Method for estimating road adhesion coefficient based on Kalman filtering

Abstract

The invention relates to the technical field of automobiles, in particular to a method for estimating a road adhesion coefficient based on Kalman filtering, which comprises the following steps: firstly, establishing a vehicle seven-degree-of-freedom model, and obtaining a calculation mode of four tire parameters; secondly, a Dugoff tire model is established, and the normalized tire force of a tire is obtained; and finally, estimating the road adhesion coefficient by using an unscented Kalman filtering algorithm. According to the method, errors caused by linearization of a Kalman filtering algorithm are solved through an unscented Kalman filtering method, state variable estimation of a nonlinear system is achieved through unscented transformation (UT) on the basis of Kalman filtering, neglecting of high-order terms caused by linearization is avoided, and estimation accuracy is improved.

Description

Technical Field

[0001] The present invention relates to the field of automobile technology, and in particular to a method for estimating a road adhesion coefficient based on Kalman filtering. Background Art

[0002] As an important variable in the vehicle's lower-level control, the accurate estimation of the road adhesion coefficient is directly related to the smooth operation of the control system. However, since some state parameters cannot be obtained through direct measurement or the measurement method is too expensive, it is necessary to obtain the parameter value indirectly through estimation.

[0003] In recent years, Kalman filter algorithm has been widely studied in the estimation of road adhesion coefficient. This type of method requires the construction of an appropriate vehicle dynamics model and the establishment of a corresponding state equation. Its advantage is that the road adhesion coefficient can be accurately estimated by only observing the relevant state parameters. At the same time, the road adhesion coefficient is updated in real time according to the observation values ​​continuously obtained during the driving process of the car to obtain the estimated result, thus achieving the purpose of real-time estimation.

[0004] However, the Kalman filter algorithm has many limitations for a random system. The state model and measurement model are linear models, and it is difficult to achieve the optimal estimation effect in nonlinear scenarios; only the mean and covariance of a distribution are given; the system obeys a Gaussian distribution, and it is still a Gaussian distribution after linear operations. Due to the constraints listed, Kalman filtering is usually used in approximate linear systems. Generally, the nonlinear system is approximately linearized and then the linear system state is estimated. However, for strong nonlinear systems, the Kalman filter's estimate of the system state quantity will seriously deviate from the true value. Summary of the invention

[0005] The purpose of the present invention is to provide a method for estimating road adhesion coefficient based on Kalman filtering, aiming to solve the cost increase caused by the need for sensors in traditional methods and the error caused by linearization of the Kalman filtering algorithm, and to improve the accuracy of estimation.

[0006] To achieve the above object, the present invention provides a method for estimating a road adhesion coefficient based on Kalman filtering, comprising the following steps:

[0007] Step 1: Establish a seven-degree-of-freedom model of the vehicle, obtain the longitudinal, lateral and yaw motion equations of the vehicle, and the calculation formulas of the vertical load, sideslip angle and slip rate of the four wheels;

[0008] Step 2: Establish the Dugoff tire model and obtain the normalized tire force;

[0009] Step 3: Estimate the road adhesion coefficient by combining the vehicle seven-degree-of-freedom model and the unscented Kalman filter algorithm.

[0010] Optionally, the vehicle longitudinal motion equation in step 1 is formulated as follows:

[0011]

[0012] The equation for the lateral motion of the vehicle is given by:

[0013]

[0014] The equation of motion for the vehicle's pitch and roll is as follows:

[0015]

[0016] The subscripts fl, fr, rl, and rr in the formula represent the front left wheel, front right wheel, rear left wheel, and rear right wheel of the car respectively. x is the longitudinal speed, v y is the lateral speed, F x_ij is the wheel longitudinal force, F y_ij is the wheel lateral force, I z is the moment of inertia about the Z axis, δ l is the left front wheel turning angle, δ r is the right front wheel turning angle, ω z is the yaw angle, B f is the front wheel track, B r is the rear wheel track, L f is the distance from the front axle to the center of mass, L r is the distance from the rear axle to the center of mass.

[0017] Optionally, the expression for the vertical wheel load in step 1 is as follows:

[0018]

[0019] Where F z_fl , F z_rl 、F z_rr are the longitudinal forces of the front left wheel, front right wheel, rear left wheel, and rear right wheel, m w is the tire weight, m b is the vehicle weight, L is the wheelbase, h is g is the height of the vehicle's center of mass, a x is the longitudinal acceleration of the vehicle, a y is the lateral acceleration of the vehicle.

[0020] Optionally, the tire slip angle is calculated as follows:

[0021]

[0022] Where α fl , α fr , αrl , α rr are the tire slip angles of the front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively, v x_fl 、v x_fr 、v x_rl 、v x_rr are the longitudinal velocities of the front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively, v y_fl 、v y_fr 、v y_rl 、v y_rr are the lateral speeds of the front left wheel, front right wheel, rear left wheel, and rear right wheel respectively;

[0023] The calculation formula of tire slip rate is as follows:

[0024]

[0025] Where λ ij is the tire slip rate, ω w_ij is the rotation angle radius, R w is the wheel rolling radius, v wx_ij is the longitudinal velocity of each wheel center.

[0026] Optionally, in the Dugoff tire model,

[0027]

[0028] Where μ represents the road adhesion coefficient, F z is the vertical load, λ is the slip rate, α is the tire side slip angle, and ε is the speed influence factor. x is the longitudinal stiffness of each tire, C y is the cornering stiffness of each tire.

[0029] Optionally, the formula for tire normalization in step 2 is as follows:

[0030]

[0031] but:

[0032]

[0033] In the formula, Represents the normalized longitudinal force and normalized lateral force of the tire.

[0034] Optionally, in step 3, set the state variable x(t) = [μ fl μ fr μ rl μ rr ] T , measured variable y(t) = [a x a y r]T , the control quantity u(t) = [δ]; the corresponding prediction equation is

[0035]

[0036] The observation equation is

[0037]

[0038] in,

[0039]

[0040] The present invention provides a method for estimating a road adhesion coefficient based on Kalman filtering. First, a vehicle seven-degree-of-freedom model is established to obtain the calculation method of four tire parameters; secondly, a Dugoff tire model is established to obtain the normalized tire force of the tire; finally, an unscented Kalman filtering algorithm is used to estimate the road adhesion coefficient. The present invention specifically solves the error caused by linearization of the Kalman filtering algorithm through the method of unscented Kalman filtering. On the basis of Kalman filtering, an unscented transform (UT) is used to realize the state variable estimation of the nonlinear system. The high-order terms will not be ignored due to linearization, thereby improving the accuracy of the estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0042] Figure 1 The present invention is a schematic flow chart of the steps of a method for estimating a road adhesion coefficient based on Kalman filtering.

[0043] Figure 2 It is a schematic diagram of the motion and force relationship of the Dugoff tire model.

[0044] Figure 3 It is a schematic diagram of the parameter processing process in each module of the present invention. DETAILED DESCRIPTION

[0045] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0046] See also Figure 1 The present invention provides a method for estimating a road adhesion coefficient based on Kalman filtering, comprising the following steps:

[0047] S1: Establish a seven-degree-of-freedom model of the vehicle, obtain the longitudinal, lateral and yaw motion equations of the vehicle, and the calculation formulas of the vertical load, sideslip angle and slip rate of the four wheels;

[0048] S2: Establish the Dugoff tire model and obtain the normalized tire force;

[0049] S3: Estimation of road adhesion coefficient by combining the vehicle seven-degree-of-freedom model and the unscented Kalman filter algorithm.

[0050] The following is a further explanation based on the specific implementation steps and the referenced algorithm:

[0051] In step S1, a seven-degree-of-freedom model of the vehicle is first established to obtain the longitudinal, lateral and yaw motion equations of the vehicle, as well as calculation formulas for the vertical loads, sideslip angles and slip rates of the four wheels.

[0052] The longitudinal motion equation of the vehicle is:

[0053]

[0054] The equation of lateral motion of the vehicle is:

[0055]

[0056] The vehicle's pitch and roll motion equations are:

[0057]

[0058] The subscripts fl, fr, rl, and rr in the letters represent the front left wheel, front right wheel, rear left wheel, and rear right wheel of the car respectively. The specific meanings of each symbol are shown in the table:

[0059] symbol unit definition symbol unit definition <![CDATA[v x ]]> km / h Longitudinal speed <![CDATA[I z ]]> <![CDATA[kg·m 2 ]]> Moment of inertia about the Z axis <![CDATA[v y ]]> km / h Lateral speed <![CDATA[ω z ]]> rad Yaw angle <![CDATA[F x_ij ]]> N Wheel longitudinal force <![CDATA[B f ]]> m Front wheel track <![CDATA[F y_ij ]]> N Wheel lateral force <![CDATA[B r ]]> m Rear wheel track <![CDATA[δ l ]]> rad Right front wheel angle <![CDATA[L f ]]> m Distance from front axle to center of mass <![CDATA[δ r ]]> rad Right front wheel angle <![CDATA[L r ]]> m Distance from rear axle to center of mass

[0060] Calculation of tire vertical load:

[0061]

[0062] Where F z_fl , F z_rl 、F z_rr are the longitudinal forces of the front left wheel, front right wheel, rear left wheel, and rear right wheel, m w is the tire weight, m b is the vehicle weight, L is the wheelbase, h is g is the height of the vehicle's center of mass, a x is the longitudinal acceleration of the vehicle, ay is the lateral acceleration of the vehicle.

[0063] Calculation of tire slip angle:

[0064]

[0065] Where α fl , α fr , α rl , α rr are the tire slip angles of the front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively, v x_fl 、v x_fr 、v x_rl 、v x_rr are the longitudinal velocities of the front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively, v y_fl 、v y_fr 、v y_rl 、v y_rr are the lateral speeds of the front left wheel, front right wheel, rear left wheel, and rear right wheel respectively;

[0066] Calculation of tire slip rate:

[0067]

[0068] Where λ ij is the tire slip rate, v w_ij is the rotation angle radius, R w is the wheel rolling radius, v wx_ij is the longitudinal velocity of each wheel center.

[0069] Step S2: Establish the Dugoff tire model (tire force and motion coordinate system as Figure 2 shown):

[0070]

[0071] In order to facilitate the design of subsequent estimation algorithms, the tire force needs to be normalized:

[0072]

[0073] but:

[0074]

[0075] According to the calculation formulas of tire vertical load, tire sideslip angle and slip rate in the vehicle seven-degree-of-freedom model, the calculated results are substituted into the Dugoff tire model to obtain the normalized tire longitudinal force and lateral force.

[0076] Step S3: Estimate the road adhesion coefficient by combining the vehicle seven-degree-of-freedom model and the unscented Kalman filter algorithm.

[0077] Set the state variable x(t) = [μ fl μ fr μ rl μ rr ] T , measured variable y(t) = [a x a y r] T , control quantity u(t)=[δ].

[0078] The prediction equation is

[0079]

[0080] Observation equation:

[0081]

[0082] in:

[0083]

[0084] Through iteration, the road adhesion coefficient is finally estimated. The specific parameter processing process is as follows Figure 3 shown.

[0085] Further, the unscented Kalman filter algorithm used in step S3 is described below in combination with the Kalman filter method:

[0086] Kalman Filter (KF) is a linear optimal filtering method proposed by REKalman in the 1960s. Compared with Wiener filtering, it does not require frequency domain conversion and is simpler to calculate. The basic principle of KF is:

[0087] (1) Posterior estimate based on K-1 moment To predict the system state value at time K based on modeling (A priori estimate at time K)

[0088]

[0089] (2) Error e based on K-1 moment k-1 The covariance matrix P k-1 and the covariance matrix Q of the process noise W to predict the error e at time K k The covariance matrix of (Prior of error covariance at time K)

[0090]

[0091] (3) Calculate the Kalman gain coefficient K at time K k

[0092]

[0093] (4) Use the Kalman gain to correct and update the state to obtain the posterior estimate at time K

[0094]

[0095] (5) For the next step of calculation, the optimal value at time K+1 is estimated and updated iteratively, that is, e is updated k The covariance matrix P k

[0096]

[0097] (6) Repeat the above five steps.

[0098] Unscented Kalman filtering is a filtering algorithm that combines UT changes with Kalman filtering theory. The algorithm approximates the nonlinear system infinitely through UT transformation based on the distribution of the current state variables of the system. The Sigma point set is calculated according to certain rules based on the distribution of the current state variables of the system. The Sigma point set is used to describe the probability distribution of the estimated points, and the mean and covariance of each sampling point are calculated, and the mean and covariance of this point set are kept equal to the mean and covariance of the current state. The system is not linearized and approximated, but the nonlinear system function is used for transmission. The point set is substituted into the nonlinear equation of the system to calculate the corresponding point set value. The corresponding mean and covariance values ​​are calculated from the transformed point set to obtain the posterior mean and covariance values. The estimated value and covariance of the state quantity are obtained through weighted statistical linear regression. Combined with the framework of Kalman filtering, the predicted value and measured value of the system state quantity at subsequent moments are solved. The UKF algorithm will not cause the high-order terms to be ignored due to linearization, so the estimation accuracy is high. In addition, the UKF algorithm does not need to calculate complex Jacobian matrices.

[0099] What is disclosed above is only a preferred embodiment of the present invention, and it certainly cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiment and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A method for estimating road adhesion coefficient based on Kalman filtering, characterized in that: The following steps are involved: Step 1: Establish a seven-degree-of-freedom model of the vehicle, obtain the longitudinal, lateral and yaw motion equations of the vehicle, and the calculation formulas of the vertical load, sideslip angle and slip rate of the four wheels; Step 2: Establish the Dugoff tire model and obtain the normalized tire force; Step 3: Estimate the road adhesion coefficient by combining the vehicle seven-degree-of-freedom model and the unscented Kalman filter algorithm.

2. The method for estimating road adhesion coefficient based on Kalman filtering as claimed in claim 1, characterized in that: The vehicle longitudinal motion equation in step 1 is formulated as follows: The equation for the lateral motion of the vehicle is given by: The equation of motion for the vehicle's pitch and roll is as follows: The subscripts fl, fr, rl, and rr in the formula represent the front left wheel, front right wheel, rear left wheel, and rear right wheel of the car respectively. x is the longitudinal speed, v y is the lateral speed, F x_ij is the wheel longitudinal force, F y_ij is the wheel lateral force, I z is the moment of inertia about the Z axis, δ l is the left front wheel turning angle, δ r is the right front wheel turning angle, ω z is the yaw angle, B f is the front wheel track, B r is the rear wheel track, L f is the distance from the front axle to the center of mass, L r is the distance from the rear axle to the center of mass.

3. The method for estimating road adhesion coefficient based on Kalman filtering as claimed in claim 2, characterized in that: The expression for the vertical wheel load in step 1 is as follows: Where F z_fl , F z_rl 、F z_rr are the tire longitudinal forces of the front left wheel, front right wheel, rear left wheel, and rear right wheel, m w is the tire weight, m b is the vehicle weight, L is the wheelbase, h is g is the height of the vehicle's center of mass, a x is the longitudinal acceleration of the vehicle, a y is the lateral acceleration of the vehicle.

4. The method for estimating road adhesion coefficient based on Kalman filtering as claimed in claim 3, characterized in that: The formula for calculating the tire slip angle is as follows: Where α fl , α fr , α rl , α rr are the tire slip angles of the front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively, v x_fl 、v x_fr 、v x_rl 、v x_rr are the longitudinal velocities of the front left wheel, front right wheel, rear left wheel, and rear right wheel, respectively, v y_fl 、v y_fr 、v y_rl 、v y_rr are the lateral speeds of the front left wheel, front right wheel, rear left wheel, and rear right wheel respectively; The calculation formula of tire slip rate is as follows: Where λ ij is the tire slip rate, ω w_ij is the rotation angle radius, R w is the wheel rolling radius, v wx_ij is the longitudinal velocity of each wheel center.

5. The method for estimating road adhesion coefficient based on Kalman filtering as claimed in claim 4, characterized in that: In the Dugoff tire model, Where μ represents the road adhesion coefficient, F z is the vertical load, λ is the slip rate, α is the tire side slip angle, ε is the speed influence factor, C x is the longitudinal stiffness of each tire, C y is the cornering stiffness of each tire.

6. The method for estimating road adhesion coefficient based on Kalman filtering as claimed in claim 5, characterized in that: The formula for tire normalization in step 2 is as follows: but: In the formula, Represents the normalized longitudinal force and normalized lateral force of the tire.

7. The method for estimating road adhesion coefficient based on Kalman filtering as claimed in claim 6, characterized in that: In step 3, set the state variable x(t) = [μ fl μ fr μ rl μ rr ] T , measured variable y(t) = [a x a y r] T , the control quantity u(t) = [δ]; the corresponding prediction equation is The observation equation is in,

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