A method for estimating the four-wheel lateral stiffness of ground vehicles considering off-road environmental disturbances

Abstract

The application belongs to the technical field of automobiles, and particularly relates to a four-wheel side stiffness estimation method for a ground vehicle considering off-road environment disturbance. First, a vehicle dynamics model and a kinematics model considering coupled slope are established through coordinate transformation and dynamics analysis, so as to ensure the accuracy of the unmanned ground vehicle model in a complex off-road environment. Second, an unmanned ground vehicle path tracking system is constructed and state space equation discretization is carried out, so that the system can be used for four-wheel independent side stiffness estimation. Finally, a four-wheel side stiffness estimation method based on adaptive forgetting least squares is provided, which can ensure accurate and reliable estimation of tire side stiffness in an off-road environment.

Description

Technical Field

[0001] This invention belongs to the field of automotive technology, specifically a method for estimating the four-wheel lateral stiffness of ground vehicles considering off-road environmental disturbances. Background Technology

[0002] With the widespread application of unmanned ground vehicles in complex off-road environments such as military reconnaissance, wilderness rescue, and planetary exploration, the requirements for vehicle handling stability and path tracking accuracy are increasing. Tire lateral stiffness, as a key parameter affecting the lateral dynamics performance of a vehicle, directly determines the stability boundary and path tracking performance of unmanned ground vehicles. In complex off-road environments, tire lateral stiffness changes significantly with operating conditions due to uneven terrain and coupled slopes. Failure to accurately estimate tire lateral stiffness in real time will severely impact the performance of the unmanned ground vehicle control system, and may even lead to instability. Therefore, achieving high-precision tire lateral stiffness estimation has become a key technology for improving the off-road driving capabilities of unmanned ground vehicles.

[0003] Currently, tire side-stiffness estimation methods mainly rely on vehicle dynamics and kinematics models and are widely used in path tracking control of unmanned ground vehicles. However, current tire side-stiffness estimation methods still have some problems in complex off-road environments. First, most existing methods assume that the vehicle is traveling on a horizontally structured road, and the vertical load fluctuation of the four wheels fluctuates relatively little with the vehicle's movement. They do not fully consider the nonlinear effects of complex disturbances in the off-road environment on tire force and tire side-stiffness, resulting in insufficient estimation accuracy. Second, traditional estimation methods mostly focus on the equivalent stiffness of a single tire or axle, and cannot achieve independent estimation of the side-stiffness of the four wheels. This makes it difficult to adapt to the actual situation in complex off-road environments where uneven tire stress is caused by potholes and road surface coupling slopes. Finally, most estimation methods rely on high-precision sensors or complex optimization algorithms, which are expensive, computationally burdensome, and have poor real-time performance, making them unsuitable for real-time applications with limited computing resources. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a method for estimating the four-wheel lateral stiffness of ground vehicles considering off-road environmental disturbances. First, a vehicle dynamics and kinematic model considering coupled slopes are established through coordinate transformation and dynamic analysis to ensure the accuracy of the established unmanned ground vehicle model in complex off-road environments. Second, an unmanned ground vehicle path tracking system is constructed and its state-space equations are discretized, enabling its use for estimating the independent lateral stiffness of the four wheels. Finally, an adaptive forgetting least squares-based four-wheel lateral stiffness estimation method is proposed, ensuring accurate and reliable estimation of tire lateral stiffness in off-road environments.

[0005] The technical solution of this invention is described below in conjunction with the accompanying drawings:

[0006] This invention provides a method for estimating the four-wheel lateral stiffness of a ground vehicle considering off-road environmental disturbances, comprising the following steps:

[0007] Step 1: Establish a vehicle dynamics model and a vehicle kinematics model that consider the coupled slope; enable unmanned ground vehicles to dynamically adapt to the influence of road surfaces covering both cross and longitudinal slopes on vehicle dynamic characteristics through vehicle dynamic coordinate transformation.

[0008] Step 2: Construct an unmanned ground vehicle system that includes independent lateral stiffness of four wheels; by selecting variables of the unmanned ground vehicle system, establish the state-space equation for estimating the lateral stiffness of four wheels and discretize it;

[0009] Step 3: Design a four-wheel lateral stiffness estimation method based on adaptive forgetting least squares; design an adaptive forgetting least squares cost function based on an adaptive filter to obtain the four-wheel independent lateral stiffness estimation law, and realize the estimation of tire lateral stiffness in off-road environment.

[0010] Furthermore, the specific method for step one is as follows:

[0011] S11: Define three coordinate systems, namely the global coordinate system. Vehicle coordinate system and vehicle projection coordinate system The global coordinate system is fixed on a flat ground, the vehicle coordinate system is located at the vehicle's center of gravity, and the origin of the vehicle projection coordinate system is the projection of the vehicle's center of gravity onto the XOY plane.

[0012] S12: The vehicle's gravity in the global coordinate system will be generated along the vehicle coordinate system. Additional force and As shown below:

[0013] (1)

[0014] (2)

[0015] (3)

[0016] In the formula, For longitudinal additional force; For lateral additional force; This is a vertical additional force; The coordinate transformation matrix from the vehicle projected coordinate system to the vehicle coordinate system; This is the coordinate transformation matrix from the global coordinate system to the vehicle projected coordinate system; The lateral slope of the road; The longitudinal slope of the road; Projected heading angle of the vehicle; For vehicle quality; ;

[0017] S13: Establish a vehicle dynamics model on a coupled slope that ignores the vehicle's roll, pitch, and vertical motion, as shown below:

[0018] (4)

[0019] (5)

[0020] In the formula, This refers to the vehicle's yaw torque. This refers to the vehicle's sideslip angle; The vehicle's yaw rate; The longitudinal speed of the vehicle; The vehicle's lateral speed; The longitudinal force of the four tires, The lateral forces of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; Ideal front wheel steering angle; This is the distance from the vehicle's center of gravity to the front axle. This is the distance from the vehicle's center of gravity to the rear axle. The wheelbase of the vehicle; For lateral attachment force;

[0021] Assuming the vehicle's turning angle and longitudinal acceleration are approximately zero, equations (4) and (5) can be rewritten as follows:

[0022] (6)

[0023] (7)

[0024] In the formula, This refers to the yaw moment of the vehicle caused by the coupling slope; This refers to the additional vehicle yaw moment caused by wheel torque distribution; The coefficient of friction of the ground; The vertical force acting on the right side of the vehicle; The vertical force acting on the left side of the vehicle;

[0025] Under the influence of coupling slope and lateral acceleration, the vertical force of the tires on both sides The calculation is as follows:

[0026] (8)

[0027] (9)

[0028] In the formula, This refers to the vehicle's wheelbase. Road slope; The height of the vehicle's center of gravity above the ground;

[0029] By linearizing the tire model, the lateral forces experienced by the tires on the front and rear axles are... It can be represented as follows:

[0030] (10)

[0031] (11)

[0032] (12)

[0033] (13)

[0034] , (14)

[0035] In the formula, The lateral stiffness of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; This is the slip angle of the front wheel; This is the slip angle of the rear wheel; This is the nominal lateral stiffness of the wheel; This represents the range of variation in tire lateral stiffness. This is the time-varying stiffness correction factor. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver;

[0036] By combining formulas (1)-(14), a vehicle dynamics model considering the coupled slope is established:

[0037] (15)

[0038] (16)

[0039] In the formula, For the lateral stiffness of the vehicle's front axle; The rear axle lateral stiffness of the vehicle;

[0040] S14: Establish the Frenet coordinate system on the reference path ; lateral error The distance between the vehicle's center of gravity and the center of gravity of the reference path, and the heading error. The actual heading angle of the vehicle and Tangential angle of reference path difference;

[0041] The vehicle kinematic model is represented as follows:

[0042] (17)

[0043] In the formula, The curvature of the road.

[0044] Furthermore, the specific method for step two is as follows:

[0045] S21: Combining the vehicle dynamics model and vehicle kinematics model considering the coupled slope, select the variables for the unmanned ground vehicle path tracking system: select state variables. Input variables Disturbance variables ,in, This is the actual front wheel steering angle;

[0046] S22: Based on the variables of the unmanned ground vehicle path tracking system, establish the state-space equation for four-wheel lateral stiffness estimation:

[0047] (18)

[0048] (19)

[0049] (20)

[0050] In the formula,

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] In the formula, For state variables; For input variables; For disturbance variables; For unmanned ground vehicle system matrix; For unmanned ground vehicle reference system matrix; For the left front tire system matrix of unmanned ground vehicles; For the right front tire system matrix of unmanned ground vehicles; For the left rear tire system matrix of unmanned ground vehicles; Matrix for the right rear tire system of unmanned ground vehicles; Input the matrix for the unmanned ground vehicle; The reference input matrix for unmanned ground vehicles; Input the matrix for the left front tire of the unmanned ground vehicle; Input the matrix for the right front tire of the unmanned ground vehicle; The state interference matrix for unmanned ground vehicles; This refers to the nominal lateral stiffness of the front wheel; This refers to the nominal lateral stiffness of the rear wheel; This represents the range of variation in the front wheel lateral stiffness. This represents the range of variation in the rear wheel lateral stiffness. This is the time-varying stiffness correction factor for the left front wheel; This is the time-varying stiffness correction factor for the right front wheel; This is the time-varying stiffness correction factor for the left rear wheel; This is the time-varying stiffness correction factor for the right rear wheel;

[0058] S23: Discretize the state-space equations of the path tracking system; Model predictive control uses a discrete model to predict the future state of the controlled object and obtains the optimal control quantity through rolling optimization; Discretize the system state-space equations in continuous time; Discretize the continuous-time matrix in (18) using the forward Euler discretization method and obtain the discretized state-space equations of the path tracking system:

[0059] (twenty one)

[0060] (twenty two)

[0061] In the formula, The reference discrete system matrix for unmanned ground vehicles; For the discrete system matrix of the left front tire of an unmanned ground vehicle; For the discrete system matrix of the right front tire of an unmanned ground vehicle; The discrete system matrix for the left rear tire of an unmanned ground vehicle. For the discrete system matrix of the right rear tire of an unmanned ground vehicle; The reference discrete input matrix for unmanned ground vehicles; The discrete input matrix is ​​the left front tire of the unmanned ground vehicle. Let be the discrete input matrix for the right front tire of the unmanned ground vehicle. It is the identity matrix; The system's discrete time interval; For the first State variables for each period; For the first Input variables for each cycle; For the first Disturbance variables for each period; For the first State variables for each period; The discrete state disturbance matrix for unmanned ground vehicles; For the discrete system matrix of the left front, right front, left rear, and right rear tires of the unmanned ground vehicle; The matrix of left front, right front, left rear, and right rear tire systems for unmanned ground vehicles; The discrete input matrices are the left and right front tires of the unmanned ground vehicle. Input matrices for the left and right front tires of the unmanned ground vehicle.

[0062] Furthermore, the specific method for step three is as follows:

[0063] S31: Establish a tire lateral stiffness estimator including an adaptive filter:

[0064] (twenty three)

[0065] (twenty four)

[0066] In the formula, This is the regression matrix; To observe residuals; This is the time-varying tire stiffness correction factor; For the first The time-varying stiffness correction factor for the left front wheel of the step; For the first The time-varying stiffness correction factor for the right front wheel of the step; For the first The time-varying stiffness correction factor for the left rear wheel of the step; For the first The time-varying stiffness correction factor for the right rear wheel of the step;

[0067] Introducing an adaptive filter To ensure the continuity of parameter updates and avoid estimation divergence:

[0068] (25)

[0069] In the formula, No. Step-adaptive filter; The Schur stable gain matrix; This is the regression matrix; ; For the first Step-adaptive filter;

[0070] The tire lateral stiffness estimator is designed as follows:

[0071] (26)

[0072] In the formula, for State variable estimates at time t; for Estimated time-varying tire stiffness correction factor at time t; for Estimation error of time-varying tire stiffness correction coefficient at time t; for Error in state variable estimation at time t; for State variable estimates at time t; for Estimated time-varying tire stiffness correction factor at time t;

[0073] S32: Design a recursive least squares cost function that includes a forgetting factor; combine equations (25) and (26) to obtain State variable estimation error at time 1 :

[0074] (27)

[0075] Constructing auxiliary variables Will Decompose into influence The true parameter error term and the parameter-independent error term. :

[0076] (28)

[0077] (29)

[0078] In the formula, for The error term at time step that is independent of the parameters; for The error term of the actual parameters at any given time;

[0079] Will Treated as an output quantity, the time-varying stiffness correction coefficient estimate is minimized. and fitting constant error term We design a forgetting recursive least squares cost function incorporating bilinear optimization, and decouple the nonlinear problem into:

[0080] (30)

[0081] In the formula, The cost function for forgetting recursive least squares; Forgetting factor; This is the constant error term for fitting. This represents the current time-domain step number; The maximum number of time-domain steps; for The error term of the actual parameters at any given time; No. Step-adaptive filter; for Estimated time-varying tire stiffness correction factor at time t; for Time-varying tire stiffness correction factor at any given moment;

[0082] S33: By minimizing the cost function Obtain the tire lateral stiffness estimation law:

[0083] (31)

[0084] Define the inverse covariance matrix Estimated value of time-varying tire stiffness correction factor It can be expressed in the following form:

[0085] (32)

[0086] (33)

[0087] In the formula, for The inverse covariance matrix at time t;

[0088] Combining equations (32) and (33), and through algebraic transformation, the following tire lateral stiffness estimator based on the AFRLS method is established:

[0089] (34)

[0090] In the formula, for Estimated time-varying tire stiffness correction factor at time t; for The inverse covariance matrix at time t.

[0091] The beneficial effects of this invention are as follows:

[0092] 1. This invention establishes a vehicle dynamics model and a vehicle kinematics model that consider the disturbances of complex off-road environments; it can dynamically adapt to the influence of the coupled slope of both cross slope and longitudinal slope on the vehicle dynamic characteristics, thereby improving the expression accuracy of unmanned ground vehicle models in complex off-road environments.

[0093] 2. This invention constructs an unmanned ground vehicle system that includes independent lateral stiffness of four wheels. It can simultaneously and independently express the time-varying characteristics of the lateral stiffness of the four wheels under the influence of transverse and longitudinal slopes and road surface potholes, effectively suppressing the influence of transverse and longitudinal slopes and road surface potholes on the estimation of the lateral stiffness of the four wheels;

[0094] 3. This invention designs a four-wheel lateral stiffness estimation method based on adaptive forgetting least squares. By using the adaptive forgetting least squares method to solve for inconsistent and time-varying four-wheel lateral stiffness, it can ensure accurate and reliable estimation of tire lateral stiffness in off-road environments;

[0095] 4. This invention designs a lightweight estimation algorithm that combines adaptive filtering, forgetting factor, and least squares. Addressing the issues of computational complexity and difficulty in vehicle-mounted deployment of existing high-precision estimation methods, a lightweight estimation algorithm is designed, achieving a balance between high-precision estimation and low computational cost. Attached Figure Description

[0096] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0097] Figure 1 Architecture diagram of a four-wheel independent lateral stiffness estimation method for unmanned ground vehicles considering disturbances in complex off-road environments;

[0098] Figure 2 A schematic diagram illustrating the coupled slope driving of an unmanned ground vehicle.

[0099] Figure 3 This is a schematic diagram of the vehicle dynamics model;

[0100] Figure 4 This is a schematic diagram of the vehicle's kinematics model.

[0101] Figure 5 This is a schematic diagram of a double lane-shifting operation on a ramp with potholes.

[0102] Figure 6 Comparison chart of four-wheel lateral force estimation results;

[0103] Figure 7 Architecture diagram of a method for estimating the four-wheel independent lateral stiffness of unmanned ground vehicles considering disturbances in complex off-road environments. Detailed Implementation

[0104] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0105] Example 1:

[0106] See Figures 1-7 This embodiment provides a method for estimating the four-wheel lateral stiffness of a ground vehicle considering off-road environmental disturbances, including the following steps:

[0107] Step 1: Establish a vehicle dynamics model and a vehicle kinematics model that consider the coupled slope; through vehicle dynamics coordinate transformation, enable unmanned ground vehicles to dynamically adapt to the influence of road surfaces covering both cross and longitudinal slopes on vehicle dynamic characteristics, as detailed below:

[0108] S11: Define three coordinate systems. A schematic diagram of the vehicle traveling on the coupled slope is shown below. Figure 2 As shown in the figure. The figure contains three coordinate systems, namely the global coordinate system. Vehicle coordinate system and vehicle projection coordinate system The global coordinate system is fixed on the flat ground, the vehicle coordinate system is located at the vehicle's center of gravity, and the origin of the vehicle projection coordinate system is the projection of the vehicle's center of gravity onto the XOY plane.

[0109] S12: The vehicle's gravity in the global coordinate system will be generated along the vehicle coordinate system. Additional force and As shown below:

[0110] (1)

[0111] (2)

[0112] (3)

[0113] In the formula, For longitudinal additional force; For lateral additional force; This is a vertical additional force; The coordinate transformation matrix from the vehicle projected coordinate system to the vehicle coordinate system; This is the coordinate transformation matrix from the global coordinate system to the vehicle projected coordinate system; The lateral slope of the road; The longitudinal slope of the road; Projected heading angle of the vehicle; For vehicle quality; ;

[0114] S13: To focus on the key lateral dynamics characteristics of unmanned ground vehicles, establish as follows: Figure 3 The vehicle dynamics model shown is based on a coupled slope that ignores the vehicle's roll, pitch, and vertical motion:

[0115] (4)

[0116] (5)

[0117] In the formula, This refers to the vehicle's yaw torque. This refers to the vehicle's sideslip angle; The vehicle's yaw rate; The longitudinal speed of the vehicle; The vehicle's lateral speed; The longitudinal force of the four tires, The lateral forces of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; Ideal front wheel steering angle; This is the distance from the vehicle's center of gravity to the front axle. This is the distance from the vehicle's center of gravity to the rear axle. The wheelbase of the vehicle; For lateral attachment force;

[0118] Since vehicles generally travel slowly in off-road environments, it is assumed that the vehicle's turning angle and longitudinal acceleration are approximately zero. Therefore, equations (4) and (5) can be rewritten as follows:

[0119] (6)

[0120] (7)

[0121] In the formula, This refers to the yaw moment of the vehicle caused by the coupling slope; This refers to the additional vehicle yaw moment caused by wheel torque distribution; The coefficient of friction of the ground; The vertical force acting on the right side of the vehicle; The vertical force acting on the left side of the vehicle;

[0122] Under the influence of coupling slope and lateral acceleration, the vertical force of the tires on both sides The calculation is as follows:

[0123] (8)

[0124] (9)

[0125] In the formula, This refers to the vehicle's wheelbase. Road slope; The height of the vehicle's center of gravity above the ground;

[0126] By linearizing the tire model, the lateral forces experienced by the tires on the front and rear axles are... It can be represented as follows:

[0127] (10)

[0128] (11)

[0129] (12)

[0130] (13)

[0131] , (14)

[0132] In the formula, The lateral stiffness of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; This is the slip angle of the front wheel; This is the slip angle of the rear wheel; This is the nominal lateral stiffness of the wheel; This represents the range of variation in tire lateral stiffness. This is the time-varying stiffness correction factor. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver;

[0133] Combining the above formulas (1)-(14), a vehicle dynamics model considering the coupled slope is established:

[0134] (15)

[0135] (16)

[0136] In the formula, For the lateral stiffness of the vehicle's front axle; The rear axle lateral stiffness of the vehicle;

[0137] S14: Establish the vehicle kinematic model. A schematic diagram of the vehicle's lateral motion is shown in Figure 4. The two red dots represent the actual position of the vehicle's center of gravity and the center of gravity along the reference path, respectively, and the blue dashed lines are the tangents along the actual path and the reference path. Establish a Frenet coordinate system on the reference path. Lateral error The distance between the vehicle's center of gravity and the center of gravity of the reference path, and the heading error. The actual heading angle of the vehicle and Tangential angle of reference path difference.

[0138] The vehicle kinematic model is represented as follows:

[0139] (17)

[0140] In the formula, The curvature of the road.

[0141] Step 2: Construct an unmanned ground vehicle system including independent four-wheel lateral stiffness; by selecting variables of the unmanned ground vehicle system, establish the state-space equation for estimating the four-wheel lateral stiffness and discretize it, as follows:

[0142] S21: Combining the vehicle dynamics model and vehicle kinematics model considering the coupled slope, select the variables for the unmanned ground vehicle path tracking system: select state variables. Input variables Disturbance variables ;

[0143] S22: Based on the variables of the unmanned ground vehicle path tracking system, establish the state-space equation for four-wheel lateral stiffness estimation:

[0144] (18)

[0145] (19)

[0146] (20)

[0147] In the formula,

[0148] ;

[0149] ;

[0150] ;

[0151] ;

[0152] ;

[0153] ;

[0154] In the formula, For state variables; For input variables; For disturbance variables; For unmanned ground vehicle system matrix; For unmanned ground vehicle reference system matrix; For the left front tire system matrix of unmanned ground vehicles; For the right front tire system matrix of unmanned ground vehicles; For the left rear tire system matrix of unmanned ground vehicles; Matrix for the right rear tire system of unmanned ground vehicles; Input the matrix for the unmanned ground vehicle; The reference input matrix for unmanned ground vehicles; Input the matrix for the left front tire of the unmanned ground vehicle; Input the matrix for the right front tire of the unmanned ground vehicle; The state interference matrix for unmanned ground vehicles; This refers to the nominal lateral stiffness of the front wheel; This refers to the nominal lateral stiffness of the rear wheel; This represents the range of variation in the front wheel lateral stiffness. This represents the range of variation in the rear wheel lateral stiffness. This is the time-varying stiffness correction factor for the left front wheel; This is the time-varying stiffness correction factor for the right front wheel; This is the time-varying stiffness correction factor for the left rear wheel; This is the time-varying stiffness correction factor for the right rear wheel;

[0155] S23: Discretize the state-space equations of the path tracking system; Model predictive control uses a discrete model to predict the future state of the controlled object and obtains the optimal control quantity through rolling optimization; Discretize the system state-space equations in continuous time; Discretize the continuous-time matrix in (18) using the forward Euler discretization method and obtain the discretized state-space equations of the path tracking system:

[0156] (twenty one)

[0157] (twenty two)

[0158] In the formula, The reference discrete system matrix for unmanned ground vehicles; For the discrete system matrix of the left front tire of an unmanned ground vehicle; For the discrete system matrix of the right front tire of an unmanned ground vehicle; The discrete system matrix for the left rear tire of an unmanned ground vehicle. For the discrete system matrix of the right rear tire of an unmanned ground vehicle; The reference discrete input matrix for unmanned ground vehicles; The discrete input matrix is ​​the left front tire of the unmanned ground vehicle. Let be the discrete input matrix for the right front tire of the unmanned ground vehicle. It is the identity matrix; The system's discrete time interval; For the first State variables for each period; For the first Input variables for each cycle; For the first Disturbance variables for each period; For the first State variables for each period; The discrete state disturbance matrix for unmanned ground vehicles; For the discrete system matrix of the left front, right front, left rear, and right rear tires of the unmanned ground vehicle; The matrix of left front, right front, left rear, and right rear tire systems for unmanned ground vehicles; The discrete input matrices are the left and right front tires of the unmanned ground vehicle. Input matrices for the left and right front tires of the unmanned ground vehicle.

[0159] Step 3: Design a four-wheel lateral stiffness estimation method based on adaptive forgetting least squares; design an adaptive forgetting least squares cost function based on an adaptive filter to obtain the independent lateral stiffness estimation law for the four wheels, thereby realizing the estimation of tire lateral stiffness in off-road environments, as detailed below:

[0160] S31: Establish a tire lateral stiffness estimator including an adaptive filter:

[0161] (twenty three)

[0162] (twenty four)

[0163] In the formula, This is the regression matrix; To observe residuals; This is the time-varying tire stiffness correction factor; For the first The time-varying stiffness correction factor for the left front wheel of the step; For the first The time-varying stiffness correction factor for the right front wheel of the step; For the first The time-varying stiffness correction factor for the left rear wheel of the step; For the first The time-varying stiffness correction factor for the right rear wheel of the step;

[0164] When the vehicle is traveling straight, the state variable and input variables All are approximately zero, resulting in Traditional least squares methods cannot guarantee the convergence of the tire lateral stiffness estimator. Therefore, an adaptive filter is introduced. To ensure the continuity of parameter updates and avoid estimation divergence:

[0165] (25)

[0166] In the formula, No. Step-adaptive filter; The Schur stable gain matrix; This is the regression matrix; ; For the first Step-adaptive filter;

[0167] The tire lateral stiffness estimator is designed as follows:

[0168] (26)

[0169] In the formula, for State variable estimates at time t; for Estimated time-varying tire stiffness correction factor at time t; for Estimation error of time-varying tire stiffness correction coefficient at time t; for Error in state variable estimation at time t; for State variable estimates at time t;

[0170] S32: Design a recursive least squares cost function that includes a forgetting factor; combine equations (25) and (26) to obtain the estimation error of the state variables. :

[0171] (27)

[0172] In the formula, for Estimated time-varying tire stiffness correction factor at time t;

[0173] To correct the error of the time-varying tire stiffness correction factor Decoupling ensures the feasibility of the estimation; constructing auxiliary variables. Will Decompose into influence The true parameter error term and the parameter-independent error term. :

[0174] (28)

[0175] (29)

[0176] In the formula, for The error term at time step that is independent of the parameters; for The error term of the actual parameters at any given time;

[0177] Will Treated as an output quantity, the time-varying stiffness correction coefficient estimate is minimized. and fitting constant error term A forgetting recursive least squares cost function incorporating bilinear optimization was designed, and the nonlinear problem was decoupled as follows:

[0178] (30)

[0179] In the formula, The cost function for forgetting recursive least squares; Forgetting factor; This is the constant error term for fitting. This represents the current time-domain step number; The maximum number of time-domain steps; for The error term of the actual parameters at any given time; No. Step-adaptive filter; for Estimated time-varying tire stiffness correction factor at time t; for Time-varying tire stiffness correction factor at any given moment;

[0180] S33: By minimizing the cost function Obtain the tire lateral stiffness estimation law:

[0181] (31)

[0182] Define the inverse covariance matrix Estimated value of time-varying tire stiffness correction factor It can be expressed in the following form:

[0183] (32)

[0184] (33)

[0185] In the formula, for The inverse covariance matrix at time t;

[0186] Combining equations (32) and (33), and through algebraic transformation, the following tire lateral stiffness estimator based on the AFRLS method can be established:

[0187] (34)

[0188] In the formula, for Estimated time-varying tire stiffness correction factor at time t; for The inverse covariance matrix at time t.

[0189] Example 2:

[0190] To verify the effectiveness and superiority of the method proposed in this embodiment, the following were selected: Figure 5 The simulation verification was performed on a double lane-shifting ramp with potholes, as shown. and There is a depression and a convex bulge at each location. The road slope is set to 20° and the vehicle speed to 10m / s.

[0191] The four-wheel lateral force is calculated based on the estimated four-wheel lateral stiffness. Figure 6 As shown.

[0192] It can be seen that the four-wheel lateral force calculated using the estimated four-wheel lateral stiffness is in high agreement with the actual four-wheel lateral force. In the absence of potholes, the method proposed in this invention can accurately capture the dynamic changes of the four-wheel lateral force, and the estimation error remains at a low level. When the vehicle passes over potholes, the four-wheel lateral force estimated by the method of this invention will experience brief fluctuations under transient road surface excitation. However, it can quickly converge to the true value after leaving the pothole. This demonstrates the accuracy and stability of the proposed method for estimating the independent four-wheel lateral stiffness of unmanned ground vehicles considering disturbances in complex off-road environments under long-term severe disturbances.

[0193] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the four-wheel lateral stiffness of a ground vehicle considering off-road environmental disturbances, characterized in that, Includes the following steps: Step 1: Establish a vehicle dynamics model and a vehicle kinematics model that consider the coupled slope; enable unmanned ground vehicles to dynamically adapt to the influence of road surfaces covering both cross and longitudinal slopes on vehicle dynamic characteristics through vehicle dynamic coordinate transformation. Step 2: Construct an unmanned ground vehicle system that includes independent lateral stiffness of four wheels; by selecting variables of the unmanned ground vehicle system, establish the state space equation for estimating the lateral stiffness of four wheels and discretize it; Step 3: Design a four-wheel lateral stiffness estimation method based on adaptive forgetting least squares; An adaptive forgetting least squares cost function is designed based on an adaptive filter to obtain the estimation law of independent four-wheel lateral stiffness, thereby realizing the estimation of tire lateral stiffness in off-road environments. The specific method for step one is as follows: S11: Define three coordinate systems, namely the global coordinate system. Vehicle coordinate system and vehicle projection coordinate system The global coordinate system is fixed on a flat ground, the vehicle coordinate system is located at the vehicle's center of gravity, and the origin of the vehicle projection coordinate system is the projection of the vehicle's center of gravity onto the XOY plane. S12: The vehicle's gravity in the global coordinate system will be generated along the vehicle coordinate system. Additional force and As shown below: （1） （2） （3） In the formula, For longitudinal additional force; For lateral additional force; This is an additional vertical force; The coordinate transformation matrix from the vehicle projected coordinate system to the vehicle coordinate system; This is the coordinate transformation matrix from the global coordinate system to the vehicle projected coordinate system; The lateral slope of the road; The longitudinal slope of the road; Projected heading angle of the vehicle; For vehicle quality; ; S13: Establish a vehicle dynamics model on a coupled slope that ignores the vehicle's roll, pitch, and vertical motion, as shown below: （4） （5） In the formula, This refers to the vehicle's yaw torque. This refers to the vehicle's sideslip angle; The vehicle's yaw rate; The longitudinal speed of the vehicle; The vehicle's lateral speed; The longitudinal force of the four tires, The lateral forces of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; Ideal front wheel steering angle; This is the distance from the vehicle's center of gravity to the front axle. This is the distance from the vehicle's center of gravity to the rear axle. The wheelbase of the vehicle; For lateral attachment force; Assuming the vehicle's turning angle and longitudinal acceleration are zero, equations (4) and (5) can be rewritten as follows: （6） （7） In the formula, This refers to the yaw moment of the vehicle caused by the coupling slope. This refers to the additional vehicle yaw moment caused by wheel torque distribution; The coefficient of friction of the ground; The vertical force acting on the right side of the vehicle; The vertical force acting on the left side of the vehicle; Under the influence of coupling slope and lateral acceleration, the vertical force of the tires on both sides The calculation is as follows: （8） （9） In the formula, This refers to the vehicle's wheelbase. Road slope; The height of the vehicle's center of gravity above the ground; By linearizing the tire model, the lateral forces experienced by the tires on the front and rear axles are... It can be represented as follows: （10） （11） （12） （13） ， （14） In the formula, The lateral stiffness of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; This is the slip angle of the front wheel; This is the slip angle of the rear wheel; This is the nominal lateral stiffness of the wheel; This represents the range of variation in tire lateral stiffness. This is the time-varying stiffness correction factor. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; By combining formulas (1)-(14), a vehicle dynamics model considering the coupled slope is established: （15） （16） In the formula, For the lateral stiffness of the vehicle's front axle; The rear axle lateral stiffness of the vehicle; S14: Establish the Frenet coordinate system on the reference path ; lateral error The distance between the vehicle's center of gravity and the center of gravity of the reference path, and the heading error. The actual heading angle of the vehicle and Tangential angle of reference path difference; The vehicle kinematic model is represented as follows: （17） In the formula, The curvature of the road.

2. The method for estimating the four-wheel lateral stiffness of a ground vehicle considering off-road environmental disturbances according to claim 1, characterized in that, The specific method for step two is as follows: S21: Combining the vehicle dynamics model and vehicle kinematics model considering the coupled slope, select the variables for the unmanned ground vehicle path tracking system: select state variables. Input variables Disturbance variables ,in, This is the actual front wheel steering angle; S22: Based on the variables of the unmanned ground vehicle path tracking system, establish the state-space equation for four-wheel lateral stiffness estimation: （18） （19） （20） In the formula, ； ； ； ； ； ； In the formula, For state variables; For input variables; For disturbance variables; For unmanned ground vehicle system matrix; For unmanned ground vehicle reference system matrix; For the left front tire system matrix of unmanned ground vehicles; For the right front tire system matrix of unmanned ground vehicles; For the left rear tire system matrix of unmanned ground vehicles; Matrix for the right rear tire system of unmanned ground vehicles; Input the matrix for the unmanned ground vehicle; Provide the reference input matrix for unmanned ground vehicles; Input the matrix for the left front tire of the unmanned ground vehicle; Input the matrix for the right front tire of the unmanned ground vehicle; The state interference matrix for unmanned ground vehicles; This refers to the nominal lateral stiffness of the front wheel; This refers to the nominal lateral stiffness of the rear wheel; This represents the range of variation in the front wheel lateral stiffness. This represents the range of variation in the rear wheel lateral stiffness. This is the time-varying stiffness correction factor for the left front wheel; This is the time-varying stiffness correction factor for the right front wheel; This is the time-varying stiffness correction factor for the left rear wheel; This is the time-varying stiffness correction factor for the right rear wheel; S23: Discretize the state-space equations of the path tracking system; Model predictive control uses a discrete model to predict the future state of the controlled object and obtains the optimal control quantity through rolling optimization; Discretize the system state-space equations in continuous time; Discretize the continuous-time matrix in (18) using the forward Euler discretization method and obtain the discretized state-space equations of the path tracking system: （21） （22） In the formula, The reference discrete system matrix for unmanned ground vehicles; For the discrete system matrix of the left front tire of an unmanned ground vehicle; For the discrete system matrix of the right front tire of an unmanned ground vehicle; The discrete system matrix for the left rear tire of an unmanned ground vehicle. For the discrete system matrix of the right rear tire of an unmanned ground vehicle; The reference discrete input matrix for unmanned ground vehicles; The discrete input matrix is ​​the left front tire of the unmanned ground vehicle. Let be the discrete input matrix for the right front tire of the unmanned ground vehicle. It is the identity matrix; The system's discrete time interval; For the first State variables for each period; For the first Input variables for each cycle; For the first Disturbance variables for each period; For the first State variables for each period; The discrete state disturbance matrix for unmanned ground vehicles; For the discrete system matrix of the left front, right front, left rear, and right rear tires of the unmanned ground vehicle; The matrix of left front, right front, left rear, and right rear tire systems for unmanned ground vehicles; The discrete input matrices are the left and right front tires of the unmanned ground vehicle. Input matrices for the left and right front tires of the unmanned ground vehicle.

3. The method for estimating the four-wheel lateral stiffness of a ground vehicle considering off-road environmental disturbances according to claim 2, characterized in that, The specific method for step three is as follows: S31: Establish a tire lateral stiffness estimator that includes an adaptive filter: （23） （24） In the formula, This is the regression matrix; To observe residuals; This is the time-varying tire stiffness correction factor; For the first The time-varying stiffness correction factor for the left front wheel of the step; For the first The time-varying stiffness correction factor for the right front wheel of the step; For the first The time-varying stiffness correction factor for the left rear wheel of the step; For the first The time-varying stiffness correction factor for the right rear wheel of the step; Introducing an adaptive filter To ensure the continuity of parameter updates and avoid estimation divergence: （25） In the formula, No. Step-adaptive filter; The Schur stable gain matrix; This is the regression matrix; ; For the first Step-adaptive filter; The tire lateral stiffness estimator is designed as follows: （26） In the formula, for State variable estimates at time t; for Estimated time-varying tire stiffness correction factor at time t; for Estimation error of time-varying tire stiffness correction coefficient at any given time; for Error in state variable estimation at time t; for State variable estimates at time t; for Estimated time-varying tire stiffness correction factor at time t; S32: Design a recursive least squares cost function that includes a forgetting factor; combine equations (25) and (26) to obtain State variable estimation error at time 1 : （27） Constructing auxiliary variables Will Decompose into influence The true parameter error term and the parameter-independent error term. : （28） （29） In the formula, for The error term at time step that is independent of the parameters; for The error term of the actual parameters at any given time; Will Treated as an output quantity, the time-varying stiffness correction coefficient estimate is minimized. and fitting constant error term We design a forgetting recursive least squares cost function incorporating bilinear optimization, and decouple the nonlinear problem into: （30） In the formula, The cost function for forgetting recursive least squares; Forgetting factor; This is the constant error term for fitting. This represents the current time-domain step number; The maximum number of time-domain steps; for The error term of the actual parameters at any given time; No. Step-adaptive filter; for Estimated time-varying tire stiffness correction factor at time t; for Time-varying tire stiffness correction factor at any given moment; S33: By minimizing the cost function Obtain the tire lateral stiffness estimation law: （31） Define the inverse covariance matrix Estimated value of time-varying tire stiffness correction factor It can be expressed in the following form: （32） （33） In the formula, for The inverse covariance matrix at time t; Combining equations (32) and (33), and through algebraic transformation, the following tire lateral stiffness estimator based on the AFRLS method is established: （34） In the formula, for Estimated time-varying tire stiffness correction factor at time t; for The inverse covariance matrix at time t.

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