons. The relevant research methods can be roughly divided into three categories: transfer function analysis method, Lyapunov analysis method and characteristic equation analysis method.

[0004] (1) The transfer function analysis method is to convert the time domain system into the frequency domain system through Laplace transform, and calculate the amplitude of the transfer function in the frequency domain system, that is, the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable to analyze the stability of the convoy. In essence, it is to observe the frequency response between the input and output of the system. The transfer function analysis method has become the most commonly used method for analyzing the stability of linear system convoys. Zhang et al. studied the influence of different connection structures and communication delays on the dynamics of the convoy by designing the longitudinal dynamics of the connected cruise vehicle, and derived the boundary conditions of the convoy stability using the transfer function theory. On this basis, Jin et al. considered the influence of the heterogeneity of convoy vehicles and the driver's reaction time on the dynamics of the convoy, and derived the head-to-tail transfer function by eliminating the middle vehicle, and analyzed the convoy stability conditions. Qin Yanyan et al. and Qin et al. started from the vehicle's own characteristic structure, introduced the vehicle's throttle control angle, and used the multi-front vehicle feedback that integrated speed, acceleration and communication delay to construct a following model. They used the local convoy head vehicle speed disturbance as the system input and the tail vehicle speed disturbance as the system output, and used the transfer function analysis method to derive the constraint conditions of the convoy motion stability. Wang Hao et al. used the vehicle following model to derive the transfer function of disturbances when propagating in traffic flow, and analyzed the stability domain in heterogeneous fleets with different proportions of connected vehicles and equilibrium speeds. The results showed that under certain conditions of equilibrium speed and proportion of connected vehicles, the system can be asymptotically stable.

[0005] The transfer function analysis method can simplify the intelligent fleet system into a mathematical model for quantitative analysis. However, for complex intelligent fleet systems, more complex mathematical derivations and calculations are required, and the applicability of nonlinear system models is limited.

[0006] (2) Lyapunov analysis is a method of analyzing the stability of a dynamic system by using Lyapunov stability theory. Its basic principle is to evaluate the stability of the system by selecting and changing the Lyapunov function of the system state variables or errors. The stability of the system is usually judged by proving whether the rate of change of the Lyapunov function is negative. Yadlapalli et al. and Klinge et al. selected vehicles with the same structure to establish an intelligent fleet system model. ∞ Based on the condition of bounded norm, the minimum time progression formula for ensuring motion stability of the system under initial condition disturbance is derived. On this basis, Besselink et al. established a nonlinear system model by considering the vehicle dynamics model and the delayed interval strategy, and analyzed the stability of the queue under the dual disturbance of initial condition disturbance and external disturbance by constructing the Lyapunov function. Subsequently, Feng et al. summarized the analysis method for the stability of the queue of nonlinear intelligent fleet system, and pointed out the analysis process of Lyapunov stability analysis method for different systems.

[0007] Even though the Lyapunov analysis method has significant advantages in nonlinear system analysis, the difficulty of constructing the Lyapunov function for specific problems limits the promotion of the Lyapunov analysis method.

[0008] (3) The characteristic equation analysis method is to linearize the vehicle dynamics equation, establish the coupling relationship between the front and rear vehicles, obtain the system equation with eigenvalues, and analyze the eigenvalues ​​of the system equation according to Lyapunov's first theorem to further obtain the conditions for system stability. Zheng et al. used feedback linearization technology to establish a linearized vehicle dynamics model considering dynamic inertia delay, analyzed the eigenvalues ​​of the system matrix based on algebraic graph theory and Routh-Hurwitz stability criterion theory, and studied the influence of three specific information flow topologies on the stability and scalability of the fleet. On this basis, Liu et al. considered the general information flow topology and obtained the necessary and sufficient conditions for the stability of the fleet by analyzing the eigenvalues ​​of the Laplace matrix of the fleet system. Liu et al. further established a third-order fleet dynamics model and designed a distributed linear control protocol based on the equal spacing strategy. By analyzing the eigenvalues ​​of the system matrix, controller gains and model parameters under the general information flow topology, they obtained the conditions that can guarantee the performance indicators of single-vehicle stability, scalability, fast convergence and fleet stability.

[0009] In summary, it is necessary to provide a method that can analyze nonlinear systems and is easy to promote and use to achieve high-speed steering intelligent fleet stability control. Summary of the invention

[0010] The technical problem to be solved by the present invention is to provide a high-speed steering intelligent vehicle fleet stability control method in view of the deficiencies of the above-mentioned prior art. The high-speed steering intelligent vehicle fleet stability control method adopts the characteristic equation analysis method to analyze the nonlinear system and is easy to promote and use. At the same time, the structural characteristics of the intelligent vehicle fleet based on virtual articulation and the influence of system parameters on system stability are analyzed, thereby providing a scientific basis for the design of high-speed steering driving stability control strategy of the intelligent vehicle fleet.

[0011] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0012] A high-speed steering intelligent fleet stability control method comprises the following steps:

[0013] Step 1: Model building:

[0014] Step 1.1, establish a single vehicle model, the single vehicle model includes a nonlinear magic formula tire model of a single vehicle and a steering system model of a single vehicle;

[0015] Step 1.2, select the continuous front and rear vehicles in the intelligent vehicle fleet and compare them with the tractor and trailer in the actual semi-trailer structure, and establish a virtual articulated model through the virtual structure method;

[0016] Step 1.3, based on a single vehicle model and a virtual articulated model, a ten-degree-of-freedom virtual articulated intelligent fleet system model is established by using the second-kind Lagrangian equation analysis method; the system kinetic energy, system potential energy, system dissipated energy and system generalized force in the system model are analyzed, and the system kinetic energy, system potential energy, system dissipated energy and system generalized force are brought into the second-kind Lagrangian equation for calculation to obtain the system dynamics differential equation; the system state space equation is calculated according to the system dynamics differential equation;

[0017] Step 2: Nonlinear state equation analysis:

[0018] Step 2.1: First, take the speed of the front vehicle as the control variable of the system, keep the front wheel angle of the front vehicle unchanged, and calculate the corresponding equilibrium point of the system at different speeds; perform Taylor expansion on the nonlinear part of the system state space equation near the equilibrium point, and ignore the high-order terms to obtain the expansion formula; calculate the system characteristic equation through the expansion formula and the system state space equation;

[0019] Step 2.2, calculating the system damping ratio according to the system characteristic equation, and then obtaining a relationship curve between the system damping ratio and the system driving speed, and obtaining the system dynamic critical vehicle speed according to the relationship curve;

[0020] Step 3: Parameter impact analysis:

[0021] Step 3.1, using the control variable analysis method to analyze the influence of the rear vehicle active steering, adjusting the vehicle spacing and adjusting the virtual hinge point position on the system dynamic critical speed;

[0022] Step 3.2: Use sensitivity analysis method to analyze the impact of vehicle characteristics on the system dynamic critical speed;

[0023] Step 4: Based on step 3, a high-speed steering intelligent fleet stability control strategy is proposed:

[0024] Step 4.1, first, analyze the system stability under the critical steering wheel angle of the front vehicle, and determine the steering wheel angle range of the front vehicle according to the actual driving speed of the system, so as to ensure the motion stability of the system;

[0025] Step 4.2, secondly, improve the motion stability of a single vehicle through the vehicle's own characteristics, which include steering system parameters, vehicle mass parameters and rotational inertia parameters;

[0026] Step 4.3. Finally, the system motion stability is further improved through the rear vehicle active characteristics, which include vehicle spacing adjustment and rear vehicle active steering.

[0027] As a further improved technical solution of the present invention, the step 1.2 comprises:

[0028] The continuous front and rear vehicles in the optional intelligent convoy are analogized to the tractor and trailer in the actual semi-trailer structure, and a virtual articulated model is established through the virtual structure method;

[0029] In the virtual articulation model, the virtual articulation point connects the front vehicle and the rear vehicle, and the relationship between the virtual traction of the front vehicle and the virtual drag of the rear vehicle is:

[0030]

[0031] Where θ is the angle between the extended lines of the longitudinal axis of the front vehicle and the rear vehicle; F xtowed The virtual longitudinal drag of the rear vehicle, F xtow represents the longitudinal virtual traction of the front vehicle, F ytow represents the lateral virtual traction of the front vehicle, F ytowed Indicates the lateral virtual drag of the rear vehicle;

[0032] The relationship between the longitudinal velocity and the lateral velocity between the leading vehicle and the trailing vehicle is:

[0033]

[0034] in, is the longitudinal velocity at the center of mass of the front vehicle, is the longitudinal velocity at the center of mass of the rear vehicle; is the lateral velocity at the center of mass of the front vehicle, is the lateral velocity at the center of mass of the rear vehicle, is the yaw rate of the front vehicle, is the yaw rate of the rear vehicle, c1 is the distance from the center of mass of the front vehicle to the hinge point, and c2 is the distance from the center of mass of the rear vehicle to the hinge point.

[0035] As a further improved technical solution of the present invention, the step 1.1 comprises:

[0036] Step 1.1.1, establish the steering system model of the front vehicle;

[0037] In the steering system model of the front vehicle, the rack movement is equivalent to the kingpin, and the equivalent proportional coefficient is P a1 ; Transmit the gear to the steering shaft equivalently, the equivalent proportional coefficient is P b1 ;

[0038] The Coulomb dry friction model is used to describe the dry friction force at the kingpin of the front vehicle:

[0039]

[0040] M f1 =F f1 ·l1 (4);

[0041] In the formula, F f1 is the dry friction force at the kingpin of the front vehicle, μ1 is the friction factor of the front vehicle, N1 is the positive pressure at the kingpin of the front vehicle, δ1 is the steering wheel angle of the front vehicle; M f1 is the dry friction torque at the kingpin of the front vehicle, l1 is the effective length of the steering knuckle arm of the front vehicle;

[0042] For symbolic functions Perform Fourier transform and Taylor formula expansion to obtain:

[0043]

[0044] Step 1.1.2, establish the steering system model of the rear vehicle;

[0045] In the steering system model of the rear vehicle, the rack movement is equivalent to the kingpin, and the equivalent proportional coefficient is P a2 ; Transmit the gear to the steering shaft equivalently, the equivalent proportional coefficient is P b2 ;

[0046] The Coulomb dry friction model is used to describe the dry friction at the kingpin of the rear vehicle:

[0047]

[0048] M f2 =F f2 ·l2 (7);

[0049] In the formula, F f2 is the dry friction force at the kingpin of the rear vehicle, μ2 is the friction factor of the rear vehicle, N2 is the positive pressure at the kingpin of the rear vehicle, δ2 is the steering wheel angle of the rear vehicle; M f2 is the dry friction torque at the kingpin of the rear vehicle, l2 is the effective length of the steering knuckle arm of the rear vehicle;

[0050] For symbolic functions Perform Fourier transform and Taylor formula expansion to obtain:

[0051]

[0052] Step 1.1.3, establish a nonlinear magic formula tire model of the front vehicle;

[0053] The nonlinear magic formula tire model of the front vehicle is used to solve the longitudinal force and lateral force on the front axle and the longitudinal force and lateral force on the rear axle of the front vehicle respectively:

[0054]

[0055]

[0056] Among them, D is the axis top factor, C is the curve shape factor, B is the stiffness factor, E is the curve curvature factor, S h is the horizontal drift of the curve, S v is the vertical drift of the curve, s1 is the longitudinal slip rate of the tire of the front vehicle, α r1 is the rear axle slip angle of the front vehicle, α f1 is the front wheel axle slip angle of the front vehicle, F lf1 is the longitudinal force on the front axle of the front vehicle, F cf1 is the lateral force on the front axle of the front vehicle, F lr1 is the longitudinal force on the rear axle of the front vehicle, F cr1 is the lateral force on the rear axle of the front vehicle;

[0057] in:

[0058]

[0059] in, is the yaw rate of the front vehicle, is the lateral velocity at the mass center of the front vehicle, a1 is the distance from the front wheel axle to the mass center of the front vehicle, b1 is the distance from the rear wheel axle to the mass center of the front vehicle, is the longitudinal velocity at the center of mass of the front vehicle;

[0060] The longitudinal slip rate of the tire of the front vehicle is expressed as:

[0061]

[0062] Where: r1 is the tire radius of the front vehicle; ω1 is the rotational angular velocity of the tire of the front vehicle;

[0063] Decomposing the longitudinal force and lateral force of the front vehicle into the vehicle body coordinate system, the resultant force on the front axle and rear axle of the front vehicle along the x and y axes is:

[0064]

[0065] Among them, F xf1 is the resultant force on the front axle of the front vehicle along the x-axis, F yf1 is the resultant force on the front axle of the front vehicle along the y-axis, F xr1 is the resultant force on the rear axle of the front vehicle along the x-axis, Fyr1 is the resultant force on the rear axle of the front vehicle along the y-axis;

[0066] Step 1.1.4, establish a nonlinear magic formula tire model of the rear vehicle;

[0067] The nonlinear magic formula tire model of the rear vehicle is used to solve the longitudinal force and lateral force on the front axle and the longitudinal force and lateral force on the rear axle of the rear vehicle respectively:

[0068]

[0069]

[0070] Among them, D is the axis top factor, C is the curve shape factor, B is the stiffness factor, E is the curve curvature factor, S h is the horizontal drift of the curve, S v is the vertical drift of the curve, s2 is the longitudinal slip rate of the tire of the rear vehicle, α r2 is the rear axle slip angle of the rear vehicle, α f2 is the side slip angle of the front wheel axle of the rear vehicle, F lf2 is the longitudinal force on the front axle of the rear vehicle, F cf2 is the lateral force on the front axle of the rear vehicle, F lr2 is the longitudinal force on the rear axle of the rear vehicle, F cr2 is the lateral force on the rear axle of the rear vehicle;

[0071] in:

[0072]

[0073] in, is the yaw rate of the rear vehicle; is the lateral velocity at the mass center of the rear vehicle, a2 is the distance from the front wheel axle of the rear vehicle to the mass center, b2 is the distance from the rear wheel axle of the rear vehicle to the mass center, is the longitudinal velocity at the center of mass of the rear vehicle;

[0074] The longitudinal slip rate of the tire of the rear vehicle is expressed as:

[0075]

[0076] Where: r2 is the radius of the rear vehicle tire; ω2 is the rotational angular velocity of the rear vehicle tire;

[0077] Decomposing the longitudinal force and lateral force on the rear vehicle to the vehicle body coordinate system, the resultant force on the front and rear axles of the rear vehicle along the x and y axes is:

[0078]

[0079] Among them, F xf2 is the resultant force on the front axle of the rear vehicle along the x-axis, F yf2 is the resultant force on the front axle of the rear vehicle along the y-axis, F xr2 is the resultant force on the rear axle of the rear vehicle along the x-axis, F yr2 is the resultant force on the rear axle of the rear vehicle along the y-axis.

[0080] As a further improved technical solution of the present invention, the system dynamics differential equation in step 1.3 includes the rotational motion of the steering wheel around the wheel kingpin, the rotational motion of the rack displacement equivalent to the kingpin, the lateral motion and the yaw motion;

[0081] The steering wheel rotates around the wheel kingpin:

[0082]

[0083] Among them, J ω1 is the moment of inertia of the front wheel of the front vehicle about the kingpin, K det1 is the equivalent deformation stiffness of the steering tie rod of the front vehicle, Y1 is the lateral linear motion displacement of the rack of the front vehicle, C det1 is the equivalent damping of the steering tie rod deformation of the front vehicle, C ω1 is the rotation damping of the front wheel of the front vehicle around the kingpin, r1 is the wheel rolling radius of the front vehicle, τ1 is the castor angle of the front wheel of the front vehicle, e1 is the tire trail of the front vehicle, J ω2 is the moment of inertia of the front wheel of the rear vehicle about the kingpin, K det2 is the equivalent deformation stiffness of the steering tie rod of the rear vehicle, Y2 is the lateral linear motion displacement of the rack of the rear vehicle, C det2 is the equivalent damping of the steering tie rod deformation of the rear vehicle, C ω2 is the rotation damping of the front wheel of the rear vehicle around the kingpin, r2 is the wheel rolling radius of the rear vehicle, τ2 is the castor angle of the front wheel of the rear vehicle, and e2 is the tire trail of the rear vehicle;

[0084] The rack displacement is equivalent to the rotational motion at the kingpin:

[0085]

[0086] Among them, K h1 is the torsional stiffness of the steering wheel of the front vehicle, K Y1 is the gear rack meshing equivalent stiffness of the front vehicle, C h1 is the steering wheel torsional damping of the front vehicle, C Y1 is the gear rack meshing equivalent damping of the front vehicle, J h1 is the moment of inertia of the steering axis of the front vehicle, J Y1 is the equivalent moment of inertia of the front vehicle’s rack to kingpin, δ h1 is the steering wheel angle of the front vehicle, Kh2 is the torsional stiffness of the steering wheel of the rear vehicle, K Y2 is the gear rack meshing equivalent stiffness of the rear vehicle, C h2 is the steering wheel torsional damping of the rear vehicle, C Y2 is the gear rack meshing equivalent damping of the rear vehicle, J h2 is the moment of inertia of the steering shaft of the rear vehicle, J Y2 is the equivalent moment of inertia of the rear vehicle’s rack-to-kingpin conversion, δ h2 is the steering wheel angle of the rear vehicle;

[0087] Lateral and yaw movements:

[0088]

[0089]

[0090] Where m1 is the mass of the front vehicle, m2 is the mass of the rear vehicle, and I z1 is the yaw moment of inertia of the front vehicle, I z2 is the yaw moment of inertia of the rear vehicle;

[0091] Define the system state variables ξ and system input μ:

[0092]

[0093] Finally, by substituting formulas (1), (2), (7), (9), (10), (13), (14), (15), and (18) into formulas (19)-(22), we can obtain the system state space equation:

[0094]

[0095] Among them, A and G are the system coefficient matrices; H is the system nonlinear matrix, which includes the nonlinear part of the system state space equation and the system input part.

[0096] As a further improved technical solution of the present invention, the step 2.2 comprises:

[0097] Calculate characteristic roots through the system characteristic equation;

[0098] The system damping ratio is defined as:

[0099]

[0100] Where i is the real part of the characteristic root of the system characteristic equation, and n is the imaginary part of the characteristic root of the system characteristic equation;

[0101] The relationship curve between the system damping ratio and the system driving speed is drawn. When the system damping ratio ζ=0, the system is in a critical stable state, and the system driving speed at this time is defined as the system dynamic critical speed.

[0102] As a further improved technical solution of the present invention, in step 4.2, the steering system parameters of the front vehicle include J h1 , J Y1 , J ω1 , K h1 , K Y1 , K det1 , C h1 , C Y1 , C det1 , C ω1 The vehicle mass parameters of the front vehicle include m1, and the moment of inertia parameters of the front vehicle include I z1 ;

[0103] The steering system parameters of the rear vehicle include J h2 , J Y2 , J ω2 , K h2 , K Y2 , K det2 , C h2 , C Y2 , C det2 , C ω2 The vehicle mass parameters of the rear vehicle include m2, and the moment of inertia parameters of the rear vehicle include I z2 .

[0104] Compared with the prior art, the present invention has the following beneficial effects:

[0105] (1) The characteristic equation analysis method adopted in the present invention is used to analyze nonlinear systems and is easy to promote and use, while the transfer function analysis method can only analyze linear systems. The Lyapunov analysis method is difficult to promote because it needs to construct a Lyapunov function.

[0106] (2) In the current design and optimization process of vehicle platoon stability control parameters, the parameters are selected by comparison with other solutions without any scientific explanation. The present invention analyzes the influence of the structural characteristics of the vehicle platoon system and the system parameters on the system stability and provides a more scientific explanation. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 This is a model diagram of a ten-degree-of-freedom virtual articulated intelligent fleet system.

[0108] Figure 2 This is the virtual force relationship diagram of the virtual hinge model.

[0109] Figure 3This is the steering system model diagram.

[0110] Figure 4 It is the damping ratio characteristic curve.

[0111] Figure 5 This is a diagram showing the impact of changes in the distance between front and rear vehicles on the system's dynamic critical speed.

[0112] Figure 6 This is a diagram showing the impact of changes in the distance from the virtual hinge point to the front axle on the system's dynamic critical speed.

[0113] Figure 7 This is a diagram showing the impact of the change in the front wheel steering angle of the rear vehicle on the dynamic critical speed of the system.

[0114] Figure 8 This is the yaw rate response curve of the front vehicle at a speed of 54km / h.

[0115] Fig. 9 This is the yaw rate response curve of the front vehicle at a speed of 60.48km / h.

[0116] Fig.10 This is the yaw rate response curve of the front vehicle at a speed of 75km / h.

[0117] Fig.11 This is the yaw rate response curve of the rear vehicle at a speed of 54km / h.

[0118] Fig.12 This is the yaw angular velocity response curve of the rear vehicle at a driving speed of 60.48km / h.

[0119] Fig.13 This is the yaw angular velocity response curve of the rear vehicle at a driving speed of 75km / h.

[0120] Fig.14 is the system stability diagram under critical steering wheel angle

[0121] Fig.15 This is a sensitivity analysis diagram of the system's own characteristics to motion stability.

[0122] Fig.16 This is the motion stability control strategy diagram for the intelligent convoy. DETAILED DESCRIPTION

[0123] The specific embodiments of the present invention are further described below according to the accompanying drawings:

[0124] Based on the influence of vehicle structural characteristics and system parameters on the motion stability of high-speed steering intelligent convoy, the present invention proposes a control strategy based on the high-speed steering motion stability of virtual articulated intelligent convoy, namely, the stability control method of high-speed steering intelligent convoy, and verifies the control strategy by using characteristic equation analysis method and time domain analysis method. Select any adjacent front and rear vehicles in the intelligent convoy, connect the front and rear vehicles into a system through the virtual articulated model constructed by the virtual structure method, and establish a ten-degree-of-freedom intelligent convoy system model considering nonlinear tires and steering systems by using the second-class Lagrangian equation theory. The system damping ratio is defined by the characteristic equation analysis method, and the dynamic critical speed of the system is obtained by analyzing the relationship between the system damping ratio and the motion stability of the intelligent convoy, and it is used as the stability index of the intelligent convoy system. The influence of the structural characteristics and system parameters of the intelligent convoy on the dynamic critical speed of the system and the motion stability of the system under lateral disturbance are analyzed by using sensitivity analysis method, control variable analysis method and time domain analysis method, thereby proving the correctness of the proposed control strategy.

[0125] Based on the characteristic equation analysis method, the present invention studies the motion stability problem of high-speed steering of intelligent fleets. Firstly, considering the nonlinear tire characteristics and nonlinear steering system characteristics under high-speed driving, a virtual articulation model is established by the virtual structure method, and the nonlinear system dynamics model of the intelligent fleet is established by the second-kind Lagrangian equation analysis method; secondly, based on the relationship between the structural characteristics of the intelligent fleet based on virtual articulation and the influence of system parameters on the high-speed steering motion stability of the intelligent fleet, a control strategy to curb the instability of high-speed steering of the intelligent fleet is proposed; finally, the relevant theories of nonlinear equations and the time domain analysis method are applied to verify the proposed intelligent fleet system control strategy, thereby providing a scientific basis for the design of high-speed steering stability control strategy for intelligent fleets.

[0126] 1. System model:

[0127] Based on the actual semi-trailer system structure, this paper constructs a dynamic model of the intelligent fleet system based on virtual articulation by analogy. First, a single vehicle model is established, including: nonlinear magic formula tire model and nonlinear steering system model; secondly, a virtual articulation model is established; finally, the second kind of Lagrangian equation analysis method combined with the virtual articulation model is used to establish the intelligent fleet system model.

[0128] 1.1. Single vehicle model and virtual articulated model:

[0129] This paper analyzes the entire intelligent convoy as a dynamic whole. By using a virtual articulated model to connect any two vehicles in the vehicle convoy as a whole, the dynamic method is used to analyze the stability of the vehicle convoy. In the actual semi-trailer system structure, the tractor tows the trailer through a rigid connecting rod to follow the tractor to make lateral turns and longitudinal acceleration and deceleration. In the intelligent convoy, considering that the rear vehicle maintains the desired distance and speed with the front vehicle, under the stimulation of the position, speed, acceleration and other information of the front vehicle, the rear vehicle maintains the convoy driving with the front vehicle through its own maneuvering. Therefore, the two consecutive front and rear vehicles in the intelligent convoy are randomly selected to be analogous to the tractor and trailer in the actual semi-trailer structure, and the concept of "virtual force" is introduced through the virtual structure method, so that the front vehicle "pulls" the rear vehicle to drive.

[0130] like Figure 1 As shown in the figure, any two vehicles in the front and rear of the convoy are connected by a virtual hinge point P to form a virtual articulated intelligent convoy system model. The vehicles in the system model all adopt a front wheel rack and pinion steering structure, and assume that the left and right wheel structures and forces are symmetrical, the steering wheel remains fixed in the steady-state response, and the effects of suspension, aerodynamics, and wheel load transfer are ignored.

[0131] Figure 1 The subscripts f and r represent the front and rear axles of the vehicle, respectively. The subscripts 1 and 2 represent the front and rear vehicles in the virtual articulated intelligent convoy system, respectively. The subscripts l and c represent the longitudinal and lateral directions of the tires, respectively. For example, F cf2 It is expressed as the lateral force on the front axle of the rear vehicle. a, b, c represent the distance from the front axle to the center of mass, the distance from the rear axle to the center of mass, and the distance from the center of mass to the virtual hinge point, respectively. P is the intersection of the extended lines of the longitudinal axes of the front and rear vehicles. v1 represents the actual speed and direction of the front vehicle, v2 represents the actual speed and direction of the rear vehicle, and the speed decomposition of v1 can be divided into v2 speed decomposition can be divided into

[0132] The mathematical model of the vehicle platoon based on virtual articulation analyzes the lateral motion state and mechanical characteristics of the vehicle platoon from the perspective of dynamics. This section mainly introduces the virtual force relationship between the front and rear vehicles in the virtual structure method, such as Figure 2 As shown in the figure, in the virtual articulation model, the virtual articulation point P connects the front and rear vehicles. This point is subject to the "traction" of the front vehicle and the "drag" of the rear vehicle, and the forces are balanced when the intelligent convoy is cruising stably. Both "traction" and "drag" are virtual forces introduced by the virtual structure method. In the actual intelligent convoy, the virtual force is realized by the vehicle's own driving force, braking force and lateral force generated by the steering system. Figure 2In the vehicle queue, two adjacent vehicles are selected: the front vehicle Follower (i) and the rear vehicle Follower (i+1), and the intersection of the longitudinal axis of the front vehicle and the extension of the longitudinal axis of the rear vehicle is taken as the hinge point P. The stimulation of the front vehicle and the reaction of the rear vehicle are analyzed at this point. This paper calls the stimulation effect of the front vehicle the virtual traction force F tow , the reaction of the rear vehicle is the virtual drag force F towed , the subscripts x and y represent the ordinate and abscissa of the vehicle, respectively, such as F ytowed It represents the lateral virtual drag acting on the rear vehicle. When the front and rear vehicle queues maintain stable cruising, the virtual force relationship at this point can be expressed by the following formula.

[0133]

[0134] Where θ is the angle between the extended lines of the longitudinal axis of the front vehicle and the rear vehicle, F xtowed The virtual longitudinal drag of the rear vehicle, F xtow represents the longitudinal virtual traction of the front vehicle, F ytow represents the lateral virtual traction of the front vehicle, F ytowed Indicates the lateral virtual drag of the rear vehicle;

[0135] When the intelligent fleet is cruising steadily, the lateral speed at the virtual point satisfies the following expression:

[0136]

[0137] in, is the longitudinal velocity at the center of mass of the front vehicle, is the longitudinal velocity at the center of mass of the rear vehicle; is the lateral velocity at the center of mass of the front vehicle, is the lateral velocity at the center of mass of the rear vehicle, is the yaw rate of the front vehicle, is the yaw rate of the rear vehicle, c1 is the distance from the center of mass of the front vehicle to the hinge point, and c2 is the distance from the center of mass of the rear vehicle to the hinge point.

[0138] In a single vehicle model, the tire model is an important component. The tire provides the force required for acceleration, deceleration and steering movement of the vehicle by contacting the road surface. At the same time, when the vehicle is turning at high speed, the contact force between the tire and the ground will show strong nonlinear characteristics because the tire characteristics are close to or in a saturated state. Therefore, this paper uses the nonlinear magic formula (Majic Formula) tire model to solve the longitudinal and lateral forces on the system tire.

[0139] Specifically, a nonlinear magic formula tire model of the front vehicle is established, and the longitudinal force and lateral force on the front axle and the longitudinal force and lateral force on the rear axle of the front vehicle are solved by using the nonlinear magic formula tire model of the front vehicle:

[0140]

[0141]

[0142] Among them, D is the axis top factor, C is the curve shape factor, B is the stiffness factor, E is the curve curvature factor, S h is the horizontal drift of the curve, S v is the vertical drift of the curve, s1 is the longitudinal slip rate of the tire of the front vehicle, α r1 is the rear axle slip angle of the front vehicle, α f1 is the front wheel axle slip angle of the front vehicle, F lf1 is the longitudinal force on the front axle of the front vehicle, F cf1 is the lateral force on the front axle of the front vehicle, F lr1 is the longitudinal force on the rear axle of the front vehicle, F cr1 is the lateral force on the rear axle of the front vehicle;

[0143] in:

[0144]

[0145] Among them, δ1 is the steering wheel angle of the front vehicle (front wheel angle of the front vehicle), is the yaw rate of the front vehicle, is the lateral velocity at the mass center of the front vehicle, a1 is the distance from the front wheel axle to the mass center of the front vehicle, b1 is the distance from the rear wheel axle to the mass center of the front vehicle, is the longitudinal velocity at the center of mass of the front vehicle.

[0146] The longitudinal slip rate of the tire of the front vehicle is expressed as:

[0147]

[0148] Where: r1 is the tire radius of the front vehicle; ω1 is the rotational angular velocity of the tire of the front vehicle;

[0149] Decomposing the longitudinal force and lateral force of the front vehicle into the vehicle body coordinate system, the resultant force on the front axle and rear axle of the front vehicle along the x and y axes is:

[0150]

[0151] Among them, F xf1 is the resultant force on the front axle of the front vehicle along the x-axis, F yf1is the resultant force on the front axle of the front vehicle along the y-axis, F xr1 is the resultant force on the rear axle of the front vehicle along the x-axis, F yr1 is the resultant force on the rear axle of the front vehicle along the y-axis.

[0152] A nonlinear magic formula tire model of the rear vehicle is established; the longitudinal force and lateral force on the front axle and the longitudinal force and lateral force on the rear axle of the rear vehicle are solved by using the nonlinear magic formula tire model of the rear vehicle:

[0153]

[0154]

[0155]

[0156] Among them, D is the axis top factor, C is the curve shape factor, B is the stiffness factor, E is the curve curvature factor, S h is the horizontal drift of the curve, S v is the vertical drift of the curve, s2 is the longitudinal slip rate of the tire of the rear vehicle, α r2 is the rear axle slip angle of the rear vehicle, α f2 is the side slip angle of the front wheel axle of the rear vehicle, F lf2 is the longitudinal force on the front axle of the rear vehicle, F cf2 is the lateral force on the front axle of the rear vehicle, F lr2 is the longitudinal force on the rear axle of the rear vehicle, F cr2 is the lateral force on the rear axle of the rear vehicle;

[0157] in:

[0158]

[0159] in, is the yaw rate of the rear vehicle; is the lateral velocity at the mass center of the rear vehicle, a2 is the distance from the front wheel axle of the rear vehicle to the mass center, b2 is the distance from the rear wheel axle of the rear vehicle to the mass center, is the longitudinal velocity at the center of mass of the rear vehicle;

[0160] The longitudinal slip rate of the tire of the rear vehicle is expressed as:

[0161]

[0162] Where: r2 is the radius of the rear vehicle tire; ω2 is the rotational angular velocity of the rear vehicle tire;

[0163] Decomposing the longitudinal force and lateral force on the rear vehicle to the vehicle body coordinate system, the resultant force on the front and rear axles of the rear vehicle along the x and y axes is:

[0164]

[0165] Among them, F xf2 is the resultant force on the front axle of the rear vehicle along the x-axis, F yf2 is the resultant force on the front axle of the rear vehicle along the y-axis, F xr2 is the resultant force on the rear axle of the rear vehicle along the x-axis, F yr2 is the resultant force on the rear axle of the rear vehicle along the y-axis.

[0166] In a single vehicle model, the steering system model is also one of its components. The steering system studied in this paper is composed of a linkage mechanism consisting of a steering wheel, a steering shaft, a steering gear, a steering tie rod, a steering knuckle arm, etc., and a vehicle steering wheel. The steering gear uses a gear rack mechanism for transmission. In order to ensure the rationality of the established steering system model, the following assumptions are made: the structure and force of the left and right wheels of the steering system are symmetrical; a gear rack is used as the steering component of the steering system; the internal components of the system are subject to spring forces in the same plane; when the steering wheel is in the initial position, the steering wheel angle remains fixed during the steady-state response.

[0167] In the steering system, the steering gear structure is a gear rack, and the spatial motion trajectory of the linkage mechanism between the rack and the kingpin is complex. However, in order to illustrate the effect of the elastic deformation of this part of the linkage mechanism on the characteristics of the steering system, this paper proposes a method for calculating the deformation of the tie rod: the equivalent method, that is, the rack movement is equivalent to the kingpin, and the equivalent proportional coefficient is P a , then the equivalent rear rack motion angle δ around the kingpin y It can be expressed by the following formula:

[0168] δ y =P a ·Y (13);

[0169] In the steering system, the steering shaft and the rack are driven by gears, so the transmission relationship between the steering shaft and the rack is also expressed by the equivalent method, that is, the gear transmission is equivalent to the steering shaft, and the equivalent proportional coefficient is P b , then the equivalent rear rack motion angle δ around the steering axis s It can be expressed by the following formula:

[0170] δ s =P b ·Y (14);

[0171] Y is the rack's lateral linear motion displacement; the steering system model is as follows Figure 3 As shown, A1 is the steering wheel, A2 is the steering shaft, A3 is the steering tie rod, A4 is the steering gear, and A5 is the steering knuckle arm. h ,Kdet are the steering wheel torsional stiffness and the steering tie rod equivalent deformation stiffness respectively. h ,C det are the steering wheel torsional damping and the steering tie rod deformation equivalent damping respectively. h is the steering wheel angle, and δ is the steering wheel angle.

[0172] Due to the elasticity of the connecting rod mechanism, the equivalent turning angle is related to the steering wheel turning angle δ and the steering wheel turning angle h There is a certain difference between them, which can be expressed as:

[0173] Δ det =δ-δ y (15);

[0174] Δ h =δ h -δ s (16);

[0175] In the formula, Δ det is the deformation of the intermediate link mechanism equivalent to the kingpin, Δ h is the deformation of the intermediate link mechanism equivalent to the steering shaft.

[0176] Specifically, a steering system model of the front vehicle is established; in the steering system model of the front vehicle, the rack movement is equivalent to the kingpin, and the equivalent proportional coefficient is P a1 ; Transmit the gear to the steering shaft equivalently, the equivalent proportional coefficient is P b1 .

[0177] In the vehicle system, when the system is unstable, the pressure on the wheel kingpin changes sharply, causing the wheel kingpin friction to change continuously. That is, when the system undergoes periodic yaw motion, the pressure on the kingpin and the steering wheel angle will change accordingly, causing the direction and magnitude of the kingpin friction to change continuously. In order to make the steering system model more accurate, the influence of the kingpin dry friction on the system cannot be ignored. Therefore, this paper uses the Coulomb dry friction model to describe the kingpin friction.

[0178] The Coulomb dry friction model is used to describe the dry friction force at the kingpin of the front vehicle:

[0179]

[0180] M f1 =F f1 ·l1 (18);

[0181] In the formula, F f1 is the dry friction force at the kingpin of the front vehicle, μ1 is the friction factor of the front vehicle, N1 is the positive pressure at the kingpin of the front vehicle, δ1 is the steering wheel angle of the front vehicle; Mf1 is the dry friction torque at the kingpin of the front vehicle, l1 is the effective length of the steering knuckle arm of the front vehicle;

[0182] For symbolic functions Perform Fourier transform and Taylor formula expansion to obtain:

[0183]

[0184] Establish the steering system model of the rear vehicle;

[0185] In the steering system model of the rear vehicle, the rack movement is equivalent to the kingpin, and the equivalent proportional coefficient is P a2 ; Transmit the gear to the steering shaft equivalently, the equivalent proportional coefficient is P b2 ;

[0186] The Coulomb dry friction model is used to describe the dry friction at the kingpin of the rear vehicle:

[0187]

[0188] M f2 =F f2 ·l2 (21);

[0189] In the formula, F f2 is the dry friction force at the kingpin of the rear vehicle, μ2 is the friction factor of the rear vehicle, N2 is the positive pressure at the kingpin of the rear vehicle, δ2 is the steering wheel angle of the rear vehicle; M f2 is the dry friction torque at the kingpin of the rear vehicle, l2 is the effective length of the steering knuckle arm of the rear vehicle;

[0190] For symbolic functions Perform Fourier transform and Taylor formula expansion to obtain:

[0191]

[0192] 1.2. Intelligent fleet state space model:

[0193] Based on the single vehicle model and the virtual articulated model, this paper adopts the second Lagrange equation analysis method to establish a ten-degree-of-freedom virtual articulated intelligent fleet system model.

[0194] The second kind of Lagrangian equation theory is aimed at complex systems with multiple degrees of freedom. It considers the changes in the kinetic energy, potential energy and dissipated energy of the entire system caused by the motion of each particle, and greatly eliminates the motion constraints and mutual influence between each particle. The expression of the second kind of Lagrangian equation is:

[0195]

[0196] In the formula, L is the Lagrange function, R is the system kinetic energy, U is the system potential energy, E is the system dissipated energy, Q k is the kth generalized coordinate q k The corresponding generalized force. Among them, subscripts 1 and 2 represent the front and rear vehicles in the system model, y is the lateral displacement of the vehicle, is the vehicle yaw angular velocity.

[0197] Secondly, analyze the system kinetic energy, system potential energy and system dissipated energy in the system model. The system kinetic energy includes: rack displacement energy, steering shaft rotation kinetic energy, front wheel rotation kinetic energy around the wheel kingpin, vehicle lateral motion kinetic energy and yaw motion kinetic energy. It can be specifically expressed as:

[0198]

[0199] Where: m is the mass of the vehicle, I z is the yaw moment of inertia of the vehicle, J h ,J Y ,J w They are the steering shaft moment of inertia, the equivalent moment of inertia of rack to kingpin, and the front wheel moment of inertia around the kingpin.

[0200] The system potential energy includes: the deformation potential energy of the steering shaft, the deformation potential energy of the gear rack meshing, and the deformation potential energy of the components between the rack and the kingpin, which can be specifically expressed as:

[0201]

[0202] Where: h is the steering wheel angle, K h ,K Y ,K det They are steering wheel torsional stiffness, gear rack meshing equivalent stiffness and steering tie rod equivalent deformation stiffness respectively.

[0203] The system dissipated energy includes: deformation of the steering shaft, deformation of the gear rack meshing, deformation of the components between the rack and the kingpin, and the energy consumed by the swing of the front wheel around the kingpin, which can be specifically expressed as:

[0204]

[0205] Where: C h ,C Y ,C det ,C w They are steering wheel torsional damping, gear rack meshing equivalent damping, steering tie rod deformation equivalent damping and front wheel rotation damping around the kingpin.

[0206] The generalized forces of the system include: the force exerted on the wheel around the kingpin, the lateral force exerted on the wheel, the lateral moment exerted on the wheel and the yaw moment exerted on the vehicle body.

[0207] Q k =[Q1Q2Q3Q4Q5Q6Q7Q8] T

[0208] Q1=-F cf1 (r1τ1+e1)-M f1

[0209] Q2=-F cf2 (r2τ2+e2)-M f2

[0210] Q3=0

[0211] Q4=0

[0212] Q5=F yf1 +F yr1 +F ytow

[0213] Q6=F yf2 +F yr2 +F ytowed

[0214] Q7=F yf1 a1-F yr1 b1+F ytow c1

[0215] Q8=F yf2 a2-F yr2 b2+F ytowed c2

[0216] (27).

[0217] The above system kinetic energy T, system potential energy U, system dissipated energy R and system generalized force Q k Substituting it into the second kind Lagrange equation for calculation, we can obtain the system dynamics differential equation.

[0218] The system dynamics differential equations include: the rotational motion of the steering wheel (wheel) around the wheel kingpin, the rotational motion equivalent to the rack displacement at the kingpin, the lateral motion and the yaw motion.

[0219] 1) The steering wheel rotates around the wheel kingpin:

[0220]

[0221] Specifically, J ω1 is the moment of inertia of the front wheel of the front vehicle about the kingpin, K det1is the equivalent deformation stiffness of the steering tie rod of the front vehicle, Y1 is the lateral linear motion displacement of the rack of the front vehicle, C det1 is the equivalent damping of the steering tie rod deformation of the front vehicle, C ω1 is the rotation damping of the front wheel of the front vehicle around the kingpin, r1 is the wheel rolling radius of the front vehicle, τ1 is the castor angle of the front wheel of the front vehicle, e1 is the tire trail of the front vehicle, J ω2 is the moment of inertia of the front wheel of the rear vehicle about the kingpin, K det2 is the equivalent deformation stiffness of the steering tie rod of the rear vehicle, Y2 is the lateral linear motion displacement of the rack of the rear vehicle, C det2 is the equivalent damping of the steering tie rod deformation of the rear vehicle, C ω2 is the rotation damping of the front wheel of the rear vehicle around the kingpin, r2 is the wheel rolling radius of the rear vehicle, τ2 is the castor angle of the front wheel of the rear vehicle, and e2 is the tire trail of the rear vehicle;

[0222] 2) Rack displacement is equivalent to the rotational motion of the kingpin:

[0223]

[0224] Specifically, K h1 is the torsional stiffness of the steering wheel of the front vehicle, K Y1 is the gear rack meshing equivalent stiffness of the front vehicle, C h1 is the steering wheel torsional damping of the front vehicle, C Y1 is the gear rack meshing equivalent damping of the front vehicle, J h1 is the moment of inertia of the steering axis of the front vehicle, J Y1 is the equivalent moment of inertia of the front vehicle’s rack to kingpin, δ h1 is the steering wheel angle of the front vehicle, K h2 is the torsional stiffness of the steering wheel of the rear vehicle, K Y2 is the gear rack meshing equivalent stiffness of the rear vehicle, C h2 is the steering wheel torsional damping of the rear vehicle, C Y2 is the gear rack meshing equivalent damping of the rear vehicle, J h2 is the moment of inertia of the steering shaft of the rear vehicle, J Y2 is the equivalent moment of inertia of the rear vehicle’s rack-to-kingpin conversion, δ h2 is the steering wheel angle of the rear vehicle;

[0225] 3) Lateral and yaw movements:

[0226]

[0227]

[0228] Specifically, m1 is the mass of the front vehicle, m2 is the mass of the rear vehicle, and Iz1 is the yaw moment of inertia of the front vehicle, I z2 is the yaw moment of inertia of the rear vehicle;

[0229] Define the system state variables ξ and system input μ:

[0230]

[0231] Finally, by combining formulas (1), (2), (3), (4), (7), (8), (9), (12), (15), (16), (17), (18), (20), (21) and formulas (28) to (31) in the specific implementation mode, the system state space equation can be obtained:

[0232]

[0233] Where: A, G are system coefficient matrices, H is the system nonlinear matrix, which includes the nonlinear part of the system state space equation and the system input part.

[0234] 2. Motion stability analysis:

[0235] 2.1. Nonlinear state equation analysis:

[0236] In order to propose the control strategy of the motion stability of the intelligent fleet later, it is necessary to analyze the motion stability of the system, and an important evaluation index for judging whether the system is stable is the system dynamic critical speed. For a general system, its state equation is:

[0237]

[0238] Where: X is the state vector, F is the linear vector function, P is the parameter vector, and u is the input vector of the system.

[0239] Through the characteristic equation of the system matrix, the system characteristic roots can be obtained as shown below:

[0240] λ 1,2 =i±nj (35);

[0241] The system damping ratio is defined as:

[0242]

[0243] Where: j is an imaginary unit, i and n are the real and imaginary parts of the characteristic root of the characteristic equation of the fleet system. When the system damping ratio ζ = 0, the system is in a critical stable state; when 0 < ζ ≤ 1, the system is in a stable state; under other conditions, the system is in an unstable state. Therefore, according to the change of the defined system damping ratio curve, the dynamic critical speed of the system can be determined.

[0244] According to the characteristic equation analysis theory, this paper uses Taylor series expansion to linearize the complex nonlinear system dynamics equations (Formulas (28) to (31) in the specific implementation) near the equilibrium point. First, the front vehicle speed is used as the control variable of the system, and the front wheel steering angle δ1 of the front vehicle is kept unchanged. The different vehicle speeds v xe1 The corresponding equilibrium point ξ of the system e , the formula is as follows.

[0245]

[0246] Secondly, the nonlinear part of the system state space equation (Formula (33) in the specific implementation method) is Taylor expanded near the equilibrium point and the high-order terms are ignored, and the following is obtained:

[0247]

[0248] The first-order derivative is expanded as:

[0249]

[0250] Finally, the characteristic equation of the system is calculated by using equations (33) and (38) in the specific implementation mode as follows:

[0251]

[0252] Further calculation of the above formula (40) can yield:

[0253]

[0254] d i Represents the coefficient. According to the above theory, the dynamic response characteristics of the system damping ratio at the equilibrium point are analyzed, and the maximum speed of the system under stable motion can be obtained. The system state equation established in this paper has 6 pairs of conjugate complex roots, so 6 damping characteristic curves can be obtained, which are the steering damping characteristics and the system yaw damping characteristics.

[0255] Figure 4 The figure shows the changes of the six damping ratio characteristic curves of the system when the vehicle speed gradually increases from 54km / h to 75.6km / h. The figure shows that as the system speed increases, the steering damping characteristic curve ζ s1 ,ζ s2 ,ζ ss1 ,ζ ss2 Almost unchanged, indicating that the steering characteristics will not change with the increase of system speed, and are only related to the inherent parameters of the vehicle steering system such as stiffness and damping. However, the system yaw damping characteristic curve ζ y1 , it decreases slowly with the increase of system speed, and the yaw damping characteristic curve ζy2 As the system speed increases, the positive damping gradually changes to negative damping, indicating that the system is transitioning from a stable state to an unstable state. Therefore, this paper defines the driving speed when ζ = 0 as the system dynamic critical speed, and the data in the figure shows that it is about 60.48 km / h.

[0256] 2.2 Parameter impact analysis:

[0257] According to the system dynamic critical speed (theoretical maximum driving speed), the maximum speed of the system for stable driving under different conditions is determined, that is, the influence of parameters on the system dynamic critical speed is analyzed, so that the intelligent fleet can turn at a higher stable speed to improve the overall steering efficiency and stability. At the same time, when the intelligent fleet is turning, the parameters between the front and rear vehicles: the front wheel turning angle of the rear vehicle, the distance between the vehicles, and the distance between the virtual hinge point and the front axle jointly affect the dynamic stability of the system. Therefore, the control variable analysis method is used to study the influence of the active steering of the rear vehicle, the adjustment of the distance between the vehicles, and the position of the virtual hinge point on the dynamic critical speed of the intelligent fleet system.

[0258] Figure 5-Figure 7 It is the influence of the changes in the front wheel turning angle of the rear vehicle, the distance between vehicles and the parameters of the virtual hinge point on the critical vehicle speed of the system. Figure 5 It is the influence of the distance between the front and rear vehicles on the dynamic critical speed of the system. Figure 5 It can be seen that with the increase of the distance between vehicles, the system dynamic critical speed approximately shows a linear growth, which enhances the system's anti-interference ability. Figure 6 is the influence of the change in the distance between the virtual hinge point and the front axle on the system dynamic critical speed. Figure 6 It can be seen that as the hinge point moves away from the front vehicle, the system dynamic critical speed first increases and then decreases, and reaches its peak value when the distance from the front vehicle is 1.5m. Figure 7 The influence of the active steering of the rear vehicle within a certain range on the dynamic critical speed of the system under different vehicle spacings, where the front wheel steering angle δ1 of the front vehicle is 20°. Considering the compactness of the intelligent convoy during driving, the rear wheel steering angle δ2 is selected to vary in the range of 11° to 30°. Figure 7 It can be seen that with the increase of δ2, the system dynamic critical speed first increases slowly, reaches a peak value, and then slowly decreases. As the distance between vehicles increases, it can be seen that the peak value slowly moves to the right. Therefore, when the intelligent convoy turns, a certain distance between the front and rear vehicles can be selected according to the road conditions, and a small amount of active steering can be performed to control the convoy to drive at high speed and stability. Therefore, the accuracy of the proposed control strategy can be proved.

[0259] 2.3, simulation analysis:

[0260] Smart vehicle fleets are often subject to lateral disturbances such as crosswind when driving on the road. In order to further clarify the stability performance of the system subjected to lateral disturbances near the dynamic critical speed, the yaw motion response of the system at different driving speeds is analyzed.

[0261] Figure 8-Figure 10 is the system's initial state response curve of the yaw rate of the front vehicle at different driving speeds. x =54km / h, the yaw rate of the front vehicle converges to zero under lateral disturbance over time, and as the initial lateral disturbance increases, the yaw rate oscillation amplitude increases, but the convergence speed slows down. x =60.48km / h, the yaw rate of the front vehicle is in a continuous oscillation state, and the amplitude increases with the increase of the initial lateral disturbance, which is about 1° / s and 6° / s respectively, indicating that the system is in a critical stable state. If the system is subject to a large external disturbance, the yaw rate amplitude will increase rapidly, causing the system to become unstable. x =75km / h, the yaw velocity of the front vehicle oscillates and diverges over time under the initial lateral disturbance, and the divergence amplitude increases with the increase of the initial lateral velocity disturbance; under the lateral disturbance of 0.5m / s, the system amplitude diverges rapidly after 10s, and reaches about 20° / s at 19s, at which time the system is in an unstable state; under the lateral disturbance of 0.1m / s, the divergence speed is slow, but with the increase of driving time, the yaw velocity will continue to increase until it becomes unstable.

[0262] Figure 11-13 is the system's initial state response curve of the rear vehicle's yaw angular velocity at different driving speeds. x =54km / h, the yaw rate of the rear vehicle converges to zero over time under different lateral speed disturbances; when the system travels at speed v x =60.48km / h, the yaw rate of the rear vehicle continues to oscillate over time; when the system travels at speed v x =75km / h, the yaw angular velocity of the rear vehicle oscillates and diverges with time, and the amplitude of the divergence is much greater than that of the front vehicle. At 19s, the amplitude reaches about 80° / s. At this time, the rear vehicle is seriously unstable and cannot keep the convoy moving.

[0263] From the above analysis, it can be seen that when the system speed is less than the critical speed, the system yaw motion oscillates and converges under different lateral disturbances; when the system speed is greater than the critical speed, the system yaw motion oscillates and diverges under different lateral disturbances. In other words, whether the system lateral motion is stable is only related to the driving speed, and the size of the lateral disturbance only affects the amplitude of the system yaw motion response oscillation and the speed of convergence or divergence.

[0264] 3. Propose control strategy:

[0265] Based on the above analysis, this paper proposes a high-speed steering stability control strategy for intersections without signal lights, considering the system dynamics model and the compact driving of the intelligent convoy. The motion stability performance of the intelligent convoy depends first on the characteristics of the intelligent convoy itself, and is also affected by external disturbances. For intelligent convoys driving at high speeds, external disturbances include disturbances to the system caused by uneven lines and disturbances of lateral wind flow.

[0266] In the study of the stability of high-speed steering intelligent fleet, due to the strong nonlinear characteristics of the system, the system will show completely different stability states when driving on different curved roads. Therefore, it is necessary to first determine the steering wheel angle of the system's front vehicle.

[0267] Fig.14 It shows that as the system speed increases, the system stable area is decreasing, the unstable area is increasing, and the critical steering wheel input angle has a gentle effect on the system speed under high-speed conditions. Therefore, in order to ensure the system motion stability, it is necessary to rely on the vehicle's own characteristics to constrain the system. The main way is to achieve vehicle stability through certain steering system parameters, vehicle mass parameters and rotational inertia parameters. Fig.15 It can be seen that the sensitivity is negative, that is, the vehicle mass m and the vehicle's yaw moment of inertia I z It is negatively correlated with the system motion stability (that is, as the vehicle mass and yaw moment of inertia increase, the system dynamic critical speed decreases); the sensitivity coefficient is positive, that is, the steering system moment of inertia (the steering system moment of inertia in the figure is the front wheel moment of inertia around the kingpin J ω ) is positively correlated with the system motion stability (i.e., as the front wheel rotates around the kingpin, J ω The dynamic critical speed of the system increases with the increase of the vehicle mass m, and the sensitivity of the vehicle mass m to the system stability is the highest. When the vehicle characteristics are not enough to improve the system motion stability, the system's stable motion ability can also be improved through the coupling between vehicles. Specifically, the steering system parameters of the front vehicle include J h1 , J Y1 , J ω1 , K h1 , K Y1 , K det1 , C h1 , C Y1 , C det1 , C ω1 The vehicle mass parameters of the front vehicle include the vehicle mass m1 of the front vehicle, and the moment of inertia parameters of the front vehicle include the yaw moment of inertia I of the front vehicle. z1 The steering system parameters of the rear vehicle include J h2 , J Y2, J ω2 , K h2 , K Y2 , K det2 , C h2 , C Y2 , C det2 , C ω2 The vehicle mass parameters of the rear vehicle include the vehicle mass m2 of the rear vehicle, and the moment of inertia parameters of the rear vehicle include the yaw moment of inertia I of the rear vehicle. z2 .

[0268] Through the above analysis, a control strategy based on the motion stability of the virtual articulated intelligent fleet is proposed, such as Fig.16 As shown in the figure, for the high-speed steering stability design of the intelligent fleet, first of all, it is necessary to ensure that the intelligent fleet system has sufficient stable driving ability; secondly, when the stability capability of the intelligent fleet system is insufficient, the vehicle's own characteristics can be considered to improve the stability effect; finally, the relationship between vehicles in the intelligent fleet system can be considered to further improve the system stability performance.

[0269] 4. Conclusion

[0270] (1) A dynamic model of the high-speed steering system of an intelligent convoy based on virtual articulation is established. Based on the relationship between the structural characteristics of the intelligent convoy and the influence of system parameters on the system motion stability, a control strategy for high-speed steering of an intelligent convoy based on virtual articulation points is proposed.

[0271] (2) The system damping ratio is defined by applying the relevant theories of nonlinear dynamics. The dynamic critical speed of the intelligent convoy system for stable driving is solved through the damping ratio characteristics. The influence of the intelligent convoy structure characteristics and system parameters is analyzed by using the sensitivity analysis method and the control variable analysis method, and the correctness of the proposed control strategy is verified.

[0272] (3) The yaw rate of the vehicles in front and behind the system subjected to external disturbances was analyzed using the time domain analysis method. The study found that the stability of the system when it is not near the critical speed is only related to the current driving speed, and external disturbances only affect the amplitude of the system oscillation and the speed of convergence or divergence.

[0273] The protection scope of the present invention includes but is not limited to the above embodiments. The protection scope of the present invention shall be based on the claims. Any replacement, deformation, and improvement of the technology that can be easily thought of by technicians in this field shall fall within the protection scope of the present invention.

Claims

1. A high-speed steering intelligent fleet stability control method, characterized in that: The following steps are involved: Step 1: Model building: Step 1.1, establish a single vehicle model, the single vehicle model includes a nonlinear magic formula tire model of a single vehicle and a steering system model of a single vehicle; Step 1.2, select the continuous front and rear vehicles in the intelligent vehicle fleet and compare them with the tractor and trailer in the actual semi-trailer structure, and establish a virtual articulated model through the virtual structure method; Step 1.3, based on a single vehicle model and a virtual articulated model, a ten-degree-of-freedom virtual articulated intelligent fleet system model is established by using the second-kind Lagrangian equation analysis method; the system kinetic energy, system potential energy, system dissipated energy and system generalized force in the system model are analyzed, and the system kinetic energy, system potential energy, system dissipated energy and system generalized force are brought into the second-kind Lagrangian equation for calculation to obtain the system dynamics differential equation; the system state space equation is calculated according to the system dynamics differential equation; Step 2: Nonlinear state equation analysis: Step 2.1: First, take the speed of the front vehicle as the control variable of the system, keep the front wheel angle of the front vehicle unchanged, and calculate the corresponding equilibrium point of the system at different speeds; perform Taylor expansion on the nonlinear part of the system state space equation near the equilibrium point, and ignore the high-order terms to obtain the expansion formula; calculate the system characteristic equation through the expansion formula and the system state space equation; Step 2.2, calculating the system damping ratio according to the system characteristic equation, and then obtaining a relationship curve between the system damping ratio and the system driving speed, and obtaining the system dynamic critical vehicle speed according to the relationship curve; Step 3: Parameter impact analysis: Step 3.1, using the control variable analysis method to analyze the influence of the rear vehicle active steering, adjusting the vehicle spacing and adjusting the virtual hinge point position on the system dynamic critical speed; Step 3.2: Use sensitivity analysis method to analyze the impact of vehicle characteristics on the system dynamic critical speed; Step 4: Based on step 3, a high-speed steering intelligent fleet stability control strategy is proposed: Step 4.1, first, analyze the system stability under the critical steering wheel angle of the front vehicle, and determine the steering wheel angle range of the front vehicle according to the actual driving speed of the system, so as to ensure the motion stability of the system; Step 4.2, secondly, improve the motion stability of a single vehicle through the vehicle's own characteristics, which include steering system parameters, vehicle mass parameters and rotational inertia parameters; Step 4.

3. Finally, the system motion stability is further improved through the rear vehicle active characteristics, which include vehicle spacing adjustment and rear vehicle active steering.

2. The high-speed steering intelligent vehicle fleet stability control method according to claim 1 is characterized in that: The step 1.2 includes: The continuous front and rear vehicles in the optional intelligent convoy are analogized to the tractor and trailer in the actual semi-trailer structure, and a virtual articulated model is established through the virtual structure method; In the virtual articulation model, the virtual articulation point connects the front vehicle and the rear vehicle, and the relationship between the virtual traction of the front vehicle and the virtual drag of the rear vehicle is: Where θ is the angle between the extended lines of the longitudinal axis of the front vehicle and the rear vehicle; F xtowed The longitudinal virtual drag of the rear vehicle, F xtow represents the longitudinal virtual traction of the front vehicle, F ytow represents the lateral virtual traction of the front vehicle, F ytowed Indicates the lateral virtual drag of the rear vehicle; The relationship between the longitudinal velocity and the lateral velocity between the leading vehicle and the trailing vehicle is: in, is the longitudinal velocity at the center of mass of the front vehicle, is the longitudinal velocity at the center of mass of the rear vehicle; is the lateral velocity at the center of mass of the front vehicle, is the lateral velocity at the center of mass of the rear vehicle, is the yaw rate of the front vehicle, is the yaw rate of the rear vehicle, c1 is the distance from the center of mass of the front vehicle to the hinge point, and c2 is the distance from the center of mass of the rear vehicle to the hinge point.

3. The high-speed steering intelligent vehicle fleet stability control method according to claim 2, characterized in that: The step 1.1 includes: Step 1.1.1, establish the steering system model of the front vehicle; In the steering system model of the front vehicle, the rack movement is equivalent to the kingpin, and the equivalent proportional coefficient is P a1 ; Transmit the gear to the steering shaft equivalently, the equivalent proportional coefficient is P b1 ; The Coulomb dry friction model is used to describe the dry friction force at the kingpin of the front vehicle: M f1 =F f1 ·l1 (4); In the formula, F f1 is the dry friction force at the kingpin of the front vehicle, μ1 is the friction factor of the front vehicle, N1 is the positive pressure at the kingpin of the front vehicle, δ1 is the steering wheel angle of the front vehicle; M f1 is the dry friction torque at the kingpin of the front vehicle, l1 is the effective length of the steering knuckle arm of the front vehicle; For symbolic functions Perform Fourier transform and Taylor formula expansion to obtain: Step 1.1.2, establish the steering system model of the rear vehicle; In the steering system model of the rear vehicle, the rack movement is equivalent to the kingpin, and the equivalent proportional coefficient is P a2 ; Transmit the gear to the steering shaft equivalently, the equivalent proportional coefficient is P b2 ; The Coulomb dry friction model is used to describe the dry friction at the kingpin of the rear vehicle: M f2 =F f2 ·l2 (7); In the formula, F f2 is the dry friction force at the kingpin of the rear vehicle, μ2 is the friction factor of the rear vehicle, N2 is the positive pressure at the kingpin of the rear vehicle, δ2 is the steering wheel angle of the rear vehicle; M f2 is the dry friction torque at the kingpin of the rear vehicle, l2 is the effective length of the steering knuckle arm of the rear vehicle; For symbolic functions Perform Fourier transform and Taylor formula expansion to obtain: Step 1.1.3, establish a nonlinear magic formula tire model of the front vehicle; The nonlinear magic formula tire model of the front vehicle is used to solve the longitudinal force and lateral force on the front axle and the longitudinal force and lateral force on the rear axle of the front vehicle respectively: Among them, D is the axis top factor, C is the curve shape factor, B is the stiffness factor, E is the curve curvature factor, S h is the horizontal drift of the curve, S v is the vertical drift of the curve, s1 is the longitudinal slip rate of the tire of the front vehicle, α r1 is the rear axle slip angle of the front vehicle, α f1 is the front wheel axle slip angle of the front vehicle, F lf1 is the longitudinal force on the front axle of the front vehicle, F cf1 is the lateral force on the front axle of the front vehicle, F lr1 is the longitudinal force on the rear axle of the front vehicle, F cr1 is the lateral force on the rear axle of the front vehicle; in: in, is the yaw rate of the front vehicle, is the lateral velocity at the mass center of the front vehicle, a1 is the distance from the front wheel axle to the mass center of the front vehicle, b1 is the distance from the rear wheel axle to the mass center of the front vehicle, is the longitudinal velocity at the center of mass of the front vehicle; The longitudinal slip rate of the tire of the front vehicle is expressed as: Where: r1 is the tire radius of the front vehicle; ω1 is the rotational angular velocity of the tire of the front vehicle; Decomposing the longitudinal force and lateral force of the front vehicle into the vehicle body coordinate system, the resultant force on the front axle and rear axle of the front vehicle along the x and y axes is: Among them, F xf1 is the resultant force on the front axle of the front vehicle along the x-axis, F yf1 is the resultant force on the front axle of the front vehicle along the y-axis, F xr1 is the resultant force on the rear axle of the front vehicle along the x-axis, F yr1 is the resultant force on the rear axle of the front vehicle along the y-axis; Step 1.1.4, establish a nonlinear magic formula tire model of the rear vehicle; The nonlinear magic formula tire model of the rear vehicle is used to solve the longitudinal force and lateral force on the front axle and the longitudinal force and lateral force on the rear axle of the rear vehicle respectively: Among them, D is the axis top factor, C is the curve shape factor, B is the stiffness factor, E is the curve curvature factor, S h is the horizontal drift of the curve, S v is the vertical drift of the curve, s2 is the longitudinal slip rate of the tire of the rear vehicle, α r2 is the rear axle slip angle of the rear vehicle, α f2 is the side slip angle of the front wheel axle of the rear vehicle, F lf2 is the longitudinal force on the front axle of the rear vehicle, F cf2 is the lateral force on the front axle of the rear vehicle, F lr2 is the longitudinal force on the rear axle of the rear vehicle, F cr2 is the lateral force on the rear axle of the rear vehicle; in: in, is the yaw rate of the rear vehicle; is the lateral velocity at the mass center of the rear vehicle, a2 is the distance from the front wheel axle of the rear vehicle to the mass center, b2 is the distance from the rear wheel axle of the rear vehicle to the mass center, is the longitudinal velocity at the center of mass of the rear vehicle; The longitudinal slip rate of the tire of the rear vehicle is expressed as: Where: r2 is the radius of the rear vehicle tire; ω2 is the rotational angular velocity of the rear vehicle tire; Decomposing the longitudinal force and lateral force on the rear vehicle to the vehicle body coordinate system, the resultant force on the front and rear axles of the rear vehicle along the x and y axes is: Among them, F xf2 is the resultant force on the front axle of the rear vehicle along the x-axis, F yf2 is the resultant force on the front axle of the rear vehicle along the y-axis, F xr2 is the resultant force on the rear axle of the rear vehicle along the x-axis, F yr2 is the resultant force on the rear axle of the rear vehicle along the y-axis.

4. The high-speed steering intelligent vehicle fleet stability control method according to claim 3 is characterized in that: The system dynamics differential equation in step 1.3 includes the rotational motion of the steering wheel around the wheel kingpin, the rotational motion of the rack displacement equivalent to the kingpin, the lateral motion and the yaw motion; The steering wheel rotates around the wheel kingpin: Among them, J ω1 is the moment of inertia of the front wheel of the front vehicle about the kingpin, K det1 is the equivalent deformation stiffness of the steering tie rod of the front vehicle, Y1 is the lateral linear motion displacement of the rack of the front vehicle, C det1 is the equivalent damping of the steering tie rod deformation of the front vehicle, C ω1 is the rotation damping of the front wheel of the front vehicle around the kingpin, r1 is the wheel rolling radius of the front vehicle, τ1 is the castor angle of the front wheel of the front vehicle, e1 is the tire trail of the front vehicle, J ω2 is the moment of inertia of the front wheel of the rear vehicle about the kingpin, K det2 is the equivalent deformation stiffness of the steering tie rod of the rear vehicle, Y2 is the lateral linear motion displacement of the rack of the rear vehicle, C det2 is the equivalent damping of the steering tie rod deformation of the rear vehicle, C ω2 is the rotation damping of the front wheel of the rear vehicle around the kingpin, r2 is the wheel rolling radius of the rear vehicle, τ2 is the castor angle of the front wheel of the rear vehicle, and e2 is the tire trail of the rear vehicle; The rack displacement is equivalent to the rotational motion at the kingpin: Among them, K h1 is the torsional stiffness of the steering wheel of the front vehicle, K Y1 is the gear rack meshing equivalent stiffness of the front vehicle, C h1 is the steering wheel torsional damping of the front vehicle, C 12 is the gear rack meshing equivalent damping of the front vehicle, J h1 is the moment of inertia of the steering axis of the front vehicle, J Y1 is the equivalent moment of inertia of the front vehicle’s rack to kingpin, δ h1 is the steering wheel angle of the front vehicle, K h2 is the torsional stiffness of the steering wheel of the rear vehicle, K Y2 is the gear rack meshing equivalent stiffness of the rear vehicle, C h2 is the steering wheel torsional damping of the rear vehicle, C Y2 is the gear rack meshing equivalent damping of the rear vehicle, J h2 is the moment of inertia of the steering shaft of the rear vehicle, J Y2 is the equivalent moment of inertia of the rear vehicle’s rack-to-kingpin conversion, δ h2 is the steering wheel angle of the rear vehicle; Lateral and yaw movements: Where m1 is the mass of the front vehicle, m2 is the mass of the rear vehicle, and I z1 is the yaw moment of inertia of the front vehicle, I z2 is the yaw moment of inertia of the rear vehicle; Define the system state variable ξ and system input u: Finally, by substituting formulas (1), (2), (7), (9), (10), (13), (14), (15), and (18) into formulas (19)-(22), we can obtain the system state space equation: Among them, A and G are the system coefficient matrices; H is the system nonlinear matrix, which includes the nonlinear part of the system state space equation and the system input part.

5. The high-speed steering intelligent vehicle fleet stability control method according to claim 4 is characterized in that: The step 2.2 includes: Calculate characteristic roots through the system characteristic equation; The system damping ratio is defined as: Where i is the real part of the characteristic root of the system characteristic equation, and n is the imaginary part of the characteristic root of the system characteristic equation; The relationship curve between the system damping ratio and the system driving speed is drawn. When the system damping ratio ζ=0, the system is in a critical stable state, and the system driving speed at this time is defined as the system dynamic critical speed.

6. The high-speed steering intelligent vehicle fleet stability control method according to claim 4, characterized in that: In step 4.2, the steering system parameters of the front vehicle include J h1 , J Y1 , J ω1 , K h1 , K Y1 , K det1 , C h1 , C Y1 , C det1 , C ω1 The vehicle mass parameters of the front vehicle include m1, and the moment of inertia parameters of the front vehicle include I z1 ; The steering system parameters of the rear vehicle include J h2 , J Y2 , J ω2 , K h2 , K Y2 , K det2 , C h2 , C Y2 , C det2 , C ω2 The vehicle mass parameters of the rear vehicle include m2, and the moment of inertia parameters of the rear vehicle include I z2 .

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