阅读说明：本技术 一种基于卡尔曼滤波和最小二乘法的车辆路面附着系数估计方法 (Vehicle road surface adhesion coefficient estimation method based on Kalman filtering and least square method ) 是由 赵健 陈志成 朱冰 于 2021-08-03 设计创作，主要内容包括：本发明属于汽车技术领域,具体的说是一种基于卡尔曼滤波和最小二乘法的车辆路面附着系数估计方法。包括以下步骤：步骤一、基于车辆动力学模型对车辆的状态参数进行求解；步骤二、基于卡尔曼滤波估计出车辆行驶过程中轮胎受到的轮胎力；步骤三、采用最小二乘法对路面附着系数进行了估计；步骤四、通过斜率法对步骤三中低滑移率下的路面附着系数估计结果进行修正。本发明有效地降低了轮胎力观测值的不确定性,能够精确的估计在车辆滑移率较高时的路面附着系数,在车辆滑移率较低时对估计的路面附着系数结果进行合理的修正。(The invention belongs to the technical field of automobiles, and particularly relates to a vehicle pavement adhesion coefficient estimation method based on Kalman filtering and a least square method. The method comprises the following steps: solving state parameters of a vehicle based on a vehicle dynamics model; estimating tire force borne by a tire in the running process of the vehicle based on Kalman filtering; estimating the road adhesion coefficient by adopting a least square method; and step four, correcting the road adhesion coefficient estimation result under the low slip ratio in the step three by a slope method. The invention effectively reduces the uncertainty of the tire force observation value, can accurately estimate the road adhesion coefficient when the vehicle slip rate is higher, and reasonably corrects the estimated road adhesion coefficient result when the vehicle slip rate is lower.)

1. A vehicle road surface adhesion coefficient estimation method based on Kalman filtering and a least square method is characterized by comprising the following steps:

solving state parameters of a vehicle based on a vehicle dynamics model;

estimating tire force borne by a tire in the running process of the vehicle based on Kalman filtering;

estimating the road adhesion coefficient by adopting a least square method;

and step four, correcting the road adhesion coefficient estimation result under the low slip ratio in the step three by a slope method.

2. The method for estimating the road surface adhesion coefficient of the vehicle based on the Kalman filtering and the least square method as claimed in claim 1, wherein the state parameters in the first step comprise vehicle speed, brake pressure, front wheel rotation angle, tire slip rate, slip angle and wheel vertical force; the vehicle speed, the brake pressure and the front wheel rotation angle are obtained by sensors; and the tire slip rate, the slip angle and the wheel vertical force are calculated by a vehicle dynamic model.

3. The vehicle road surface adhesion coefficient estimation method based on Kalman filtering and least square method according to claim 2,

the specific method for calculating the tire slip rate, the slip angle and the wheel vertical force by the vehicle dynamics model is as follows:

11) establishing a three-degree-of-freedom model containing longitudinal, lateral and yaw motions of the vehicle, and obtaining a vehicle dynamic model equation as follows:

ma_x＝[cosδ cosδ 1 1 -sinδ 0]F_tire (1)

ma_y＝[sinδ sinδ 0 0 cosδ 1]F_tire (2)

in the formula, F_tire＝[F_xfl F_xfr F_xrl F_xrr F_yf F_yr]^TRepresenting a set of tire forces; f_xflRepresenting a front left wheel longitudinal force; f_xfrRepresenting the front right wheel longitudinal force; f_xrlRepresenting a rear left wheel longitudinal force; f_xrrRepresenting the rear right wheel longitudinal force; f_yf＝(F_yfl+F_yfr) Representing the total lateral force of the front wheel; f_yr＝(F_yrl+F_yrr) Representing the total lateral force of the rear wheel; f_yflRepresenting a front left wheel lateral force; f_yfrRepresenting front right wheel side forces; f_yrlRepresenting rear left wheel side forces; f_yrrRepresenting the rear right wheel lateral force; m represents the vehicle mass, a_xRepresents a vehicle longitudinal acceleration; a is_yRepresents vehicle lateral acceleration; δ represents a vehicle front wheel steering angle; i is_zRepresenting the moment of inertia of the vehicle about the z-axis; l_fRepresenting the vehicle center-of-mass to front axle distance; l_rRepresenting the vehicle center-of-mass to rear axle distance; t is t_wRepresenting a wheel track;representing yaw angular acceleration at the vehicle's center of mass;

12) the dynamic equation of the wheel obtained according to the dynamic balance relation is as follows:

wherein i ═ fl, fr, rl, rr denote the corresponding front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; i is_wiRepresenting the inertial mass of rotation of the tyre;representing the wheel turning angular acceleration; t is_diRepresenting the driving torque of the wheel; t is_biRepresenting the driving torque and the braking torque of the wheels; f_xiRepresenting the longitudinal reaction force of the wheel to the ground; r represents a vehicle rolling radius; t is_Fi＝(a+bv_i)F_zir represents the rolling resistance moment to which the wheel is subjected; a and b represent rolling resistance coefficient parameter values; vi represents the longitudinal speed at the wheel center; f_ziIndicating the vertical reaction force of the wheel to the ground;

13) the four-wheel driving torque of the intelligent electric vehicle can be expressed as:

in the formula, T_dflRepresenting the driving torque of the front left wheel; t is_dfrRepresenting the driving torque of the front right wheel; t is_drlRepresenting the driving torque of the rear left wheel; t is_drrRepresenting the driving torque of the rear right wheel; t is_eThe output torque of the power motor of the whole vehicle is represented; i.e. i₀Representing a gear ratio of the driveline; eta_tRepresenting the transmission efficiency of the transmission system;

14) the braking torque developed by the braking force during braking of the vehicle is expressed as:

T_bi＝k_biP_wi (6)

wherein i ═ fl, fr, rl, rr denote the corresponding front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; t is_biIndicating wheel systemDynamic torque; k is a radical of_biRepresenting a braking effectiveness factor; p_wiRepresenting a wheel cylinder brake pressure;

15) the vertical reaction force of the wheel on the ground and the inertia force formed by the acceleration and deceleration of the vehicle have a relationship, and are expressed as follows:

in the formula, F_zflIndicating that the front left wheel is subjected to a vertical reaction force of the ground; f_zfrIndicating the vertical reaction force of the front right wheel to the ground; f_zrlIndicating that the rear left wheel is subjected to a vertical reaction force of the ground; f_zrrIndicating the vertical reaction force of the rear right wheel to the ground; m represents the mass of the whole vehicle; a is_xRepresents a vehicle longitudinal acceleration; a is_yRepresents vehicle lateral acceleration; l_fRepresenting the vehicle center-of-mass to front axle distance; l_rRepresenting the vehicle center-of-mass to rear axle distance; h is_gRepresenting the centroid height; t is t_wRepresenting a wheel track;

16) selecting front left wheel longitudinal force, front right wheel longitudinal force, rear left wheel longitudinal force, rear right wheel longitudinal force, front wheel total lateral force, rear wheel total lateral force, front left wheel rotation angular velocity, front right wheel rotation angular velocity, rear left wheel rotation angular velocity, rear right wheel rotation angular velocity and yaw angular velocity at the vehicle mass center as system state variables, namely front left wheel longitudinal force, front right wheel longitudinal force, rear left wheel longitudinal force, rear right wheel longitudinal force, rear left wheel total lateral force, rear left wheel rotation angular velocity, rear right wheel rotation angular velocity and yaw angular velocity at the vehicle mass centerThe longitudinal acceleration of the vehicle, the lateral acceleration of the vehicle, the rotating angular velocity of the front left wheel, the rotating angular velocity of the front right wheel, the rotating angular velocity of the rear left wheel, the rotating angular velocity of the rear right wheel and the yaw angular velocity at the mass center of the vehicle are selected as system outputs,then the vehicle dynamics space equation is obtained as:

wherein X represents a system state variable;a differential representing a system state variable; u represents the system input; phi represents a system state variable matrix; b represents a system input matrix; y represents the system output; h represents the system output matrix and has:

H_x＝[cosδ cosδ 1 1 -sinδ 0]，

H_y＝[sinδ sinδ 0 0 cosδ 1]，

in the formula, phi represents a system state variable matrix; b represents a system input matrix; h represents a system output matrix; r represents a vehicle rolling radius; i represents an identity matrix; t is_dflRepresenting the driving torque of the front left wheel; t is_dfrRepresenting the driving torque of the front right wheel; t is_drlRepresenting the driving torque of the rear left wheel; t is_drrRepresenting the driving torque of the rear right wheel; t is_bflRepresenting the braking torque of the front left wheel; t is_bfrRepresenting the braking torque of the front right wheel; t is_brlRepresenting the braking torque of the rear left wheel; t is_brrRepresenting the braking torque of the rear right wheel; i is_wflRepresenting the tire rotational inertial mass of the front left wheel; i is_wfrRepresenting the tire rotational inertial mass of the front right wheel; i is_wrlRepresenting the rotational inertial mass of the tyre of the rear left wheel；I_wrrRepresenting the tire rotational inertial mass of the rear right wheel; i is_zRepresenting the moment of inertia of the vehicle about the Z axis; h_xRepresenting a longitudinal force matrix; h_yRepresenting a lateral force matrix;representing a yaw angle matrix; l_fRepresenting the distance of the vehicle's center of mass to the front axle; l_rRepresenting the distance from the vehicle's center of mass to the rear axle; δ represents a vehicle front wheel steering angle; t is t_wRepresenting a wheel track; m represents the mass of the whole vehicle; t is_FflRepresenting the rolling resistance moment to which the front left wheel is subjected; t is_FfrRepresenting the rolling resistance moment to which the front right wheel is subjected; t is_FrlRepresenting the rolling resistance moment to which the rear left wheel is subjected; t is_FrrRepresenting the rolling resistance moment to which the rear right wheel is subjected;

17) the brush model is used to characterize the relationship between the longitudinal force of a vehicle tire and the lateral force of a vehicle tire, expressed as:

wherein i ═ fl, fr, rl, rr denote the corresponding front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; f_xiRepresenting the longitudinal reaction force of the wheel to the ground; f_yiIndicating the lateral reaction force of the wheel to the ground; c_xiTire with indicationLongitudinal stiffness of (a); c_αiRepresents the lateral stiffness of the tire; kappa_iRepresents the slip ratio of the tire; alpha is alpha_iRepresents a tire slip angle; f. of_iRepresenting a brush model stiffness coefficient; f_tiRepresenting a brush model representative force; μ represents a road surface adhesion coefficient; f_ziIndicating the vertical reaction force of the wheel to the ground;

18) calculating the slip ratio of each tire according to the wheel rotation angular velocity, the front wheel rotation angle, the vehicle speed and the vehicle structure parameters:

in the formula, κ_flRepresents the front left wheel slip ratio; kappa_frRepresenting the front right wheel slip ratio; kappa_rlRepresenting the rear left wheel slip ratio; kappa_rrRepresenting the rear right wheel slip ratio; omega_flRepresenting the front left wheel turning angular velocity; omega_frRepresenting the front right wheel turning angular velocity; omega_rlRepresenting the rotational angular velocity of the rear left wheel; omega_rrRepresenting the rear right wheel turning angular velocity; r represents a vehicle rolling radius; v. of_xRepresenting a vehicle longitudinal speed; v. of_yRepresenting a vehicle lateral speed; t is t_wRepresenting a wheel track; delta_flIndicating a front left wheel steering angle of the vehicle; delta_frRepresenting the front right wheel angle of the vehicle; l_fRepresenting the vehicle center-of-mass to front axle distance;representing yaw rate at the center of mass of the vehicle;

19) during the driving process of the intelligent electric automobile, the corresponding tire slip angle is as follows:

in the formula, alpha_flRepresenting a front left wheel tire sidewall deflection angle; alpha is alpha_frRepresenting a front right wheel tire sidewall deviation angle; alpha is alpha_rlIndicating a rear left wheel tire slip angle; alpha is alpha_rrRepresenting the sidewall deflection angle of the rear right wheel tire;representing yaw rate at the center of mass of the vehicle; l_fRepresenting the vehicle center-of-mass to front axle distance; l_rRepresenting the vehicle center-of-mass to rear axle distance; delta_flIndicating a front left wheel steering angle of the vehicle; delta_frRepresenting the front right wheel angle of the vehicle; beta represents the vehicle centroid slip angle; v. of_xRepresenting the vehicle longitudinal speed.

4. The vehicle road surface adhesion coefficient estimation method based on Kalman filtering and least square method according to claim 3, characterized in that the specific method of the second step is as follows:

21) converting the continuous vehicle dynamics space equation (8) into a discrete system state space equation, namely:

wherein, X (k) represents a state variable of the discrete system at the k-th time; u (k) represents the input of the discrete system at time k; x (k +1) represents a state variable of the discrete system at the k +1 th moment; phi_kA state variable matrix representing the discrete system at the kth time; b is_kAn input matrix representing the discrete system at time k; y (k) representing discrete systems at time kOutputting; h_kAn output matrix representing the discrete system at time k; w (k) represents the excitation noise of the discrete system at the k-th moment; v (k) represents the observation noise of the discrete system at the k-th moment;

22) assuming that excitation noise w (k) and observation noise v (k) of the discrete system are uncorrelated white noise with a mean value of zero and variances of Q and R, respectively, the initial state X (0) of the discrete system is uncorrelated with the excitation noise w (k) and the observation noise v (k); then the one-step prediction of kalman filtering is:

in the formula (I), the compound is shown in the specification,a value representing the prediction of the state variable of the discrete system at the k +1 moment from the state variable of the discrete system at the k-th moment;a discrete system variable representing a time of k; phi_kA state variable matrix representing the discrete system at the kth time; b is_kAn input matrix representing the discrete system at time k; u (k) represents the input of the discrete system at time k;

23) the discrete system state update matrix is:

in the formula (I), the compound is shown in the specification,a value representing the prediction of the state variable of the discrete system at the k +1 moment from the state variable of the discrete system at the k-th moment; k (K +1) represents a Kalman filtering gain matrix at the K +1 th moment; y (k +1) represents the output of the discrete system at the k +1 th moment; h_kAn output matrix representing the discrete system at time k;representing the corrected estimated value of Kalman filtering at the k +1 th moment;

24) the kalman filter gain matrix is expressed as:

in the formula, K (K +1) represents a Kalman filtering gain matrix at the K +1 th moment; p (k +1| k) represents a prediction covariance matrix for time k +1 from the error covariance and state vector at time k; h_kAn output matrix representing the discrete system at time k; r represents the variance of the observed noise v (k);

25) the one-step prediction covariance matrix is:

in the formula, P (k + l | k) represents a prediction covariance matrix for the k +1 time point from the error covariance and state vector at the k time point; phi_kA state variable matrix representing the discrete system at the kth time; p (k | k) represents the covariance matrix of the discrete system at the k-th time; q represents the variance of the excitation noise w (k);

26) introducing a forgetting factor into the one-step prediction covariance matrix for correction, namely:

in the formula, P (k +1| k) represents a prediction covariance matrix for the k +1 time point from the error covariance and state vector at the k time point; phi_kA state variable matrix representing the discrete system at the kth time; p (k | k) represents the covariance matrix of the discrete system at the k-th time; q represents the variance of the excitation noise w (k); s represents a forgetting factor;

the covariance matrix update equation is:

P(k+1|k+1)＝(I-K(k+1)H_k)P(k+1|k) (24)

in the formula, K (K +1) represents a Kalman filtering gain matrix at the K +1 th moment; h_kAn output matrix representing the discrete system at time k; p (k +1| k) represents a prediction covariance matrix for time k +1 from the error covariance and state vector at time k; p (k +1| k +1) is the corrected covariance matrix; i represents an identity matrix;

27) through the iteration of the formulas (19) to (24), the state variable of the discrete system is obtained through estimationLongitudinal and lateral forces of the tire;

wherein, F_xflRepresenting a front left wheel longitudinal force; f_xfrRepresenting the front right wheel longitudinal force; f_xrlRepresenting a rear left wheel longitudinal force; f_xrrRepresenting the rear right wheel longitudinal force; f_yf＝(F_yfl+F_yfr) Representing the total lateral force of the front wheel; f_yr＝(F_yrl+F_yrr) Representing the total lateral force of the rear wheel; f_yflRepresenting a front left wheel lateral force; f_yfrRepresenting front right wheel side forces; f_yrlRepresenting rear left wheel side forces; f_yrrRepresenting the rear right wheel lateral force; omega_flRepresenting the front left wheel turning angular velocity; omega_frRepresenting the front right wheel turning angular velocity; omega_rlRepresenting the rotational angular velocity of the rear left wheel; omega_rrRepresenting the rear right-wheel turning angular velocity,representing the yaw rate at the center of mass of the vehicle.

5. The vehicle road surface adhesion coefficient estimation method based on Kalman filtering and least square method according to claim 1, characterized in that the concrete method of the third step is as follows:

31) the brush model is rewritten, namely:

y(k)＝f(k，θ(k)) (25)

in the formula，y(k)＝[F_x，F_y]Represents the tire force at the k-th time; f_xRepresenting the longitudinal reaction force of the wheel to the ground; f_yIndicating the lateral reaction force of the wheel to the ground; f (k, θ (k)) represents the brush tire model at the k-th time; θ (k) ═ C_x，C_α，μ]^TA state vector representing the brush tire model at the k-th time; c_xRepresents the longitudinal stiffness of the tire; c_αRepresents the lateral stiffness of the tire; μ represents a road surface adhesion coefficient;

32) and (5) performing first-order Taylor expansion on the y (k), and neglecting high-order terms to obtain:

y(k)≈F(k)(θ(k)-θ(k-1))+f(θ(k-1)，k-1) (26)

wherein y (k) represents a tire force at the k-th time; theta (k-1) is a state vector of the brush tire model at the k-1 moment; theta (k) is a state vector of the brush tire model at the kth moment; f (theta (k-1), k-1) represents the brush tire model at the k-1 moment; f (k) represents the transpose of the jacobian matrix at time k, y (k), to θ (k), where:

wherein F (k) represents a transpose of y (k) to a Jacobian matrix of θ (k); theta (k) is a state vector of the brush tire model at the kth moment; f (k, θ) represents a brush tire model; θ represents a state vector of the brush tire model; theta (k-1) is a state vector of the brush tire model at the k-1 moment;

let z (k) y (k) -f (θ (k-1), k-1) + f (k) θ (k-1), then:

z(k)≈F(k)θ(k) (28)

wherein f (k) represents a transpose of a jacobian matrix of θ (k) to the k-th time y (k); y (k) represents the tire force at time k; θ (k) a state vector of the brush tire model at the kth time; z (k) is the measurable tire force matrix at time k;

33) estimating the road adhesion coefficient by a least square method, and setting a least square method cost function as follows:

in the formula (I), the compound is shown in the specification,representing a recursive least squares cost function based on a brush tire model; Λ represents a forgetting factor matrix of a least square method; z (i) represents the measurable tire force matrix at time i; f (i) represents the transpose of the jacobian matrix at the i-th time y (i) to θ (i); theta (i) is a state vector of the brush tire model at the ith moment;a state vector representing the brush tire model estimated at the ith time;

34) to minimize the cost function, the recursive least squares method based on the brush tire model is:

L(k)＝P(k-1)F^T(k)(I+F(k)P(k-1)F^T(k))^-1 (31)

P(k)＝Λ^-1(I-L(k)F(k))P(k-1)Λ^-1 (32)

in the formula (I), the compound is shown in the specification,a state vector representing the brush tire model estimated at the k-th time;representing the state vector of the brush tire model estimated at the k-1 time; z (k) is the measurable tire force matrix at time k; f (k-1) represents the transpose of the Jacobian matrix of y (k-1) to theta (k-1) at the k-1 th time; y (k-1) represents the tire force at the k-1 time, θ (k-1) represents the state vector of the brush tire model at the k-1 time, and L (k) represents the k timeCarving a recursion minimum dyadic gain matrix based on a brush model; f (k) denotes the transpose of the jacobian matrix at time k (y) (k) to θ (k); y (k) represents the tire force at time k; p (k) represents a least square method updating matrix based on the brush model at the k-th moment; p (k-1) represents a least square method updating matrix based on a brush model at the k-1 moment; Λ represents a forgetting factor matrix of a least square method, and I represents an identity matrix;

35) estimating to obtain an estimated state vector of the brush tire model through iteration of (30) - (32)Road surface adhesion coefficient of (1); wherein the content of the first and second substances,representing the longitudinal stiffness of the tyre estimated on the basis of the brush model,representing the lateral stiffness of the tyre estimated on the basis of the brush model,representing the road adhesion coefficient estimated based on the brush model.

6. The vehicle road surface adhesion coefficient estimation method based on Kalman filtering and least square method according to claim 1, characterized in that the concrete method of the fourth step is as follows:

41) when the slip ratio is small, the adhesion coefficient μ and the slip ratio κ are approximately in a direct proportional relationship, that is:

in the formula, κ^-1(k) Represents the reciprocal of the slip ratio of the tire at the k-th time; f_z(k) Indicating that the wheel receives the vertical reaction force of the ground at the k-th moment; f_x(k) Indicating that the wheel receives the longitudinal reaction force of the ground at the k-th moment; mu.s_s(k) Representing the real road adhesion coefficient used for the slope method at the kth moment;

42) the least square method cost function based on the slope method is set as follows:

in the formula (I), the compound is shown in the specification,representing a recursive least square method cost function based on a slope method; Λ represents a forgetting factor matrix of a least square method; kappa^-1(i) Represents the reciprocal of the slip ratio of the tire at the ith time; f_z(i) Indicating the vertical reaction of the wheel to the ground at time i, F_x(i) Indicating that the wheel is subjected to a longitudinal reaction force from the ground at time i,a road surface adhesion coefficient estimated by a slope method at the ith moment;

43) in order to minimize the cost function, a recursive least square method based on a slope method is designed as follows:

in the formula (I), the compound is shown in the specification,representing the road adhesion coefficient estimated by the slope method at the k-th moment;representing the road adhesion coefficient estimated by the slope method at the k-1 th moment; kappa^-1(k) Represents the reciprocal of the slip ratio of the tire at the k-th time; f_z(k) Indicating that the wheel receives the vertical reaction force of the ground at the k-th moment; f_x(k) Indicating that the wheel receives the longitudinal reaction force of the ground at the k-th moment; l is_s(k) Representing a recursion minimum dyadic gain matrix based on a slope method at the kth moment; ps (k) represents a least square method update matrix based on a slope method at the kth moment; p_s(k-1) updating the matrix by a least square method based on a slope method at the k-1 moment; Λ represents a forgetting factor matrix of a least square method; i represents an identity matrix;

44) and (5) iterating through formulas (35) - (37) to estimate and obtain the road adhesion coefficient estimated by the slope method

Finally, the corrected road adhesion coefficient estimation result is expressed as:

in the formula (I), the compound is shown in the specification,representing the corrected road adhesion coefficient estimation result; κ represents the tire slip ratio;representing a road adhesion coefficient estimated based on a slope method;representing the road adhesion coefficient estimated based on the brush model.

Technical Field

The invention belongs to the technical field of automobiles, and particularly relates to a vehicle pavement adhesion coefficient estimation method based on Kalman filtering and a least square method.

Background

The intelligent electric automobile runs on the ground, and is limited by the driving force of a vehicle bottom layer driving system and the braking force of a braking system on one hand, and is also limited by different road adhesion conditions on the other hand. The road adhesion coefficient is one of the most critical parameters in a vehicle-road system, and has a crucial influence on the driving safety performance of the intelligent electric vehicle.

A new method for identifying the road surface in recent years is based on a vehicle-mounted camera, a laser radar, an ultrasonic radar and the like, but the equipment is high in cost and strong in practical application uncertainty, so that the method is not widely popularized. The method is a means which is closer to practical low-cost application by relying on the information of the existing vehicle-mounted sensor and adopting an observation and estimation theory to accurately identify the road surface adhesion coefficient. However, in practical applications, the uncertainty of the tire force applied to the road adhesion coefficient estimation is strong, and a proper strategy needs to be adopted to reasonably predict and estimate the tire force, so that the road adhesion coefficient estimation divergence is avoided. In addition, when the tire slip rate is too low, the reliability of the road adhesion coefficient estimated based on the classical tire model is low, and potential safety hazards are caused to vehicle motion control.

Disclosure of Invention

The invention provides a vehicle road adhesion coefficient estimation method based on Kalman filtering and a least square method, which effectively reduces the uncertainty of a tire force observation value, can accurately estimate the road adhesion coefficient when the vehicle slip rate is higher, and reasonably corrects the estimated road adhesion coefficient result when the vehicle slip rate is lower.

The technical scheme of the invention is described as follows by combining the attached drawings:

a vehicle road surface adhesion coefficient estimation method based on Kalman filtering and a least square method comprises the following steps:

solving state parameters of a vehicle based on a vehicle dynamics model;

estimating tire force borne by a tire in the running process of the vehicle based on Kalman filtering;

estimating the road adhesion coefficient by adopting a least square method;

and step four, correcting the road adhesion coefficient estimation result under the low slip ratio in the step three by a slope method.

The state parameters in the first step comprise vehicle speed, brake pressure, front wheel rotation angle, tire slip rate, slip angle and wheel vertical force; the vehicle speed, the brake pressure and the front wheel rotation angle are obtained by sensors; and the tire slip rate, the slip angle and the wheel vertical force are calculated by a vehicle dynamic model.

The specific method for calculating the tire slip rate, the slip angle and the wheel vertical force by the vehicle dynamics model is as follows:

11) establishing a three-degree-of-freedom model containing longitudinal, lateral and yaw motions of the vehicle, and obtaining a vehicle dynamic model equation as follows:

ma_x＝[cosδcosδ1 1-sinδ0]F_tire (1)

ma_y＝[sinδsinδ0 0 cosδ1]F_tire (2)

in the formula, F_tire＝[F_xfl F_xfr F_xrl F_xrr F_yf F_yr]^TRepresenting a set of tire forces; f_xflRepresenting a front left wheel longitudinal force; f_xfrRepresenting the front right wheel longitudinal force; f_xrlRepresenting a rear left wheel longitudinal force; f_xrrRepresenting the rear right wheel longitudinal force; f_yf＝(F_yfl+F_yfr) Representing the total lateral force of the front wheel; f_yr＝(F_yrl+F_yrr) Representing the total lateral force of the rear wheel; f_yflRepresenting a front left wheel lateral force; f_yfrRepresenting front right wheel side forces; f_yrlRepresenting rear left wheel side forces; f_yrrRepresenting the rear right wheel lateral force; m represents the vehicle mass, a_xRepresents a vehicle longitudinal acceleration; a is_yRepresents vehicle lateral acceleration; δ represents a vehicle front wheel steering angle; i is_zRepresenting the moment of inertia of the vehicle about the z-axis; l_fRepresenting the center of mass of the vehicle toThe distance of the front axle; l_rRepresenting the vehicle center-of-mass to rear axle distance; t is t_wRepresenting a wheel track;representing yaw angular acceleration at the vehicle's center of mass;

12) the dynamic equation of the wheel obtained according to the dynamic balance relation is as follows:

wherein i ═ fl, fr, rl, rr denote the corresponding front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; i is_wiRepresenting the inertial mass of rotation of the tyre;representing the wheel turning angular acceleration; t is_diRepresenting the driving torque of the wheel; t is_biRepresenting the driving torque and the braking torque of the wheels; f_xiRepresenting the longitudinal reaction force of the wheel to the ground; r represents a vehicle rolling radius; t is_Fi＝(a+bv_i)F_zir represents the rolling resistance moment to which the wheel is subjected; a and b represent rolling resistance coefficient parameter values; v. of_iRepresenting the longitudinal speed at the wheel center; f_ziIndicating the vertical reaction force of the wheel to the ground;

13) the four-wheel driving torque of the intelligent electric vehicle can be expressed as:

in the formula, T_dflRepresenting the driving torque of the front left wheel; t is_dfrRepresenting the driving torque of the front right wheel; t is_drlRepresenting the driving torque of the rear left wheel; t is_drrRepresenting the driving torque of the rear right wheel; t is_eThe output torque of the power motor of the whole vehicle is represented; i.e. i₀Representing a gear ratio of the driveline; eta_tRepresenting the transmission efficiency of the transmission system;

14) the braking torque developed by the braking force during braking of the vehicle is expressed as:

T_bi＝k_biP_wi (6)

wherein i ═ fl, fr, rl, rr denote the corresponding front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; t is_biRepresenting the braking torque of the wheel; k is a radical of_biRepresenting a braking effectiveness factor; p_wiRepresenting a wheel cylinder brake pressure;

15) the vertical reaction force of the wheel on the ground and the inertia force formed by the acceleration and deceleration of the vehicle have a relationship, and are expressed as follows:

in the formula, F_zflIndicating that the front left wheel is subjected to a vertical reaction force of the ground; f_zfrIndicating the vertical reaction force of the front right wheel to the ground; f_zrlIndicating that the rear left wheel is subjected to a vertical reaction force of the ground; f_zrrIndicating the vertical reaction force of the rear right wheel to the ground; m represents the mass of the whole vehicle; a is_xRepresents a vehicle longitudinal acceleration; a is_yRepresents vehicle lateral acceleration; l_fRepresenting the vehicle center-of-mass to front axle distance; l_rRepresenting the vehicle center-of-mass to rear axle distance; h is_gRepresenting the centroid height; t is t_wRepresenting a wheel track;

16) selecting front left wheel longitudinal force, front right wheel longitudinal force, rear left wheel longitudinal force, rear right wheel longitudinal force, front wheel total lateral force, rear wheel total lateral force, front left wheel rotation angular velocity, front right wheel rotation angular velocity, rear left wheel rotation angular velocity, rear right wheel rotation angular velocity and yaw angular velocity at the vehicle mass center as system state variables, namely front left wheel longitudinal force, front right wheel longitudinal force, rear left wheel longitudinal force, rear right wheel longitudinal force, rear left wheel total lateral force, rear left wheel rotation angular velocity, rear right wheel rotation angular velocity and yaw angular velocity at the vehicle mass centerSelecting the longitudinal acceleration of the vehicle, the lateral acceleration of the vehicle, the rotational angular velocity of the front left wheel, the rotational angular velocity of the front right wheel, the rotational angular velocity of the rear left wheel, the rotational angular velocity of the rear right wheel and the yaw angular velocity at the mass center of the vehicleIs the output of the system, and is,then the vehicle dynamics space equation is obtained as:

wherein X represents a system state variable;a differential representing a system state variable; u represents the system input; phi represents a system state variable matrix; b represents a system input matrix; y represents the system output; h represents the system output matrix and has:

H_x＝[cosδcosδ1 1 -sinδ0],

H_y＝[sinδsinδ0 0 cosδ1],

in the formula, phi represents a system state variable matrix; b represents a system input matrix; h represents a system output matrix; r represents a vehicle rolling radius; i represents an identity matrix; t is_dflRepresenting the driving torque of the front left wheel; t is_dfrRepresenting the driving torque of the front right wheel; t is_drlRepresenting the driving torque of the rear left wheel; t is_drrRepresenting the driving torque of the rear right wheel; t is_bflRepresenting the braking torque of the front left wheel; t is_bfrRepresenting the braking torque of the front right wheel; t is_brlRepresenting the braking torque of the rear left wheel; t is_brrRepresenting the braking torque of the rear right wheel; i is_wflRepresenting the tire rotational inertial mass of the front left wheel; i is_wfrRepresenting the tire rotational inertial mass of the front right wheel; i is_wrlRepresenting the tire rotational inertial mass of the rear left wheel; i is_wrrRepresenting the tire rotational inertial mass of the rear right wheel; i is_zRepresenting the moment of inertia of the vehicle about the Z axis; h_xRepresenting a longitudinal force matrix; h_yRepresenting a lateral force matrix;representing a yaw angle matrix; l_fRepresenting the distance of the vehicle's center of mass to the front axle; l_rRepresenting the distance from the vehicle's center of mass to the rear axle; δ represents a vehicle front wheel steering angle; t is t_wRepresenting a wheel track; m represents the mass of the whole vehicle; t is_FflRepresenting the rolling resistance moment to which the front left wheel is subjected; t is_FfrRepresenting the rolling resistance moment to which the front right wheel is subjected; t is_FrlRepresenting the rolling resistance moment to which the rear left wheel is subjected; t is_FrrRepresenting the rolling resistance moment to which the rear right wheel is subjected;

17) the brush model is used to characterize the relationship between the longitudinal force of a vehicle tire and the lateral force of a vehicle tire, expressed as:

wherein i ═ fl, fr, rl, rr denote the corresponding front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; f_xiRepresenting the longitudinal reaction force of the wheel to the ground; f_yiIndicating the lateral reaction force of the wheel to the ground; c_xiRepresents the longitudinal stiffness of the tire; c_αiRepresents the lateral stiffness of the tire; kappa_iRepresents the slip ratio of the tire; alpha is alpha_iRepresents a tire slip angle; f. of_iRepresenting a brush model stiffness coefficient; f_tiRepresenting a brush model representative force; μ represents a road surface adhesion coefficient; f_ziIndicating the vertical reaction force of the wheel to the ground;

18) calculating the slip ratio of each tire according to the wheel rotation angular velocity, the front wheel rotation angle, the vehicle speed and the vehicle structure parameters:

in the formula, κ_flRepresents the front left wheel slip ratio; kappa_frRepresenting the front right wheel slip ratio; kappa_rlRepresenting the rear left wheel slip ratio; kappa_rrRepresenting the rear right wheel slip ratio; omega_flRepresenting the front left wheel turning angular velocity; omega_frRepresenting the front right wheel turning angular velocity; omega_rlRepresenting the rotational angular velocity of the rear left wheel; omega_rrRepresenting the rear right wheel turning angular velocity; r represents a vehicle rolling radius; v. of_xRepresenting a vehicle longitudinal speed; v. of_yRepresenting a vehicle lateral speed; t is t_wRepresenting a wheel track; delta_flIndicating a front left wheel steering angle of the vehicle; delta_frRepresenting the front right wheel angle of the vehicle; l_fRepresenting the center of mass of the vehicle toThe distance of the front axle;representing yaw rate at the center of mass of the vehicle;

19) during the driving process of the intelligent electric automobile, the corresponding tire slip angle is as follows:

in the formula, alpha_flRepresenting a front left wheel tire sidewall deflection angle; alpha is alpha_frRepresenting a front right wheel tire sidewall deviation angle; alpha is alpha_rlIndicating a rear left wheel tire slip angle; alpha is alpha_rrRepresenting the sidewall deflection angle of the rear right wheel tire;representing yaw rate at the center of mass of the vehicle; l_fRepresenting the vehicle center-of-mass to front axle distance; l_rRepresenting the vehicle center-of-mass to rear axle distance; delta_flIndicating a front left wheel steering angle of the vehicle; delta_frRepresenting the front right wheel angle of the vehicle; beta represents the vehicle centroid slip angle; v. of_xRepresenting a vehicle longitudinal speed;

the specific method of the second step is as follows:

21) converting the continuous vehicle dynamics space equation (8) into a discrete system state space equation, namely:

wherein, X (k) represents a state variable of the discrete system at the k-th time; u (k) represents the input of the discrete system at time k; x (k +1) represents a state variable of the discrete system at the k +1 th moment; phi_kA state variable matrix representing the discrete system at the kth time; b is_kAn input matrix representing the discrete system at time k; y (k) represents the output of the discrete system at the k-th time; h_kAn output matrix representing the discrete system at time k; w (k) represents the excitation noise of the discrete system at the k-th moment; v (k) represents the k-th discrete systemThe observation noise of (2);

22) assuming that excitation noise w (k) and observation noise v (k) of the discrete system are uncorrelated white noise with a mean value of zero and variances of Q and R, respectively, the initial state X (0) of the discrete system is uncorrelated with the excitation noise w (k) and the observation noise v (k); then the one-step prediction of kalman filtering is:

in the formula (I), the compound is shown in the specification,a value representing the prediction of the state variable of the discrete system at the k +1 moment from the state variable of the discrete system at the k-th moment;a discrete system variable representing a time of k; phi_kA state variable matrix representing the discrete system at the kth time; b is_kAn input matrix representing the discrete system at time k; u (k) represents the input of the discrete system at time k;

23) the discrete system state update matrix is:

in the formula (I), the compound is shown in the specification,a value representing the prediction of the state variable of the discrete system at the k +1 moment from the state variable of the discrete system at the k-th moment; k (K +1) represents a Kalman filtering gain matrix at the K +1 th moment; y (k +1) represents the output of the discrete system at the k +1 th moment; h_kAn output matrix representing the discrete system at time k;representing the corrected estimated value of Kalman filtering at the k +1 th moment;

24) the kalman filter gain matrix is expressed as:

in the formula, K (K +1) represents a Kalman filtering gain matrix at the K +1 th moment; p (k +1| k) represents a prediction covariance matrix for time k +1 from the error covariance and state vector at time k; h_kAn output matrix representing the discrete system at time k; r represents the variance of the observed noise v (k);

25) the one-step prediction covariance matrix is:

in the formula, P (k +1| k) represents a prediction covariance matrix for the k +1 time point from the error covariance and state vector at the k time point; phi_kA state variable matrix representing the discrete system at the kth time; p (k | k) represents the covariance matrix of the discrete system at the k-th time; q represents the variance of the excitation noise w (k);

26) introducing a forgetting factor into the one-step prediction covariance matrix for correction, namely:

in the formula, P (k +1| k) represents a prediction covariance matrix for the k +1 time point from the error covariance and state vector at the k time point; phi_kA state variable matrix representing the discrete system at the kth time; p (k | k) represents the covariance matrix of the discrete system at the k-th time; q represents the variance of the excitation noise w (k); s represents a forgetting factor;

the covariance matrix update equation is:

P(k+1|k+1)＝(I-K(k+1)H_k)P(k+1|k) (24)

in the formula, K (K +1) represents a Kalman filtering gain matrix at the K +1 th moment; h_kAn output matrix representing the discrete system at time k; p (k +1 $)k) A prediction covariance matrix representing a prediction covariance matrix for the k +1 time based on the error covariance and the state vector at the k time; p (k +1| k +1) is the corrected covariance matrix; i represents an identity matrix;

27) through the iteration of the formulas (19) to (24), the state variable of the discrete system is obtained through estimationLongitudinal and lateral forces of the tire;

wherein, F_xflRepresenting a front left wheel longitudinal force; f_xfrRepresenting the front right wheel longitudinal force; f_xrlRepresenting a rear left wheel longitudinal force; f_xrrRepresenting the rear right wheel longitudinal force; f_yf＝(F_yfl+F_yfr) Representing the total lateral force of the front wheel; f_yr＝(F_yrl+F_yrr) Representing the total lateral force of the rear wheel; f_yflRepresenting a front left wheel lateral force; f_yfrRepresenting front right wheel side forces; f_yrlRepresenting rear left wheel side forces; f_yrrRepresenting the rear right wheel lateral force; omega_flRepresenting the front left wheel turning angular velocity; omega_frRepresenting the front right wheel turning angular velocity; omega_rlRepresenting the rotational angular velocity of the rear left wheel; omega_rrRepresenting the rear right-wheel turning angular velocity,representing yaw rate at the center of mass of the vehicle;

the concrete method of the third step is as follows:

31) the brush model is rewritten, namely:

y(k)＝f(k,θ(k)) (25)

wherein y (k) ═ F_x,F_y]Represents the tire force at the k-th time; f_xRepresenting the longitudinal reaction force of the wheel to the ground; f_yIndicating the lateral reaction force of the wheel to the ground; f (k, θ (k)) represents the brush tire model at the k-th time; θ (k) ═ C_x,C_α,μ]^TA state vector representing the brush tire model at the k-th time; c_xRepresents the longitudinal stiffness of the tire; c_αRepresents the lateral stiffness of the tire; mu represents the road surface adhesion coefficient；

32) And (5) performing first-order Taylor expansion on the y (k), and neglecting high-order terms to obtain:

y(k)≈F(k)(θ(k)-θ(k-1))+f(θ(k-1),k-1) (26)

wherein y (k) represents a tire force at the k-th time; theta (k-1) is a state vector of the brush tire model at the k-1 moment; theta (k) is a state vector of the brush tire model at the kth moment; f (theta (k-1), k-1) represents the brush tire model at the k-1 moment; f (k) represents the transpose of the Jacobian matrix of time k (y) (k) to θ (k), and includes:

wherein F (k) represents a transpose of y (k) to a Jacobian matrix of θ (k); theta (k) is a state vector of the brush tire model at the kth moment; f (k, θ) represents a brush tire model; θ represents a state vector of the brush tire model; theta (k-1) is a state vector of the brush tire model at the k-1 moment;

let z (k) y (k) -f (θ (k-1), k-1) + f (k) θ (k-1), then:

z(k)≈F(k)θ(k) (28)

wherein f (k) represents a transpose of a jacobian matrix of θ (k) to the k-th time y (k); y (k) represents the tire force at time k; θ (k) a state vector of the brush tire model at the kth time; z (k) is the measurable tire force matrix at time k;

33) estimating the road adhesion coefficient by a least square method, and setting a least square method cost function as follows:

in the formula (I), the compound is shown in the specification,representing a recursive least squares cost function based on a brush tire model; Λ represents a forgetting factor matrix of a least square method; z (i) represents the measurable tire force matrix at time i; f (i) denotes the followingi time y (i) transpose of the jacobian matrix to θ (i); theta (i) is a state vector of the brush tire model at the ith moment;a state vector representing the brush tire model estimated at the ith time;

34) to minimize the cost function, the recursive least squares method based on the brush tire model is:

L(k)＝P(k-1)F^T(k)(I+F(k)P(k-1)F^T(k))^-1 (31)

P(k)＝Λ^-1(I-L(k)F(k))P(k-1)Λ^-1 (32)

in the formula (I), the compound is shown in the specification,a state vector representing the brush tire model estimated at the k-th time;representing the state vector of the brush tire model estimated at the k-1 time; z (k) is the measurable tire force matrix at time k; f (k-1) represents the transpose of the Jacobian matrix of y (k-1) to theta (k-1) at the k-1 th time; y (k-1) represents the tire force at the k-1 moment, theta (k-1) the state vector of the brush tire model at the k-1 moment, and L (k) represents the recursion minimum dyadic gain matrix based on the brush model at the k moment; f (k) denotes the transpose of the jacobian matrix at time k (y) (k) to θ (k); y (k) represents the tire force at time k; p (k) represents a least square method updating matrix based on the brush model at the k-th moment; p (k-1) represents a least square method updating matrix based on a brush model at the k-1 moment; Λ represents a forgetting factor matrix of a least square method, and I represents an identity matrix;

35) estimating to obtain an estimated state vector of the brush tire model through iteration of (30) - (32)Road surface adhesion coefficient of (1); wherein the content of the first and second substances,representing the longitudinal stiffness of the tyre estimated on the basis of the brush model,representing the lateral stiffness of the tyre estimated on the basis of the brush model,representing the road adhesion coefficient estimated based on the brush model.

The concrete method of the fourth step is as follows:

41) when the slip ratio is small, the adhesion coefficient μ and the slip ratio κ are approximately in a direct proportional relationship, that is:

in the formula, κ^-1(k) Represents the reciprocal of the slip ratio of the tire at the k-th time; f_z(k) Indicating that the wheel receives the vertical reaction force of the ground at the k-th moment; f_x(k) Indicating that the wheel receives the longitudinal reaction force of the ground at the k-th moment; mu.s_s(k) Representing the real road adhesion coefficient used for the slope method at the kth moment;

42) the least square method cost function based on the slope method is set as follows:

in the formula (I), the compound is shown in the specification,representing a recursive least square method cost function based on a slope method; Λ represents a forgetting factor matrix of a least square method; kappa^-1(i) Represents the reciprocal of the slip ratio of the tire at the ith time; f_z(i) Indicating the ith timeVertical reaction of the wheels to the ground, F_x(i) Indicating that the wheel is subjected to a longitudinal reaction force from the ground at time i,a road surface adhesion coefficient estimated by a slope method at the ith moment;

43) in order to minimize the cost function, a recursive least square method based on a slope method is designed as follows:

in the formula (I), the compound is shown in the specification,representing the road adhesion coefficient estimated by the slope method at the k-th moment;representing the road adhesion coefficient estimated by the slope method at the k-1 th moment; kappa^-1(k) Represents the reciprocal of the slip ratio of the tire at the k-th time; f_z(k) Indicating that the wheel receives the vertical reaction force of the ground at the k-th moment; f_x(k) Indicating that the wheel receives the longitudinal reaction force of the ground at the k-th moment; l is_s(k) Representing a recursion minimum dyadic gain matrix based on a slope method at the kth moment; p_s(k) A least square method updating matrix which represents the kth moment and is based on a slope method; p_s(k-1) updating the matrix by a least square method based on a slope method at the k-1 moment; Λ represents a forgetting factor matrix of a least square method; i represents an identity matrix;

44) and (5) iterating through formulas (35) to (37) to estimate and obtain the road surface estimated by the slope methodCoefficient of adhesion

Finally, the corrected road adhesion coefficient estimation result is expressed as:

in the formula (I), the compound is shown in the specification,representing the corrected road adhesion coefficient estimation result; κ represents the tire slip ratio;representing a road adhesion coefficient estimated based on a slope method;representing the road adhesion coefficient estimated based on the brush model.

The invention has the beneficial effects that:

1) the built vehicle dynamics model completely considers the problem of nonlinear dynamics in the vehicle driving process, and fully represents the key behavior characteristics of the intelligent electric vehicle in the structured road driving;

2) the tire force observer designed based on the Kalman filtering algorithm effectively reduces the uncertainty of the tire force observation value and provides accurate and stable tire force information for the estimation of the road adhesion coefficient;

3) the method can accurately estimate the road adhesion coefficient when the vehicle slip rate is higher based on the least square method and the brush model;

4) the method can reasonably correct the estimated road adhesion coefficient result when the vehicle slip rate is low based on the least square method and the slope method.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.

FIG. 1 is an algorithmic diagram of the present invention;

FIG. 2 is a schematic diagram of a three-degree-of-freedom vehicle dynamics model;

FIG. 3 is a schematic view of wheel stress;

FIG. 4 is a low adhesion road tire force observer results plot;

FIG. 5 is a diagram showing a result of estimating the road surface adhesion coefficient under a low-adhesion road surface;

FIG. 6 is a high adhesion road tire force observer results plot;

fig. 7 is a diagram showing the result of estimating the road surface adhesion coefficient under a high-adhesion road surface.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.

Referring to fig. 1, a vehicle road adhesion coefficient estimation method based on kalman filtering and least square method includes the following steps:

step one, referring to fig. 2, in order to facilitate analysis, the pitching and rolling characteristics of the vehicle are ignored, the stress of the left wheel and the stress of the right wheel of the vehicle are assumed to be symmetrical, and the state parameters of the vehicle are solved based on a vehicle dynamic model;

the state parameters comprise vehicle speed, brake pressure, front wheel rotation angle, tire slip rate, slip angle and wheel vertical force; the vehicle speed, the brake pressure and the front wheel rotation angle are obtained by sensors; and the tire slip rate, the slip angle and the wheel vertical force are calculated by a vehicle dynamic model.

The specific method for calculating the tire slip rate, the slip angle and the wheel vertical force by the vehicle dynamics model is as follows:

11) establishing a three-degree-of-freedom model containing longitudinal, lateral and yaw motions of the vehicle, and obtaining a vehicle dynamic model equation as follows:

ma_x＝[cosδcosδ1 1 -sinδ0]F_tire (1)

ma_y＝[sinδsinδ0 0 cosδ1]F_tire (2)

in the formula, F_tire＝[F_xfl F_xfr F_xrl F_xrr F_yf F_yr]^TRepresenting a set of tire forces; f_xflRepresenting a front left wheel longitudinal force; f_xfrRepresenting the front right wheel longitudinal force; f_xrlRepresenting a rear left wheel longitudinal force; f_xrrRepresenting the rear right wheel longitudinal force; f_yf＝(F_yfl+F_yfr) Representing the total lateral force of the front wheel; f_yr＝(F_yrl+F_yrr) Representing the total lateral force of the rear wheel; f_yflRepresenting a front left wheel lateral force; f_yfrRepresenting front right wheel side forces; f_yrlRepresenting rear left wheel side forces; f_yrrRepresenting the rear right wheel lateral force; m represents the vehicle mass, a_xRepresents a vehicle longitudinal acceleration; a is_yRepresents vehicle lateral acceleration; δ represents a vehicle front wheel steering angle; i is_zRepresenting the moment of inertia of the vehicle about the z-axis; l_fRepresenting the vehicle center-of-mass to front axle distance; l_rRepresenting the vehicle center-of-mass to rear axle distance; t is t_wRepresenting a wheel track;representing yaw angular acceleration at the vehicle's center of mass;

12) the stress condition of the wheels on the ground during the running of the vehicle is shown in fig. 3. The dynamic equation of the wheel obtained according to the dynamic balance relation is as follows:

wherein i ═ fl, fr, rl, rr denote the corresponding front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; i is_wiRepresenting the inertial mass of rotation of the tyre;representing the wheel turning angular acceleration; t is_diRepresenting the driving torque of the wheel; t is_biRepresenting the driving torque and the braking torque of the wheels; f_xiRepresenting the longitudinal reaction force of the wheel to the ground; r represents a vehicle rolling radius; t is_Fi＝(a+bv_i)F_zir represents the rolling resistance moment to which the wheel is subjected; a and b represent rolling resistance coefficient parameter values; v. of_iRepresenting the longitudinal speed at the wheel center; f_ziIndicating the vertical reaction force of the wheel to the ground;

13) the four-wheel driving torque of the intelligent electric vehicle can be expressed as:

in the formula, T_dflRepresenting the driving torque of the front left wheel; t is_dfrRepresenting the driving torque of the front right wheel; t is_drlRepresenting the driving torque of the rear left wheel; t is_drrRepresenting the driving torque of the rear right wheel; t is_eThe output torque of the power motor of the whole vehicle is represented; i.e. i₀Representing a gear ratio of the driveline; eta_tRepresenting the transmission efficiency of the transmission system;

14) the braking torque developed by the braking force during braking of the vehicle is expressed as:

T_bi＝k_biP_wi (6)

wherein i ═ fl, fr, rl, rr denote the corresponding front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; t is_biRepresenting the braking torque of the wheel; k is a radical of_biRepresenting a braking effectiveness factor; p_wiRepresenting a wheel cylinder brake pressure;

15) the vertical reaction force of the wheel on the ground and the inertia force formed by the acceleration and deceleration of the vehicle have a relationship, and are expressed as follows:

in the formula, F_zflIndicating that the front left wheel is subjected to a vertical reaction force of the ground; f_zfrIndicating the vertical reaction force of the front right wheel to the ground; f_zrlIndicating that the rear left wheel is subjected to a vertical reaction force of the ground; f_zrrIndicating the vertical reaction force of the rear right wheel to the ground; m represents the mass of the whole vehicle; a is_xRepresents a vehicle longitudinal acceleration; a is_yRepresents vehicle lateral acceleration; l_fRepresenting the vehicle center-of-mass to front axle distance; l_rRepresenting the vehicle center-of-mass to rear axle distance; h is_gRepresenting the centroid height; t is t_wRepresenting a wheel track;

16) selecting front left wheel longitudinal force, front right wheel longitudinal force, rear left wheel longitudinal force, rear right wheel longitudinal force, front wheel total lateral force, rear wheel total lateral force, front left wheel rotation angular velocity, front right wheel rotation angular velocity, rear left wheel rotation angular velocity, rear right wheel rotation angular velocity and yaw angular velocity at the vehicle mass center as system state variables, namely front left wheel longitudinal force, front right wheel longitudinal force, rear left wheel longitudinal force, rear right wheel longitudinal force, rear left wheel total lateral force, rear left wheel rotation angular velocity, rear right wheel rotation angular velocity and yaw angular velocity at the vehicle mass centerThe longitudinal acceleration of the vehicle, the lateral acceleration of the vehicle, the rotating angular velocity of the front left wheel, the rotating angular velocity of the front right wheel, the rotating angular velocity of the rear left wheel, the rotating angular velocity of the rear right wheel and the yaw angular velocity at the mass center of the vehicle are selected as system outputs,then the vehicle dynamics space equation is obtained as:

wherein X represents a system stateA variable;a differential representing a system state variable; u represents the system input; phi represents a system state variable matrix; b represents a system input matrix; y represents the system output; h represents the system output matrix and has:

H_x＝[cosδcosδ1 1 -sinδ0],

H_y＝[sinδsinδ0 0 cosδ1],

in the formula, phi represents a system state variable matrix; b represents a system input matrix; h represents a system output matrix; r represents a vehicle rolling radius; i represents an identity matrix; t is_dflRepresenting the driving torque of the front left wheel; t is_dfrRepresenting the driving torque of the front right wheel; t is_drlRepresenting the driving torque of the rear left wheel; t is_drrRepresenting the driving torque of the rear right wheel; t is_bflRepresenting the braking torque of the front left wheel; t is_bfrRepresenting the braking torque of the front right wheel; t is_brlRepresenting the braking torque of the rear left wheel; t is_brrRepresenting the braking torque of the rear right wheel; i is_wflRepresenting the tire rotational inertial mass of the front left wheel; i is_wfrRepresenting the tire rotational inertial mass of the front right wheel; i is_wrlRepresenting the tire rotational inertial mass of the rear left wheel; i is_wrrRepresenting the tire rotational inertial mass of the rear right wheel; i is_zRepresenting the moment of inertia of the vehicle about the Z axis; h_xRepresenting a longitudinal force matrix; h_yRepresenting a lateral force matrix;representing a yaw angle matrix; l_fRepresenting the distance of the vehicle's center of mass to the front axle; l_rRepresenting the distance from the vehicle's center of mass to the rear axle; δ represents a vehicle front wheel steering angle; t is t_wRepresenting a wheel track; m represents the mass of the whole vehicle; t is_FflRepresenting the rolling resistance moment to which the front left wheel is subjected; t is_FfrRepresenting the rolling resistance moment to which the front right wheel is subjected; t is_FrlRepresenting the rolling resistance moment to which the rear left wheel is subjected; t is_FrrRepresenting the rolling resistance moment to which the rear right wheel is subjected;

17) the longitudinal and lateral forces of a vehicle tire are closely related to the road adhesion coefficient. The brush model is used to characterize the relationship between the longitudinal force of a vehicle tire and the lateral force of a vehicle tire, expressed as:

wherein i ═ fl, fr, rl, rr denote the corresponding front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively; f_xiRepresenting the longitudinal reaction force of the wheel to the ground; f_yiIndicating the lateral reaction force of the wheel to the ground; c_xiRepresents the longitudinal stiffness of the tire; c_αiRepresents the lateral stiffness of the tire; kappa_iRepresents the slip ratio of the tire; alpha is alpha_iRepresents a tire slip angle; f. of_iRepresenting a brush model stiffness coefficient; f_tiRepresenting a brush model representative force; mu.sRepresents a road surface adhesion coefficient; f_ziIndicating the vertical reaction force of the wheel to the ground;

18) calculating the slip ratio of each tire according to the wheel rotation angular velocity, the front wheel rotation angle, the vehicle speed and the vehicle structure parameters:

in the formula, κ_flRepresents the front left wheel slip ratio; kappa_frRepresenting the front right wheel slip ratio; kappa_rlRepresenting the rear left wheel slip ratio; kappa_rrRepresenting the rear right wheel slip ratio; omega_flRepresenting the front left wheel turning angular velocity; omega_frRepresenting the front right wheel turning angular velocity; omega_rlRepresenting the rotational angular velocity of the rear left wheel; omega_rrRepresenting the rear right wheel turning angular velocity; r represents a vehicle rolling radius; v. of_xRepresenting a vehicle longitudinal speed; v. of_yRepresenting a vehicle lateral speed; t is t_wRepresenting a wheel track; delta_flIndicating a front left wheel steering angle of the vehicle; delta_frRepresenting the front right wheel angle of the vehicle; l_fRepresenting the vehicle center-of-mass to front axle distance;representing yaw rate at the center of mass of the vehicle;

19) the intelligent electric automobile is at the in-process of traveling, and front wheel corner is less, corresponds the tire sideslip angle and is:

in the formula, alpha_flRepresenting a front left wheel tire sidewall deflection angle; alpha is alpha_frRepresenting a front right wheel tire sidewall deviation angle; alpha is alpha_rlIndicating a rear left wheel tire slip angle; alpha is alpha_rrRepresenting the sidewall deflection angle of the rear right wheel tire;representing yaw rate at the center of mass of the vehicle; l_fRepresenting the vehicle center-of-mass to front axle distance; l_rRepresenting the vehicle center-of-mass to rear axle distance; delta_flIndicating a front left wheel steering angle of the vehicle; delta_frRepresenting the front right wheel angle of the vehicle; beta represents the vehicle centroid slip angle; v. of_xRepresenting a vehicle longitudinal speed;

estimating tire force borne by a tire in the running process of the vehicle based on Kalman filtering; the algorithm is based on known observed values, and estimation of unknown values is achieved by minimizing mean square error of estimated values.

The specific method comprises the following steps:

21) converting the continuous vehicle dynamics space equation (8) into a discrete system state space equation, namely:

wherein, X (k) represents a state variable of the discrete system at the k-th time; u (k) represents the input of the discrete system at time k; x (k +1) represents a state variable of the discrete system at the k +1 th moment; phi_kA state variable matrix representing the discrete system at the kth time; b is_kAn input matrix representing the discrete system at time k; y (k) represents the output of the discrete system at the k-th time; h_kAn output matrix representing the discrete system at time k; w (k) represents the excitation noise of the discrete system at the k-th moment; v (k) represents the observation noise of the discrete system at the k-th moment;

22) assuming that excitation noise w (k) and observation noise v (k) of the discrete system are uncorrelated white noise with a mean value of zero and variances of Q and R, respectively, the initial state X (0) of the discrete system is uncorrelated with the excitation noise w (k) and the observation noise v (k); then the one-step prediction of kalman filtering is:

in the formula (I), the compound is shown in the specification,a value representing the prediction of the state variable of the discrete system at the k +1 moment from the state variable of the discrete system at the k-th moment;a discrete system variable representing a time of k; phi_kA state variable matrix representing the discrete system at the kth time; b is_kAn input matrix representing the discrete system at time k; u (k) represents the input of the discrete system at time k;

23) the discrete system state update matrix is:

in the formula (I), the compound is shown in the specification,a value representing the prediction of the state variable of the discrete system at the k +1 moment from the state variable of the discrete system at the k-th moment; k (K +1) represents a Kalman filtering gain matrix at the K +1 th moment; y (k +1) represents the output of the discrete system at the k +1 th moment; h_kAn output matrix representing the discrete system at time k;representing the corrected estimated value of Kalman filtering at the k +1 th moment;

24) the kalman filter gain matrix is expressed as:

in the formula, K (K +1) represents a Kalman filtering gain matrix at the K +1 th moment; p (k +1| k) represents a prediction covariance matrix for time k +1 from the error covariance and state vector at time k; h_kAn output matrix representing the discrete system at time k; r represents the variance of the observed noise v (k);

25) the one-step prediction covariance matrix is:

in the formula, P (k +1| k) represents a prediction covariance matrix for the k +1 time point from the error covariance and state vector at the k time point; phi_kA state variable matrix representing the discrete system at the kth time; p (k | k) represents the covariance matrix of the discrete system at the k-th time; q represents the variance of the excitation noise w (k);

26) introducing a forgetting factor into the one-step prediction covariance matrix for correction, namely:

in the formula, P (k +1| k) represents a prediction covariance matrix for the k +1 time point from the error covariance and state vector at the k time point; phi_kA state variable matrix representing the discrete system at the kth time; p (k | k) represents the covariance matrix of the discrete system at the k-th time; q represents the variance of the excitation noise w (k); s represents a forgetting factor;

the covariance matrix update equation is:

P(k+1|k+1)＝(I-K(k+1)H_k)P(k+1|k) (24)

in the formula, K (K +1) represents a Kalman filtering gain matrix at the K +1 th moment; h_kAn output matrix representing the discrete system at time k; p (k +1| k) represents a prediction covariance matrix for time k +1 from the error covariance and state vector at time k; p (k +1| k +1) is the corrected covariance matrix; i representsAn identity matrix;

27) through the iteration of the formulas (19) to (24), the state variable of the discrete system is obtained through estimationLongitudinal and lateral forces of the tire;

wherein, F_xflRepresenting a front left wheel longitudinal force; f_xfrRepresenting the front right wheel longitudinal force; f_xrlRepresenting a rear left wheel longitudinal force; f_xrrRepresenting the rear right wheel longitudinal force; f_yf＝(F_yfl+F_yfr) Representing the total lateral force of the front wheel; f_yr＝(F_yrl+F_yrr) Representing the total lateral force of the rear wheel; f_yflRepresenting a front left wheel lateral force; f_yfrRepresenting front right wheel side forces; f_yflRepresenting rear left wheel side forces; f_yrrRepresenting the rear right wheel lateral force; omega_flRepresenting the front left wheel turning angular velocity; omega_frRepresenting the front right wheel turning angular velocity; omega_rlRepresenting the rotational angular velocity of the rear left wheel; omega_rrRepresenting the rear right-wheel turning angular velocity,representing the yaw rate at the center of mass of the vehicle.

Estimating the road adhesion coefficient by adopting a least square method;

the specific method comprises the following steps:

31) the brush model is rewritten, namely:

y(k)＝f(k,θ(k)) (25)

wherein y (k) ═ F_x,F_y]Represents the tire force at the k-th time; f_xRepresenting the longitudinal reaction force of the wheel to the ground; f_yIndicating the lateral reaction force of the wheel to the ground; f (k, θ (k)) represents the brush tire model at the k-th time; θ (k) ═ C_x,C_α,μ]^TA state vector representing the brush tire model at the k-th time; c_xRepresents the longitudinal stiffness of the tire; c_αRepresents the lateral stiffness of the tire; μ represents a road surface adhesion coefficient;

32) and (5) performing first-order Taylor expansion on the y (k), and neglecting high-order terms to obtain:

y(k)≈F(k)(θ(k)-θ(k-1))+f(θ(k-1),k-1) (26)

wherein y (k) represents a tire force at the k-th time; theta (k-1) is a state vector of the brush tire model at the k-1 moment; theta (k) is a state vector of the brush tire model at the kth moment; f (theta (k-1), k-1) represents the brush tire model at the k-1 moment; f (k) represents the transpose of the Jacobian matrix of time k (y) (k) to θ (k), and includes:

wherein F (k) represents a transpose of y (k) to a Jacobian matrix of θ (k); theta (k) is a state vector of the brush tire model at the kth moment; f (k, θ) represents a brush tire model; θ represents a state vector of the brush tire model; theta (k-1) is a state vector of the brush tire model at the k-1 moment;

let z (k) y (k) -f (θ (k-1), k-1) + f (k) θ (k-1), then:

z(k)≈F(k)θ(k) (28)

wherein f (k) represents a transpose of a jacobian matrix of θ (k) to the k-th time y (k); y (k) represents the tire force at time k; θ (k) a state vector of the brush tire model at the kth time; z (k) is the measurable tire force matrix at time k;

33) estimating the road adhesion coefficient by a least square method, and setting a least square method cost function as follows:

in the formula (I), the compound is shown in the specification,representing a recursive least squares cost function based on a brush tire model; Λ represents a forgetting factor matrix of a least square method; z (i) represents the measurable tire force matrix at time i; f (i) represents the transpose of the jacobian matrix at the i-th time y (i) to θ (i); theta (i) isi, state vectors of the brush tire model at moment;a state vector representing the brush tire model estimated at the ith time;

34) to minimize the cost function, the recursive least squares method based on the brush tire model is:

L(k)＝P(k-1)F^T(k)(I+F(k)P(k-1)F^T(k))^-1 (31)

P(k)＝Λ^-1(I-L(k)F(k))P(k-1)Λ^-1 (32)

in the formula (I), the compound is shown in the specification,a state vector representing the brush tire model estimated at the k-th time;representing the state vector of the brush tire model estimated at the k-1 time; z (k) is the measurable tire force matrix at time k; f (k-1) represents the transpose of the Jacobian matrix of y (k-1) to theta (k-1) at the k-1 th time; y (k-1) represents the tire force at the k-1 moment, theta (k-1) the state vector of the brush tire model at the k-1 moment, and L (k) represents the recursion minimum dyadic gain matrix based on the brush model at the k moment; f (k) denotes the transpose of the jacobian matrix at time k (y) (k) to θ (k); y (k) represents the tire force at time k; p (k) represents a least square method updating matrix based on the brush model at the k-th moment; p (k-1) represents a least square method updating matrix based on a brush model at the k-1 moment; Λ represents a forgetting factor matrix of a least square method, and I represents an identity matrix;represents XX;

35) estimating to obtain an estimated brush tire model by (30) - (32) iterationState vectorRoad surface adhesion coefficient of (1); wherein the content of the first and second substances,representing the longitudinal stiffness of the tyre estimated on the basis of the brush model,representing the lateral stiffness of the tyre estimated on the basis of the brush model,representing the road adhesion coefficient estimated based on the brush model.

And step four, correcting the road adhesion coefficient estimation result under the low slip ratio in the step three by a slope method.

The specific method comprises the following steps:

41) when the slip ratio is small, the adhesion coefficient μ and the slip ratio κ are approximately in a direct proportional relationship, that is:

in the formula, κ^-1(k) Represents the reciprocal of the slip ratio of the tire at the k-th time; f_z(k) Indicating that the wheel receives the vertical reaction force of the ground at the k-th moment; f_x(k) Indicating that the wheel receives the longitudinal reaction force of the ground at the k-th moment; mu.s_s(k) Representing the real road adhesion coefficient used for the slope method at the kth moment;

42) the least square method cost function based on the slope method is set as follows:

in the formula (I), the compound is shown in the specification,representing a recursive least square method cost function based on a slope method; Λ represents a forgetting factor matrix of a least square method; kappa^-1(i) Represents the reciprocal of the slip ratio of the tire at the ith time; f_z(i) Indicating the vertical reaction of the wheel to the ground at time i, F_x(i) Indicating that the wheel is subjected to a longitudinal reaction force from the ground at time i,a road surface adhesion coefficient estimated by a slope method at the ith moment;

43) in order to minimize the cost function, a recursive least square method based on a slope method is designed as follows:

in the formula (I), the compound is shown in the specification,representing the road adhesion coefficient estimated by the slope method at the k-th moment;representing the road adhesion coefficient estimated by the slope method at the k-1 th moment; kappa^-1(k) Represents the reciprocal of the slip ratio of the tire at the k-th time; f_z(k) Indicating that the wheel receives the vertical reaction force of the ground at the k-th moment; f_x(k) Indicating that the wheel receives the longitudinal reaction force of the ground at the k-th moment; l is_s(k) Representing a recursion minimum dyadic gain matrix based on a slope method at the kth moment; p_s(k) A least square method updating matrix which represents the kth moment and is based on a slope method; p_s(k-1) denotes the slope-based time at the k-1 th timeUpdating a matrix by a least square method of the method; Λ represents a forgetting factor matrix of a least square method; i represents an identity matrix;

44) and (5) iterating through formulas (35) - (37) to estimate and obtain the road adhesion coefficient estimated by the slope method

Finally, the corrected road adhesion coefficient estimation result is expressed as:

in the formula (I), the compound is shown in the specification,representing the corrected road adhesion coefficient estimation result; κ represents the tire slip ratio;representing a road adhesion coefficient estimated based on a slope method;representing the road adhesion coefficient estimated based on the brush model.

Examples

A joint simulation platform is built based on MATLAB/Simulink and vehicle dynamics software CarSim and used for testing the trajectory tracking controller of the application.

The first group of working conditions are braking working conditions under a low-adhesion road surface, a vehicle braking system starts to intervene when 0s is set, the braking pressure is 2Mpa, the road surface adhesion coefficient is 0.3, and the initial vehicle speed of the vehicle is 100 km/h. The experimental results are shown in fig. 4 and 5.

As can be seen from the figure, the tire force observer is established to have high estimation accuracy of the tire force and the road surface adhesion coefficient on a low-adhesion road surface. The road surface adhesion coefficient estimation algorithm can converge to the estimated road surface adhesion coefficient, which is about 0.2816, quickly. Compared with the actual road surface adhesion coefficient of the road, the estimated relative error is 6.13%, and the use requirement of actual vehicle motion control is met.

The second group of working conditions are braking working conditions under a high-adhesion road surface, the adhesion coefficient of the road surface is set to be 0.7, the braking pressure of the vehicle is set to be 2MPa, the braking starting time is 0s, and the initial vehicle speed of the vehicle is 100 km/h. The experimental results are shown in fig. 6 and 7.

It can be seen from the figure that the maximum value of the error of the tire longitudinal force estimation after the convergence of the measuring device is 202.76N, and the estimated relative error is 6.31%. The estimated value of the road adhesion coefficient is 0.7152, the estimated relative error is 2.17%, and meanwhile, the RLS algorithm can be converged within 0.4s, which shows that the recognition algorithm has good response speed under the high-adhesion road surface.