Road surface adhesion coefficient estimation method and medium based on fast converging sckf and adaptive tire stiffness

Abstract

The application discloses a road surface adhesion coefficient estimation method and medium based on a fast convergence SCKF and adaptive tire stiffness, and the method comprises the following steps: 1) acquiring automobile parameters and real-time sensor signals; 2) establishing a vehicle dynamics model based on the automobile parameters and the real-time sensor signals; 3) calculating tire slip ratio κ ij , tire side slip angle α ij , tire rotation angle δ ij , tire vertical force F z,ij , and establishing a combined brush tire model; 4) establishing a road surface adhesion coefficient estimation system based on the vehicle dynamics model, the combined brush tire model and a fast convergence SCKF estimation algorithm; and 5) solving the road surface adhesion coefficient estimation system to obtain the road surface adhesion coefficient and the tire stiffness. The medium stores a computer program. The application can accurately calculate the road surface adhesion coefficient under various working conditions, and even when the vertical elastic stiffness changes due to tire damage, the method can correctly identify the road surface adhesion coefficient.

Description

TECHNICAL FIELD

[0001] The application relates to the field of road surface information research, and particularly relates to a road surface adhesion coefficient estimation method based on a fast convergence SCKF and adaptive tire stiffness and a medium. BACKGROUND

[0002] As key information of a road surface, a road surface adhesion coefficient influences the actual effect of many vehicle active safety systems and advanced driving assistance systems (ADAS), including an anti-lock braking system (ABS), an electronic stability control (ESC), a traction control system (TCS), adaptive cruise control (ACC), automatic emergency braking (AEB) and the like. Therefore, research on road surface adhesion coefficient estimation has important value for vehicle driving safety and intended function safety. Road surface adhesion coefficient estimation methods can be generally divided into two categories: experimental and model-based methods. The experimental method is to install special sensors on a vehicle, and estimate the road surface adhesion coefficient according to the corresponding relationship between the special sensor parameters and the road surface adhesion coefficient. This method is highly dependent on the reliability of the special sensors, and has a high implementation cost. The model-based method is the main method for estimating the road surface adhesion coefficient, which uses common vehicle sensors to obtain vehicle dynamic response signals related to the road surface adhesion coefficient, and estimates the road surface adhesion coefficient in combination with a related model. However, when the vertical elastic stiffness of the tire changes due to damage in actual use, the calculation result of the existing estimation method deviates greatly and converges to an error value. SUMMARY

[0003] The application aims to provide a road surface adhesion coefficient estimation method based on a fast convergence SCKF and adaptive tire stiffness, which comprises the following steps:

[0004] 1) obtaining automobile parameters and real-time sensor signals;

[0005] 2) establishing a vehicle dynamics model based on the automobile parameters and the real-time sensor signals;

[0006] 3) calculating a tire slip ratio κ ij , a tire side slip angle α ij , a tire rotation angle δ ij , a tire vertical force F z,ij , and establishing a combined brush tire model;

[0007] 4) establishing a road surface adhesion coefficient estimation system based on the vehicle dynamics model, the combined brush tire model and a fast convergence SCKF estimation algorithm;

[0008] 5) solving the road surface adhesion coefficient estimation system to obtain the road surface adhesion coefficient.

[0009] Further, the vehicle parameters include vehicle mass m, yaw moment of inertia I z , distance from vehicle center of gravity to front axle l f and to rear axle l r , front wheel track B f and rear wheel track B r , front wheel toe angle and rear wheel toe angle vehicle center of mass height h g , longitudinal unit stiffness of tire c px and lateral unit stiffness of tire c py , vertical stiffness of tire k z , unloaded radius of tire R u ;

[0010] The real-time sensor signals are obtained by vehicle-mounted sensors, including vehicle longitudinal acceleration a x and lateral acceleration a y , yaw rate γ, wheel speed ω ij , steering wheel angle δ sw .

[0011] Further, the vehicle dynamics model is as follows:

[0012]

[0013]

[0014]

[0015] wherein v x and v y are longitudinal and lateral velocities respectively; γ is yaw rate; a x and a y are longitudinal and lateral accelerations respectively; M z is yaw moment; I z is moment of inertia of vehicle about z axis. Superscript “.” represents derivative;

[0016] wherein vehicle longitudinal acceleration a x , lateral acceleration a y and yaw moment M z are as follows:

[0017]

[0018]

[0019]

[0020] wherein m is total mass of vehicle; l fand l r respectively the distance from the vehicle center of gravity to the front and rear axles; B f and B r respectively the front and rear wheel track; F x,ij and F y,ij are the longitudinal and lateral forces of the tire; δ ij is the tire cornering angle; the lower index ij = fl, fr, rl, rr respectively indicate the front left, front right, rear left, rear right wheel.

[0021] Further, the tire slip ratio κ ij , the tire side slip angle α ij , the tire cornering angle δ ij , the tire vertical force F z,ij are respectively as follows:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] where h g is the vehicle center of gravity height; δ sw is the steering wheel cornering angle; and are respectively the front and rear wheel toe angle; i ω is the steering system angular transmission ratio; ω ij is the wheel angular velocity; R e is the effective radius of the wheel; v ij is the speed of the wheel center in the direction of the steering angle.

[0028] Further, the combined brush tire model is as follows:

[0029]

[0030]

[0031]

[0032]

[0033] where C x and C y are respectively the tire longitudinal and lateral stiffness; κ is the wheel slip ratio; α is the wheel side slip angle; μ is the road adhesion coefficient; F zis the vertical load of the tire; f and F are intermediate variables; F x is the longitudinal load of the tire; F y is the lateral load of the tire;

[0034] wherein the longitudinal stiffness C x and the lateral stiffness C y of the tire are expressed as follows:

[0035]

[0036]

[0037] wherein k z is the vertical stiffness of the tire; c px and c py are the longitudinal and lateral stiffness per unit length of the tread element, respectively; and R u is the unloaded radius of the tire.

[0038] Further, the state vector x, the input vector u, and the observation vector z of the road adhesion coefficient estimation system are expressed as follows:

[0039]

[0040] u = [F z,ij , a ij , d ij , k ij ] T (19)

[0041]

[0042] wherein m is the road adhesion coefficient; C x,ij and C y,ij are the longitudinal and lateral stiffness of each tire, respectively;

[0043] wherein the yaw angular acceleration is expressed as follows:

[0044]

[0045] wherein At is the estimation period of the estimator; and k indicates the time.

[0046] Further, the discrete state equation and the measurement equation of the road adhesion coefficient estimation system are expressed as follows:

[0047] x k = f(x k-1 , u k-1 ) + w k-1 (22)

[0048] zk = h(x k , u k ) + v k (23)

[0049] wherein, and are the system state vector and the observation vector at discrete time k, respectively; f() and h() are the system state transition function and the observation function, respectively; u k-1 is the system input vector; and are mutually independent process noise and measurement noise, respectively;

[0050] The process noise and the measurement noise satisfy the following equations:

[0051]

[0052]

[0053] wherein Q k-1 and R k are the covariance matrices of the process noise w k-1 and the measurement noise v k , respectively; E denotes mathematical expectation;

[0054] wherein the state transition function f() and the observation function h() are as follows, respectively:

[0055]

[0056]

[0057] wherein B f and B r are the front wheel track and the rear wheel track, respectively.

[0058] Further, the steps for solving the road adhesion coefficient estimation system include:

[0059] 5.1) Construct 2n volume points with the same weight according to the volume rule to obtain:

[0060]

[0061] wherein S k-1 is the square root factor of the error covariance P k-1 at time k-1; is the estimated value of the system state vector at time k-1; is the volume point;

[0062] The parameter ξ i is as follows:

[0063]

[0064] where I n is the n-dimensional identity matrix;

[0065] 5.2) Calculate propagating volume points i.e.

[0066]

[0067] where u k-1 is the road adhesion coefficient at the k-1 time;

[0068] 5.3) Calculate predicted state and its error covariance matrix square root factor of i.e.

[0069]

[0070]

[0071] where Tria() denotes the transpose of the upper triangular matrix obtained by QR decomposition; is the square root factor of Q k-1 ; matrix

[0072] Weighted center matrix is as follows:

[0073]

[0074] 5.4) Establish augmented regression model, i.e.

[0075]

[0076] where z k is an augmented variable;

[0077] where vector λ k is as follows:

[0078]

[0079] where is the prior error;

[0080] vector λ k satisfies the following formula:

[0081]

[0082] where B k , and are respectively error covariance matrix and measurement covariance matrix R k Cholesky decomposition of R;

[0083] 5.5) multiply both sides of equation (34) by to obtain the normalized regression equation, i.e.,

[0084] D k = W(x k ,u k ) + E k (37)

[0085] where the vector D k , the vector W k = W(x k ,u k ), and the vector E k are respectively given by

[0086]

[0087]

[0088]

[0089] where the parameter L = m + n; d L,k , w L,k , e L,k denote the elements in the vector D k , the vector W k , and the vector E k respectively;

[0090] 5.6) establish the cost function J MEE (x k ) based on the minimum error entropy criterion, i.e.,

[0091]

[0092] where the parameter e i,k = d i,k - w i,k , and the parameter e j,k = d j,k - w j,k ; G σ is the Gaussian kernel function;

[0093] 5.7) solve the maximum of the cost function J MEE (x k ) to obtain the optimal solution of the state vector ;

[0094] When solving, let the cost function J MEE (x k ) about x k The gradient is 0, that is:

[0095]

[0096] In the formula, σ 2 is the variance;

[0097] Wherein, the matrix Ψ k , the matrix Φ k As follows:

[0098]

[0099]

[0100] In the formula, the parameter φ ij,k =G σ (e i,k -e j,k );

[0101] 5.8) Define the matrix A k As follows:

[0102]

[0103] In the formula, the element The element The element The element The element

[0104] 5.9) Extract the diagonal elements of the matrix To establish a diagonal matrix Use the reconstructed measurement information;

[0105] The reconstructed measurement covariance matrix is as follows:

[0106]

[0107] 5.10) Determine whether the measurement covariance matrix Is a non-positive definite matrix;

[0108] If the measurement covariance matrix Is a non-positive definite matrix, execute the steps of the standard SCKF, including steps 5.1) to 5.3), and the steps of correcting the road adhesion coefficient estimation system;

[0109] If the measurement covariance matrix is positive definite, then the steps of the fast SCKF are performed, including steps 5.1) to 5.9), and the step of updating the road adhesion coefficient estimation system.

[0110] wherein the step of updating the road adhesion coefficient estimation system comprises:

[0111] 5.11) Constructing the volume point i.e.:

[0112]

[0113] wherein ξ i is the argument;

[0114] 5.12) Computing the propagated volume point i.e.:

[0115]

[0116] 5.13) Computing the predicted observation and its new covariance matrix the square root factor of:

[0117]

[0118]

[0119] wherein is the square root factor of R k , the weighted center matrix of the new covariance matrix

[0120]

[0121]

[0122] 5.14) Computing the system cross-covariance matrix i.e.:

[0123]

[0124] wherein the weighted center matrix of the cross-covariance matrix is given by:

[0125]

[0126] 5.15) Computing the Kalman gain K k i.e.:

[0127]

[0128] 5.16) Computing the updated state ​​and its error covariance matrix P k The square root factor S k ,get:

[0129]

[0130]

[0131] 5.17) Updated status and its error covariance matrix P k The square root factor S k The result is used as the estimation result of the state vector at time k, and the result is used to update and correct the data at time k+1.

[0132] A computer-readable storage medium having a computer program stored thereon;

[0133] When the computer program is invoked, the steps of the above method are executed.

[0134] The technical effect of this invention is beyond doubt. This invention can accurately calculate the road adhesion coefficient under various working conditions. Even when the vertical elastic stiffness changes due to a certain degree of tire damage, this method can still correctly identify the road adhesion coefficient. Attached Figure Description

[0135] Figure 1 Here is a diagram of the estimation method structure;

[0136] Figure 2 It is a four-wheeled vehicle model;

[0137] Figure 3 Solving for the length of the tire contact patch;

[0138] Figure 4 To accelerate the estimation of road surface adhesion coefficient under the working condition: Figure 4 (a) is a high-adhesion road surface; Figure 4 (b) is a low-adhesion road surface; Figure 4 (c) is a variable adhesion road surface.

[0139] Figure 5 To accelerate the adaptive tire stiffness change on high-adhesion road surfaces under operating conditions: Figure 5 (a) represents the longitudinal tire stiffness; Figure 5 (b) represents the lateral tire stiffness;

[0140] Figure 6 The following are the estimation results for the road surface adhesion coefficient under steering conditions: Figure 6 (a) is a high-adhesion road surface; Figure 6 (b) is a low-adhesion road surface; Figure 6 (c) Variable adhesion road surface

[0141] Figure 7 For adaptive tire stiffness change on high adhesion road surface in steering condition: Figure 7 (a) is the longitudinal tire stiffness; Figure 7 (b) is the lateral tire stiffness;

[0142] Figure 8 For road adhesion coefficient estimation results in tire damage condition: Figure 8 (a) is the constant tire stiffness; Figure 8 (b) is the adaptive tire stiffness;

[0143] Figure 9 For adaptive tire stiffness change in tire damage condition: Figure 9 (a) is the longitudinal tire stiffness; Figure 9 (b) is the lateral tire stiffness DETAILED DESCRIPTION

[0144] The application will be further described below in conjunction with examples, but should not be understood as limiting the above-mentioned subject matter of the application to the following examples. According to ordinary technical knowledge and conventional means in the art, various substitutions and modifications can be made without departing from the above-mentioned technical idea of the application, and all should be included in the protection scope of the application.

[0145] Example 1:

[0146] Referring to Figures 1 to 9 , the road adhesion coefficient estimation method based on fast convergence SCKF and adaptive tire stiffness includes the following steps:

[0147] 1) Obtain vehicle parameters and real-time sensor signals;

[0148] 2) Based on the vehicle parameters and real-time sensor signals, establish a vehicle dynamics model;

[0149] 3) Calculate the tire slip ratio κ ij , the tire side slip angle α ij , the tire rotation angle δ ij , the tire vertical force F z,ij , and establish a combined brush tire model;

[0150] 4) Based on the vehicle dynamics model, the combined brush tire model and the fast convergence SCKF estimation algorithm, establish a road adhesion coefficient estimation system;

[0151] 5) Solve the road adhesion coefficient estimation system to obtain the road adhesion coefficient.

[0152] The vehicle parameters include vehicle mass m, yaw moment of inertia I z , the distance from the vehicle center of gravity to the front axle l f and the distance to the rear axle lr , front track B f and rear track B r , front toe angle and rear toe angle vehicle center of mass height h g , longitudinal unit stiffness c px and lateral unit stiffness c py , tire vertical stiffness k z , unloaded tire radius R u ;

[0153] The real-time sensor signals are obtained by vehicle-mounted sensors, including vehicle longitudinal acceleration a x and lateral acceleration a y , yaw rate γ, wheel speed ω ij , steering wheel angle δ sw .

[0154] The vehicle dynamics model is as follows:

[0155]

[0156]

[0157]

[0158] In the formula, v x and v y are longitudinal and lateral speeds respectively; γ is the yaw rate; a x and a y are longitudinal and lateral accelerations respectively; M z is the yaw moment; I z is the rotational inertia of the vehicle about the z-axis.

[0159] Wherein, the longitudinal acceleration a x , lateral acceleration a y and yaw moment M z of the vehicle are as follows:

[0160]

[0161]

[0162] In the formula, m is the total mass of the vehicle; l f and l r are the distances from the center of mass of the vehicle to the front axle and the rear axle respectively; B f and B r are the front track and the rear track respectively; F x,ij and F y,ijare the longitudinal and lateral forces of the tire; δ ij is the tire cornering angle; the subscripts ij = fl, fr, rl, rr represent the front left, front right, rear left, and rear right tires, respectively. The vehicle longitudinal acceleration a x and lateral acceleration a y are substituted into Equations 4 and 5 to solve for the unknowns in Equations 4-5. The superscript "·" represents the derivative;

[0163] The tire slip ratio κ ij , tire side slip angle α ij , tire cornering angle δ ij , and tire vertical force F z,ij are given by:

[0164]

[0165]

[0166]

[0167]

[0168]

[0169] where h g is the vehicle center of mass height, δ sw is the steering wheel angle, and and are the front and rear toe angles, respectively. i ω is the steering system angular ratio, ω ij is the wheel angular velocity, R e is the effective radius of the wheel, and v ij is the speed of the wheel center in the direction of the steering angle.

[0170] The combined brush tire model is given by:

[0171]

[0172]

[0173]

[0174]

[0175] where C x and C y are the longitudinal and lateral stiffness of the tire, respectively, κ is the wheel slip ratio, α is the wheel side slip angle, μ is the road adhesion coefficient, F z is the tire vertical load, and f and F represent intermediate variables. F x , Fy for longitudinal and lateral loads of the tire;

[0176] wherein the longitudinal stiffness C x and the lateral stiffness C y of the tire are expressed as follows, respectively:

[0177]

[0178]

[0179] wherein k z is the vertical stiffness of the tire; c px and c py are the longitudinal and lateral stiffness per unit length of the tread element, respectively; R u is the unloaded radius of the tire.

[0180] The state vector x, the input vector u, and the observation vector z of the road adhesion coefficient estimation system are expressed as follows, respectively:

[0181]

[0182] u = [F z,ij , a ij , δ ij , κ ij ] T (19)

[0183]

[0184] wherein μ is the road adhesion coefficient; C x,ij and C y,ij are the longitudinal and lateral stiffness of each tire, respectively;

[0185] wherein the yaw angular acceleration is expressed as follows:

[0186]

[0187] wherein Δt is the estimation period of the estimator; k denotes the time.

[0188] The discrete state equation and the measurement equation of the road adhesion coefficient estimation system are expressed as follows, respectively:

[0189] x k = f(x k-1 , u k-1 ) + w k-1 (22)

[0190] z k = h(x k , u k ) + vk (23)

[0191] wherein, and are the system state vector and the observation vector at discrete time k, respectively; f() and h() are the system state transition function and the observation function, respectively; u k-1 is the system input vector; and are mutually independent process noise and measurement noise, respectively;

[0192] The process noise and the measurement noise satisfy the following equations:

[0193]

[0194]

[0195] wherein, Q k-1 and R k are the covariance matrices of the process noise w k-1 and the measurement noise v k , respectively; E represents the mathematical expectation;

[0196] wherein, the state transition function f() and the observation function h() are as follows, respectively:

[0197]

[0198]

[0199] wherein, B f and B r are the front wheel track and the rear wheel track, respectively.

[0200] The steps for solving the road adhesion coefficient estimation system include:

[0201] 5.1) Construct 2n volume points with the same weight according to the volume rule to obtain:

[0202]

[0203] wherein, S k-1 is the square root factor of the error covariance P k-1 at time k-1; is the estimated value of the system state vector at time k-1; is the volume point;

[0204] The parameter ξ i is as follows:

[0205]

[0206] where I n is the n-dimensional identity matrix;

[0207] 5.2) Calculate propagating volume points i.e.

[0208]

[0209] where u k-1 is the road adhesion coefficient at the k-1 time;

[0210] 5.3) Calculate predicted state and its error covariance matrix square root factor of i.e.

[0211]

[0212]

[0213] where Tria() denotes the transpose of the upper triangular matrix obtained by QR decomposition; is the square root factor of Q k-1 ; matrix

[0214] Weighted center matrix is as follows:

[0215]

[0216] 5.4) Establish an augmented regression model, i.e.

[0217]

[0218] where z k is an augmented variable;

[0219] where vector λ k is as follows:

[0220]

[0221] where is the prior error;

[0222] Vector λ k satisfies the following formula:

[0223]

[0224] where B k , and are respectively error covariance matrix and the measurement covariance matrix R k Cholesky decomposition of R

[0225] 5.5) Multiply both sides of equation (34) by The normalized regression equation is obtained, i.e.,

[0226] D k = W(x k , u k ) + E k (37)

[0227] where the vector D k , the vector W k , the vector E k are given as follows:

[0228]

[0229]

[0230]

[0231] where L = m + n; d L,k , w L,k , e L,k denote the elements in the vector D k , the vector W k , the vector E k , respectively; 5.6) Establish the cost function J MEE (x k ) based on the minimum error entropy criterion, i.e.,

[0232]

[0233] where the parameter e i,k = d i,k - w i,k , the parameter e j,k = d j,k - w j,k ; G σ is the Gaussian kernel function;

[0234] 5.7) Solve the maximum value of the cost function J MEE (x k ), and obtain the optimal solution of the state vector ;

[0235] When solving, let the gradient of the cost function J MEE (x k ) with respect to x k be 0, i.e.,

[0236]

[0237] where σ 2 is the variance;

[0238] where the matrix Ψ k , the matrix Φ k are given as follows:

[0239]

[0240]

[0241] where the parameter φ ij,k = G σ (e i,k -e j,k );

[0242] 5.8) Define the matrix A k as follows:

[0243]

[0244] where

[0245] 5.9) Extract the diagonal elements of the matrix to build the diagonal matrix which is used to reconstruct the measurement information;

[0246] The reconstructed measurement covariance matrix is given as follows:

[0247]

[0248] 5.10) Check if the measurement covariance matrix is non-positive definite;

[0249] If the measurement covariance matrix is non-positive definite, perform the steps of the standard SCKF, including steps 5.1) to 5.3), and the steps of the correction of the road adhesion coefficient estimation system;

[0250] If the measurement covariance matrix is positive definite, perform the steps of the fast SCKF, including steps 5.1) to 5.9), and the steps of the correction of the road adhesion coefficient estimation system.

[0251] where the steps of the correction of the road adhesion coefficient estimation system include:

[0252] 5.11) Construct the cubature points i.e.

[0253]

[0254] In the formula, ξ i As a parameter, the method of obtaining its value is the same as that of parameter ξ. i Similarly, it is determined by n and the unit vector In;

[0255] 5.12) Calculate the propagation volume point Right now:

[0256]

[0257] 5.13) Calculate and predict observations and its new covariance matrix The square root factor:

[0258]

[0259]

[0260] In the formula, For R k The square root factor,

[0261] The weighted center matrix of the new covariance matrix As shown below:

[0262]

[0263] 5.14) Calculate the system cross-covariance matrix, i.e.:

[0264]

[0265] Among them, the weighted central matrix of the cross-covariance matrix As shown below:

[0266]

[0267] 5.15) Calculate the Kalman gain K k ,Right now:

[0268]

[0269] 5.16) Calculate and update the state and its error covariance matrix P k The square root factor S k ,get:

[0270]

[0271]

[0272] 5.17) Updated status and its error covariance matrix P k the square root factor S k is the estimation result of the state vector at time k, and the result is used for data updating and correction at time k+1.

[0273] A computer readable storage medium having stored thereon a computer program; when the computer program is invoked, the steps of the above method are executed.

[0274] Embodiment 2:

[0275] The road adhesion coefficient estimation method based on the fast convergence SCKF and the adaptive tire stiffness comprises the following steps:

[0276] First, the necessary vehicle parameters and real-time sensor signals need to be obtained. The vehicle parameters include the vehicle mass m, the yaw moment of inertia I z , the distance from the vehicle center of gravity to the front axle l f and to the rear axle l r , the front wheel track B f and the rear wheel track B r , the front wheel toe angle and the rear wheel toe angle , the vehicle center of gravity height h g , the longitudinal unit stiffness of the tire c px and the lateral unit stiffness of the tire c py , the tire vertical stiffness k z , and the tire unloaded radius R u . The sensor signals include the vehicle longitudinal acceleration a x and lateral acceleration a y , the yaw rate γ, the wheel speed ω ij , and the steering wheel angle δ sw . It is worth mentioning that the above signals can be obtained by commonly used vehicle sensors without the need for additional special sensors. The vehicle speed estimator can use, for example, a vehicle speed estimation method that does not involve road adhesion coefficients to output the vehicle longitudinal speed v x and lateral speed v y to the parameter calculator. The tire slip ratio κ ij , the tire side slip angle α ij , the tire rotation angle δ ij , and the tire vertical force F z,ij are obtained by the parameter calculator, and are all necessary parameters of the vehicle model and the tire model. The road adhesion coefficient estimator is composed of the vehicle dynamics model, the tire model, and the fast convergence SCKF estimation algorithm. The tire model combines the above parameters and the road adhesion coefficient μ, the tire longitudinal stiffness C x,ij and the lateral stiffness C y,ij, the longitudinal and lateral forces of the tires F x,ij and F y,ij are provided to the vehicle model. The vehicle model transmits corresponding data to the estimation algorithm using vehicle parameters, sensor signals, calculated parameters, and tire forces. Finally, the estimation value of the road adhesion coefficient is obtained by performing the operation of the SCKF estimation algorithm using the above parameters.

[0277] The steps are as follows:

[0278] 1. A four-wheel vehicle model as shown in Figure 2 is established, and the following assumptions are made:

[0279] (1) The air dynamics of the car are ignored;

[0280] (2) The roll, pitch, and vertical movements of the car are ignored, and only the longitudinal, lateral, and yaw movements are considered;

[0281] (3) The road slope angle and inclination angle are zero;

[0282] (4) The mass center of the car is fixed and coincides with the origin of the car coordinate system;

[0283] (5) The front wheel steering angle is linearly related to the steering wheel angle, and the rear wheel steering angle is fixed;

[0284] The motion equations of the vehicle in the longitudinal, lateral, and yaw directions are obtained:

[0285]

[0286]

[0287]

[0288] where v x and v y are the longitudinal and lateral speeds, respectively; γ is the yaw angular velocity; a x and a y are the longitudinal and lateral accelerations, respectively; M z is the yaw moment; and I z is the rotational inertia of the vehicle around the z-axis.

[0289] 2. The longitudinal acceleration a x , the lateral acceleration a y , and the yaw moment M z of the car can be calculated by the following formulas:

[0290]

[0291]

[0292] where m is the total mass of the vehicle; l f and l r are the distances from the vehicle's center of gravity to the front and rear axles, respectively; B f and B r are the front and rear wheel track, respectively; F x,ij and F y,ij are the longitudinal and lateral forces of the tire; δ ij is the tire cornering angle; and the subscripts ij = fl, fr, rl, rr represent the front left, front right, rear left, and rear right wheels, respectively.

[0293] 3. The formula for calculating the tire cornering angle δ ij is:

[0294]

[0295] where δ sw is the steering wheel angle; δ and δ are the front and rear toe angles, respectively; and i ω is the steering system angle ratio.

[0296] The formula for calculating the tire side slip angle α ij is:

[0297]

[0298] The formula for calculating the wheel slip ratio κ ij is:

[0299]

[0300] where ω ij is the wheel angular velocity; R e is the effective radius of the wheel; and v ij is the speed of the wheel center in the direction of the steering angle. The formula for calculating v ij is:

[0301]

[0302] The tire vertical force F z,ij is estimated using the sum of the tire static normal force, longitudinal load transfer, and lateral load transfer, and the formula for calculating it is:

[0303]

[0304] where h g is the height of the vehicle's center of mass.

[0305] 4. Establishing the combined brush tire model:

[0306]

[0307]

[0308]

[0309]

[0310] where C x and C y are the tire longitudinal and lateral stiffness, respectively; κ is the wheel slip ratio; α is the wheel side slip angle; μ is the road adhesion coefficient; F z is the tire vertical load.

[0311] 5. The adaptive tire stiffness expression is:

[0312] C x = 2a 2 c px (16)

[0313] C y = 2a 2 c py (17)

[0314] where a is half of the tire-ground contact patch length; c px and c py are the longitudinal and lateral tread element stiffness per unit length, respectively. Figure 3 The solution of the tire-ground contact patch half length a is shown in the figure, where the tire vertical deformation ΔR u can be calculated by:

[0315]

[0316] where k z is the tire vertical elastic stiffness. Therefore, the calculation formula of the tire-ground contact patch half length a can be obtained as:

[0317]

[0318] Combining equations 16, 17, and 19, the calculation formulas of the tire longitudinal stiffness C x and the lateral stiffness C y are:

[0319]

[0320]

[0321] 6. Define the system state vector as:

[0322]

[0323] In the formula, μ is the road surface adhesion coefficient; C x,ij and C y,ij These are the longitudinal and lateral stiffness of each tire, respectively.

[0324] Define the input vector as:

[0325] u = [F z,ij ,α ij ,δ ij ,κ ij ] T (twenty three)

[0326] Define the observation vector as:

[0327]

[0328] Since commonly used vehicle-mounted gyroscope sensors can only measure the vehicle's yaw rate, not its yaw acceleration, we use the difference method to obtain the yaw acceleration at time k:

[0329]

[0330] In the formula, Δt is the sampling period of the estimator.

[0331] Establish discrete state equations and measurement equations:

[0332] x k =f(x) k-1 ,u k-1 )+w k-1 (26)

[0333] z k =h(x k ,u k )+v k (27)

[0334] In the formula, and These are the system state vector and observation vector at discrete time k, respectively; f() and h() are the system state transition function and observation function, respectively; u k-1 The system input vector; and They are independent process noise and measurement noise, respectively, and satisfy the following conditions:

[0335]

[0336]

[0337] In the formula, Q k-1 and Rk the process noise w k-1 and the measurement noise v k respectively.

[0338] According to the established vehicle dynamics model, tire model and adaptive tire stiffness expression, the state transition function f() and the observation function h() in the estimation algorithm can be written as:

[0339]

[0340]

[0341] 7. Construct 2n cubature points with the same weight according to the cubature rule:

[0342]

[0343] where S k-1 is the square root factor of the error covariance P k-1 at time k-1; is the estimated value of the system state vector at time k-1; ξ i can be calculated by:

[0344]

[0345] where I n is the n-dimensional identity matrix.

[0346] Calculate the propagated cubature points:

[0347]

[0348] Calculate the predicted state and the square root factor of its error covariance matrix :

[0349]

[0350]

[0351] where Tria() represents the transpose of the upper triangular matrix obtained by QR decomposition; is the square root factor of Q k-1 , which satisfies The weighted center matrix can be calculated by:

[0352]

[0353] 8. Combining equations (35) and (27), we can write an augmented regression model:

[0354]

[0355] where,

[0356]

[0357] and satisfies:

[0358]

[0359] where B k , and are the Cholesky decomposition of and R k , respectively. To obtain the residual information with covariance as an identity matrix, multiply both sides of equation (38) by A normalized regression equation can be obtained:

[0360] D k = W(x k , u k ) + E k (41)

[0361] where,

[0362]

[0363]

[0364]

[0365] where L = m + n.

[0366] According to the minimum error entropy (MEE) criterion, the cost function based on MEE is:

[0367]

[0368] where e i,k = d i,k - w i,k , e j,k = d j,k - w j,k . The optimal solution of x can be obtained by finding the maximum of the cost function J MEE (x k ). Let the gradient of the cost function J MEE (x k ) with respect to x k be zero, i.e.:

[0369]

[0370] where,

[0371]

[0372]

[0373] where φ ij,k = G σ (e i,k -e j,k ).

[0374] We make the following definitions:

[0375]

[0376] where,

[0377] We extract the diagonal elements of to build a diagonal matrix We reconstruct the measurement information in the SCKF framework using The reconstructed measurement covariance matrix is:

[0378]

[0379] We use the new measurement covariance matrix and its square root factor to replace the initial measurement covariance matrix R k and its square root factor for the SCKF calculation. Since the reconstructed measurement covariance matrix may be non-positive definite, we specify that if the reconstructed measurement covariance matrix is non-positive definite, we perform the standard SCKF steps; otherwise, we modify the SCKF using the new measurement covariance matrix

[0380] 9. Construct the cubature points:

[0381]

[0382] Compute the propagated cubature points:

[0383]

[0384] Compute the predicted observation and its innovation covariance matrix and its square root factor:

[0385]

[0386] ​

[0387] wherein, is the square root factor of R k satisfying the weighted central matrix can be calculated by the following formula:

[0388]

[0389] The system cross-covariance matrix is calculated:

[0390]

[0391] wherein the weighted central matrix can be calculated by the following formula:

[0392]

[0393] The Kalman gain is calculated:

[0394]

[0395] The updated state and its error covariance matrix P k are calculated:

[0396]

[0397]

[0398] The estimation results of the fast-converging SCKF state vector at time k, i.e., formula (59) and (60), will participate in the data update and correction at time k+1.

[0399] Embodiment 3:

[0400] The verification experiment of the road adhesion coefficient estimation method is as follows:

[0401] The joint simulation test is performed based on the vehicle dynamics software CarSim and the mathematical software MATLAB / Simulink. The test conditions are divided into acceleration conditions, steering conditions, and tire damage conditions. The test road surfaces are divided into high adhesion road surfaces with an adhesion coefficient of 0.8, low adhesion road surfaces with an adhesion coefficient of 0.3, and variable adhesion road surfaces with an adhesion coefficient from 1.0 to 0.4. In order to demonstrate the advantages of the method, methods one (based on adaptive tire stiffness), method two (based on fast SCKF), and the present method (based on fast SCKF and adaptive tire stiffness) are used for comparison.

[0402] 1. Acceleration condition test

[0403] In the acceleration test, the vehicle is set to accelerate from 30 km / h to 80 km / h in 6 s and then maintain a constant speed in CarSim. The road adhesion coefficient estimation results on high, low and variable adhesion coefficient road surfaces are shown in Figure 4 , and the adaptive tire stiffness change on the high adhesion coefficient road surface is shown in Figure 5 .

[0404] On the high adhesion coefficient road surface, the steady-state errors of both Method 1 and the present method are less than 1% due to the adaptive change of tire stiffness. However, Method 1 requires 4.28 s to complete convergence, while the present method only requires 1.52 s, with a convergence speed increase of 64.5% (the convergence time is defined as the time required for the deviation of the estimated value from the true value to decrease to 5% of the true value and then remain within this range). Method 2 has relatively low precision on the high adhesion coefficient road surface, but due to the use of the fast SCKF algorithm, it converges to within 10% of the true value in 3.18 s, with a steady-state error of about 9.5%.

[0405] On the low adhesion coefficient road surface, the steady-state error of all three methods is less than 4% due to the high wheel slip rate and the saturation of tire force. The estimation results of Method 2 and the present method are almost identical, both completing convergence within 2 s. The convergence speed of Method 1 is significantly slower, taking 5.51 s to complete convergence, with a decrease of 68.4% compared to the present method.

[0406] On the variable adhesion coefficient road surface, the present method can quickly converge to the true value before and after the road changes. Method 1 completes convergence before the road changes and has a relatively slow convergence speed after the road changes. Method 2 uses a constant tire stiffness, so it cannot accurately estimate the true value of the road adhesion coefficient before the road changes.

[0407] 2. Steering test

[0408] In the steering test, the vehicle is set to perform a steering operation with a steering wheel angle of 60 deg at a speed of 60 km / h in CarSim. The road adhesion coefficient estimation results on high, low and variable adhesion coefficient road surfaces are shown in Figure 6 , and the adaptive tire stiffness change on the high adhesion coefficient road surface is shown in Figure 7 .

[0409] On the high adhesion coefficient road surface, both Method 1 and the present method can quickly converge to the true value, completing convergence in 1.97 s and 0.88 s, respectively. Method 2 cannot accurately complete convergence due to the use of a constant tire stiffness, which results in a large error in the model.

[0410] On low μ road, the tire force reaches saturation, and the estimation errors of the three methods are all within 3%. It can be seen that the estimation results of method two and the present method are almost the same, and both of them converge at about 1.55s. Method one converges at 1.78s, and the convergence speed is slightly slower. Although the convergence speeds are not much different, the present method converges to the true value within 10% in 0.35s, while the identification result of method one is a smooth curve that approaches the true value almost uniformly.

[0411] On variable μ road, the convergence speed of method one before the road changes is slower than that of the present method, and they converge at 1.62s and 1.05s respectively. After the road changes, the convergence speed of method one is slightly faster. However, the present method can react very quickly after the road changes, and the identification result decreases sharply in a very short time, and then approaches the true value at a slow speed within a range of 0.4. Method two cannot converge to the true value before the road changes, and it is not very sensitive to the change of the road, but it can eventually converge to the low μ after the road changes.

[0412] 3. Tire damage test

[0413] In practical application, the tire stiffness will change with the use of the tire (e.g. tire wear, aging, etc.), and general road μ estimation algorithms are not sensitive to the change of the tire stiffness, which leads to incorrect results when the tire is abnormal. The present method can adaptively adjust the tire stiffness according to the motion response of the vehicle, so it can correctly identify the road μ to a certain extent when the tire characteristics change. In order to verify this feature, the actual vertical elastic stiffness of the tire in CarSim is reduced to 50000N / m (the vertical elastic stiffness in the estimation algorithm is still the standard value), to simulate the situation where the tire characteristics change due to wear, aging, etc. in actual use.

[0414] The test is performed on high μ road in acceleration condition, Figure 9 The estimation results of adaptive tire stiffness (the present method) and constant tire stiffness (method two) are shown. When the present method is used, both the standard tire and the damaged tire can converge to the true value of μ 0.8. The difference is that the identification curve of the standard tire is smooth, while the identification curve of the damaged tire has some fluctuations, and the convergence speed is also slightly slower than that of the standard tire. When the tire stiffness is constant, the identification result of the damaged tire deviates from the true value compared with the standard tire, and converges to an error value. It can be seen that when the tire is damaged to a certain extent and the vertical elastic stiffness changes in actual use, the present method can also correctly identify the road μ.

Claims

1. A road adhesion coefficient estimation method based on fast converging SCKF and adaptive tire stiffness, characterized in that, The method comprises the following steps: 1) obtaining vehicle parameters and real-time sensor signals; 2) establishing a vehicle dynamics model based on the vehicle parameters and real-time sensor signals; 3) calculating the tire slip ratio K ij , the tire side slip angle a ij , the tire rotation angle D ij , the tire vertical force F z,ij , and establishing a combined brush tire model; 4) establishing a road adhesion coefficient estimation system based on the vehicle dynamics model, the combined brush tire model and the fast-converging SCKF estimation algorithm; 5) solving the road adhesion coefficient estimation system to obtain the road adhesion coefficient; The combined brush tire model is as follows: wherein C x and C y are the longitudinal and lateral stiffness of the tire, respectively; K is the wheel slip ratio; a is the wheel slip angle; m is the road adhesion coefficient; F z is the vertical load of the tire; f and F represent intermediate variables; F x , F y are the longitudinal and lateral loads of the tire; wherein the tire longitudinal stiffness C x and lateral stiffness C y are expressed respectively as follows: wherein k z is the vertical stiffness of the tire; c px and c py are the longitudinal and lateral per-unit-length tread stiffness, respectively; R u is the unloaded radius of the tire; The step of solving the road adhesion coefficient estimation system comprises: 5.1) constructing 2n volume points with the same weight according to the volume rule to obtain: where S k-1 is the square root factor of the error covariance P k-1 at time k - 1; is the estimate of the system state vector at time k - 1; is the volume point; Parameter ξ i As follows: wherein I is a n-dimensional identity matrix; and n is a n-dimensional identity matrix; and 5.2) Calculate propagating volume points That is: In the formula, u k-1 is the road adhesion coefficient at the k-1 time point; 5.3) Compute the predicted state and its error covariance matrix the square root factor of which is i.e.: In the formula, Tria() represents the transpose of an upper triangular matrix obtained by QR decomposition; Q = sqrtm(A) k-1 sqrtm(A) = sqrtm(A) * sqrtm(A) weighted central moment matrix as follows: 5.4) establishing an augmented regression model, i.e. wherein z k is an augmenting variable; where the vector λ k As shown below: In the formula, is the a priori error; Vector λ k satisfies the following equation: In the formula, B k , and They are respectively Error covariance matrix And the measurement covariance matrix R k Cholesky decomposition; 5.5) Multiplying both sides of equation (34) by The normalized regression equation is obtained, i.e. D k = W(x k ,u k ) + E k (37) where the vector D k , the vector W k = W(x k , u k ), and the vector E k are given by where the parameters L = m + n; d L,k , w L,k , e L,k denote elements in the vector D k , the vector W k , the vector E k , respectively. 5.6) A cost function J based on the minimum error entropy criterion is established MEE (x k ), i.e.: where the parameter e i,k = d i,k -w i,k , the parameter e j,k = d j,k -w j,k ; G σ is a Gaussian kernel function; 5.7) Solving the cost function J MEE (x k ) for the maximum, yielding the optimal solution of the state vector xopt When solving, let the gradient of the cost function J MEE (x k ) about x k be 0, that is: where σ 2 is the variance; where the matrix Ψ k , the matrix Φ k are given by wherein the parameter φ ij,k = G σ (e i,k -e j,k ); 5.8) Defining the matrix A k As follows: In the formula, the elements Element Element Element Element 5.9) Extracting the matrix The diagonal elements of the matrix establish a diagonal matrix with the reconstructed measurement information; The reconstructed measurement covariance matrix is as follows: 5.10) judging the measurement covariance matrix whether it is non-positive definite; If the measurement covariance matrix is not positive definite, the steps of the standard SCKF are performed, including steps 5.1) to 5.3), and the steps of the correction of the road adhesion coefficient estimation system; If the measurement covariance matrix is positive definite, then the steps of the fast SCKF are performed, including steps 5.1) to 5.9), and the steps of the correction of the road adhesion coefficient estimation system.

2. The road adhesion coefficient estimation method based on fast converging SCKF and adaptive tire stiffness according to claim 1, characterized in that, The vehicle parameters include vehicle mass m, yaw moment of inertia I z , distance from vehicle center of gravity to front axle l f , and distance to rear axle l r , front wheel track B f , and rear wheel track B r , front wheel toe angle , and rear wheel toe angle vehicle center of mass height h g , longitudinal unit stiffness c px , and lateral unit stiffness c py of the tire, vertical stiffness k z of the tire, and unloaded radius R u of the tire; The real-time sensor signals are obtained by means of vehicle sensors, including the longitudinal acceleration a x and lateral acceleration a y , the yaw rate γ, the wheel rotational speed ω ij , the steering wheel angle δ sw .

3. The road adhesion coefficient estimation method based on fast converging SCKF and adaptive tire stiffness of claim 1, wherein, The vehicle dynamics model is as follows: where v x and v y are the longitudinal and lateral velocities, respectively; γ is the yaw rate; a x and a y are the longitudinal and lateral accelerations, respectively; M z is the yaw moment; I z is the moment of inertia of the vehicle about the z-axis; and the superscript "·" denotes the derivative. wherein the longitudinal acceleration a x , the lateral acceleration a y and the yaw moment M z of the vehicle are as follows: where m is the total mass of the vehicle; l f and l r are the distances from the center of gravity of the vehicle to the front and rear axles, respectively; B f and B r are the front and rear wheel tracks, respectively; F x,ij and F y,ij are the longitudinal and lateral forces of the tires; δ ij is the tire cornering angle; and the subscripts ij = fl, fr, rl, rr represent the front left, front right, rear left, and rear right wheels, respectively.

4. The road adhesion coefficient estimation method based on fast converging SCKF and adaptive tire stiffness of claim 1, wherein, Tire slip ratio κ ij Tire side slip angle α ij Tire turn angle δ ij Tire vertical force F z,ij are respectively as follows: where h g is the vehicle center of mass height; δ sw is the steering wheel angle; and are the front and rear toe angles, respectively; i ω is the steering system angular transmission ratio; ω ij is the wheel angular velocity; R e is the effective radius of the wheel; v ij is the speed of the wheel center in the direction of the steering angle.

5. The road adhesion coefficient estimation method based on fast converging SCKF and adaptive tire stiffness of claim 1, wherein, The state vector x, the input vector u and the observation vector z of the road adhesion coefficient estimation system are as follows, respectively: u = [F z,ij , a ij , δ ij , K ij ] T (19) where μ is the road adhesion coefficient; C x,ij and C y,ij are the longitudinal and lateral stiffness of each tire, respectively; α ij is the tire side slip angle; wherein the yaw angular acceleration as follows: In the formula, Δt is an estimator sampling period; k represents a time.

6. The road adhesion coefficient estimation method based on fast converging SCKF and adaptive tire stiffness of claim 1, wherein, The discrete state equation and the measurement equation of the road adhesion coefficient estimation system are as follows, respectively: x k = f(x k-1 , u k-1 ) + w k-1 (22) z k = h(x k , u k ) + v k (23) wherein and are the system state vector and the observation vector at discrete time instant k, respectively; f() and h() are the system state transition function and the observation function, respectively; u k-1 is the system input vector; and are mutually independent process noise and measurement noise, respectively. The process noise and the measurement noise satisfy the following formula: where Q k-1 and R k are the covariance matrices of process noise w k-1 and measurement noise v k , respectively; E denotes mathematical expectation. In the formula, the state transition function f() and the observation function h() are as follows, respectively: In the formula, B f and B r are the front and rear wheel tracks, respectively.

7. The road adhesion coefficient estimation method based on fast converging SCKF and adaptive tire stiffness of claim 1, wherein, The step of correcting the road adhesion coefficient estimation system comprises: 1) Constructing the volume point That is: wherein ξ is a parameter; and i is a parameter; and 2) Calculate propagation volume points That is: 3) Compute predicted observations and their new covariance matrix square root factors: wherein R is the square root factor, k of the square root factor, a weighted centering matrix of the new covariance matrix as follows: 4) Computing the system cross-covariance matrix That is: where the weighted centering matrix of the cross-covariance matrix is given by: 5) Calculate Kalman gain K k i.e.: 6) Compute update state and its error covariance matrix P k the square root factor S k of which is obtained as: 7) with updated state and its error covariance matrix P k the square root factor S k as the estimate of the state vector at time k and use this result for data update and correction at time k+1.

8. A computer-readable storage medium, characterized in that: The computer program is stored on the computer-readable medium; When the computer program is called, the steps of the method according to any one of claims 1 to 7 are executed.

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