Wheel rotation angle estimation method based on multi-model adaptive law

Abstract

The invention discloses a wheel steering angle estimation method based on a multi-model adaptive law. The method comprises the following steps: establishing a vehicle dynamics model and a steering execution mechanism model; selecting N groups of cornering rigidities as the cornering rigidities of the vertex model; deriving a corresponding multi-model adaptive law based on the convex inclusion property, and distributing the weight of each vertex model through the multi-model adaptive law; according to the selected N groups of cornering rigidities, estimating a front wheel steering angle through the vehicle dynamics model and the steering execution mechanism model in the S1; and carrying out weighted fusion on the N front wheel steering angle estimation values. According to the method, the weight of each vertex model is distributed through the multi-model adaptive law, the front wheel steering angle is estimated through the vehicle dynamics model and the steering execution mechanism model according to the N groups of cornering rigidities, then weighted fusion is performed based on a plurality of front wheel steering angle estimated values, the anti-disturbance performance is relatively good, and an index function is introduced in weight distribution, so that the robustness of the method is improved. Convergence conditions are relaxed, and higher convergence speed can be obtained while convergence stability is guaranteed.

Description

Technical Field

[0001] The invention relates to the technical field of automobile steering control, and more specifically to a wheel angle estimation method based on a multi-model adaptive law. Background Art

[0002] In the automotive steer-by-wire system, the effectiveness of the vehicle angle sensor is crucial to the reliability and safety of the steer-by-wire system. However, under some extreme conditions, the measurement signal of the vehicle angle sensor is not always accurate, including signal corruption caused by angle sensor failure. Therefore, it is necessary to estimate the wheel angle in real time.

[0003] A Chinese patent application with publication number CN 112829766A discloses an adaptive path tracking method based on a distributed drive electric vehicle, comprising: 1. establishing a vehicle dynamics model and converting it into a state space equation; 2. establishing a vehicle vertex dynamics model based on the vehicle dynamics model and combining the variation range of the tire cornering stiffness; 3. calculating the parameter estimation adaptation rate of the vehicle vertex dynamics model, and estimating the adaptive coefficient according to the real-time system state of the vehicle; 4. establishing a vehicle state prediction model based on the adaptive coefficient estimation result to predict the future state of the vehicle and the system output; 5. establishing and solving a path tracking optimization objective function and a lateral speed constraint objective function to obtain a first set of results of the optimal control sequence.

[0004] This patent improves the robustness of vehicle path tracking by designing vertex models and adaptive rates, and performing online identification of the unmeasurable front and rear wheel cornering stiffness based on the real-time status of the system. C , B C The weighted fusion is performed to obtain an estimated adaptive rate value. This calculation method has relatively poor anti-disturbance performance. Moreover, the constraints in the definition formula of the estimated adaptive rate of the estimated weight are relatively limited, and it is impossible to take into account both the convergence stability and the convergence speed. To this end, we provide a wheel angle estimation method based on the multi-model adaptive law. Summary of the invention

[0005] The present invention provides a wheel angle estimation method based on a multi-model adaptive law to solve the shortcomings of the existing wheel angle estimation method, such as relatively poor anti-disturbance performance, relatively limited constraints in the definition formula of the estimated adaptive rate of the estimated weight, and inability to take into account both convergence stability and convergence speed.

[0006] The present invention adopts the following technical solution:

[0007] A wheel angle estimation method based on a multi-model adaptive law is characterized by comprising the following steps: S1, establishing a vehicle dynamics model and a steering actuator model; S2, selecting N groups of cornering stiffnesses as cornering stiffnesses of vertex models according to the accessibility of the magic tire model in Carsim under several relatively extreme working conditions; S3, deriving a corresponding multi-model adaptive law based on the convex inclusion property, and allocating weights of each vertex model through the multi-model adaptive law, specifically comprising: 1) designing an index function l according to the specific situation i ′(t); 2) Compare the index function and select the minimum performance function value l at the current moment min ′(t); 3) according to the error at the current moment, a weight iteration index is obtained by a stepwise iterative multiplication method; 4) finally, the corresponding weight is obtained by the overall proportion of the weight iteration index; S4, the front wheel steering angle is estimated according to the selected N groups of cornering stiffness through the vehicle dynamics model and the steering actuator model of step S1; S5, the N front wheel steering angle estimation values ​​obtained in step S4 are weightedly fused.

[0008] The above vehicle dynamics model is as follows:

[0009]

[0010] where k f and k r are the equivalent cornering stiffness of the front and rear axles, β is the sideslip angle of the center of mass, γ is the yaw rate of the vehicle, a and b are the distances from the center of mass of the vehicle to the front and rear axles, m is the vehicle mass, and v x is the vehicle speed, δ is the front wheel turning angle of the vehicle, I z is the moment of inertia of the vehicle around the oz axis.

[0011] The steering actuator model is as follows:

[0012]

[0013] Among them, M r is the rack mass, B r is the rack damping coefficient, F R is the front wheel steering resistance acting on the rack, k i is the steering actuator motor reduction ratio, k m is the electromagnetic torque coefficient of the steering actuator motor, k z is the angular transmission ratio of the wire-controlled steering system, η is the total efficiency of the steering actuator motor and its reduction mechanism, I m is the total current of the redundant dual-winding motor, r p is the radius of the pinion, t p is the tire trail, t m is the kingpin drag.

[0014] In the above step S2, preferably a two-degree-of-freedom vehicle model is used as the vertex model, and the specific formula is as follows: Among them A s (k f , k r ) and B s (k f , k r ) is the uncertain state matrix, whose uncertainty depends on the parameters.

[0015] The above adopts N groups of cornering stiffness (k f1 , k r1 ), (k f2 , k r2 ),...,(k fn , k rn ) is used as the cornering stiffness of the vertex model, and the uncertainty matrix is ​​expressed as: [A s (k f , k r )B s (k f , k r )]∈Co{[A i B i ]: i=1,...,N}(28); Co{[A in formula (29) i B i ]: i = 1, ..., N} represents the convex inclusion of the matrix set. For each vertex i∈{1, ..., N} of the convex inclusion in equation (5), its fixed parameter dynamic model is as follows:

[0016] Based on the convex inclusion property, the corresponding multi-model adaptive law is introduced as follows: where w i (t) represents the weight of each vertex model at time t.

[0017] When allocating weights in step S3, at the initial moment of the weighted algorithm, the weight w i (0) and weight iteration index l i (0) The initial value is averaged with probability 1, i = 1, ..., N: The indicator function l i ′(t) is expressed as follows: where e i (t) is the error between the output of each local model and the real system output. i ′(t)=0 occurs, it is necessary that α>0 and be a smaller value; the minimum performance function value l min ′(t) is expressed as follows: min '(t)=min{l′ i(t)}, i = 1, ..., n. (34); The specific formula of the weight iteration index is as shown in formula (35) and (36): Wherein ceil(x) is the upper limit function that generates the smallest integer not less than x, that is, ceil(x)=min{n∈Z|x≤n}(39); the overall proportion of the weight iteration index is obtained by the corresponding weight as follows:

[0018] The weights of the above vertex models must satisfy: Considering that the above algorithm is difficult to meet the requirements after the local model converges to 0, it is necessary to limit the threshold of weight convergence to ensure that the weight is not 0; therefore, the limiting condition is: when w i When (t)<0.001, Guaranteed weight w i (t), i=1, ..., N. are not less than 0.001.

[0019] The above step S4 specifically includes:

[0020] 1) The established vehicle dynamics model is combined with the steering actuator model to obtain a joint dynamics model for state estimation:

[0021]

[0022] in As a state variable, y = [a y ] is the observed value, [I m ] is the input of the system;

[0023] 2) Given the following initial parameters: sampling time T = 0.001s, initial error covariance matrix P 0 =[I 4×4 ], the initial state variable x 0 =[0 0 0 0] T , the process excitation noise covariance Q = diag[1×10 -1 1×10 -1 5×10 -5 4×10 -4 ], the measurement noise covariance R = [1 × 10 -4 ];get:

[0024]

[0025] 3) Adoption As a state variable, [I m ] as input, y = [γ] as the measurement value, and estimate another set of front wheel steering angle signals through the above algorithm.

[0026] It can be seen from the above description of the present invention that, compared with the prior art, the present invention has the following advantages:

[0027] 1. The present invention allocates the weights of each vertex model through the multi-model adaptive law, and then estimates the front wheel angle according to N groups of cornering stiffness through the vehicle dynamics model and the steering actuator model, and then performs weighted fusion based on multiple front wheel angle estimation values. Its anti-disturbance performance is relatively good, and in the weight allocation, an indicator function is introduced to relax the convergence conditions, which can ensure the convergence stability while obtaining a faster convergence speed.

[0028] 2. The present invention has the characteristics of simple design and clear logical concepts. It is suitable for intelligent automobile controller design and can be effectively used in the estimation of the steering angle of autonomous driving vehicles. It provides signal reference for the fault diagnosis and fault-tolerant control of the wheel steering angle of autonomous driving vehicles and solves the diversity problem of the existing autonomous driving environment. The front wheel steering angle can still be accurately estimated under complex working conditions. The maximum estimation error and maximum root mean square deviation are 0.855 degrees and 0.297 respectively, which are 22.17% and 44.69% lower than those of the traditional Kalman filter. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is the estimated value of the first group of front wheel turning angles of the present invention.

[0030] Figure 2 is the estimation error of the first group of front wheel steering angles of the present invention.

[0031] Figure 3 is the estimated value of the second group of front wheel turning angles of the present invention.

[0032] Figure 4 is the estimation error of the second group of front wheel steering angles of the present invention. DETAILED DESCRIPTION

[0033] The specific implementation of the present invention is described below with reference to the accompanying drawings. In order to fully understand the present invention, many details are described below, but for those skilled in the art, the present invention can be implemented without these details. For well-known components, methods and processes, they are not described in detail below.

[0034] This embodiment provides a wheel angle estimation method based on a multi-model adaptive law, comprising the following steps:

[0035] 1. Establish vehicle dynamics model and steering actuator model.

[0036] 1. The vehicle dynamics model is as follows:

[0037]

[0038] where k f and k r are the equivalent cornering stiffness of the front and rear axles, β is the sideslip angle of the center of mass, γ is the yaw rate of the vehicle, a and b are the distances from the center of mass of the vehicle to the front and rear axles, m is the vehicle mass, and v x is the vehicle speed, δ is the front wheel turning angle of the vehicle, I z is the moment of inertia of the vehicle around the oz axis.

[0039] 2. Steering actuator model

[0040]

[0041] Among them, M r is the rack mass, B r is the rack damping coefficient, F R is the front wheel steering resistance acting on the rack, k i is the steering actuator motor reduction ratio, k m is the electromagnetic torque coefficient of the steering actuator motor, k z is the angular transmission ratio of the wire-controlled steering system, η is the total efficiency of the steering actuator motor and its reduction mechanism, I m is the total current of the redundant dual-winding motor, r p is the radius of the pinion, t p is the tire trail, t m is the kingpin drag.

[0042] 2. Take the two-degree-of-freedom vehicle model as the vertex model, as follows:

[0043]

[0044] Among them, A s (k f , k r ) and B s (k f , k r ) is the uncertain state matrix, whose uncertainty depends on the parameter k f , k r .

[0045] 3. According to the accessibility of the magic tire model in Carsim under some extreme working conditions, N groups of cornering stiffness (k f1 , k r1 ), (k f2 , k r2 ),…,(k fn , k rn ), as the cornering stiffness of the vertex model, the uncertainty matrix can be expressed as:

[0046] [A s (kf , k r ) B s (k f , k r )]∈Co{[A i B i ]:i=1,…,N} (51)

[0047] In the formula, Co{[A i B i ]: i = 1, ..., N} represents the convex inclusion of the matrix set. Most of the situations of the vehicle under different loads, different speeds and different road adhesion coefficients can be linearly represented by N vertices.

[0048] For each vertex i∈{1,…,N} in the convex inclusion in equation (51), its fixed-parameter dynamic model is as follows:

[0049]

[0050] Fourth, based on the convex inclusion property, the corresponding multi-model adaptive law is derived. The above formula (53) can be rewritten as:

[0051]

[0052] where w i (t) represents the weight of each vertex model at time t.

[0053] 5. Allocate the weight of each vertex model through the multi-model adaptive law.

[0054] At the initial moment of the weighted algorithm, the weight w i (0) and weight iteration index l i (0) The initial value is taken on average with probability 1, i=1,...,N.

[0055]

[0056] Design the index function l according to the specific situation i ′(t), the basic indicator function is as follows:

[0057]

[0058] where e i (t) is the error between the output of each local model and the real system output. i The situation of ′(t)=0 occurs, which requires α>0 and a smaller value.

[0059] Compare the index functions and select the minimum performance function value l at the current moment min '(t):

[0060] l min ′(t)=min{l′ i (t)}, i = 1, ..., n. (57)

[0061] According to the error at the current moment, the weight iteration index is obtained by using the method of step-by-step iterative multiplication:

[0062]

[0063] Where ceil(x) is the ceiling function that generates the smallest integer not less than x, that is:

[0064] ceil(x)=min{n∈Z|x≤n} (60)

[0065] Finally, the corresponding weight is obtained from the overall proportion of the weight iteration index:

[0066]

[0067] According to formula (61), the model weight of each vertex must satisfy:

[0068]

[0069] Considering that the above algorithm is difficult to meet the requirements after the local model converges to 0, it is necessary to limit the threshold of weight convergence to ensure that the weight is not 0. Therefore, the limiting condition is: when w i When (t)<0.001, Guaranteed weight w i (t), i=1, ..., N. are not less than 0.001.

[0070] Assume M j The model set M = {M i , i=1,...,N}, the model that is closest to the truth, according to probability 1:

[0071]

[0072] Where d is the system delay. Then the weighted algorithm, i.e., equations (55)-(61), has the following characteristics:

[0073]

[0074] Equations (55)-(61) and (63) can ensure that the following probability is 1:

[0075]

[0076] like It can be seen that:

[0077]

[0078] Combining equations (65), (66) and (59), we can obtain:

[0079]

[0080] Then based on formula (61), we get:

[0081]

[0082] 6. Estimate the front wheel steering angle based on the selected N groups of cornering stiffnesses using the Kalman filter algorithm.

[0083] Combining the established vehicle dynamics model with the steering actuator model, a joint dynamics model for state estimation is obtained:

[0084]

[0085] in As a state variable, y = [a y ] is the observed value, [I m ] is the input of the system.

[0086] In order to accurately estimate the front wheel angle, the following initial parameters are given: sampling time T = 0.001s, initial error covariance matrix P 0 =[I 4×4 ], the initial state variable x 0 =[0 0 0 0] T , the process excitation noise covariance Q = diag[1×10 -1 1×10 -1 5×10 -5 4×10 -4 ], the measurement noise covariance R = [1 × 10 -4 ].

[0087]

[0088] Similarly, further adopting As a state variable, [I m ] is used as the system input, y=[γ] is used as the observation value, and an algorithm is used to estimate another set of front wheel steering angle signals.

[0089] Reference Figures 1 to 4 , Figure 1 and Figure 2 The estimated values ​​and estimated errors of the first set of front wheel steering angles are shown respectively; and Figure 3 and Figure 4 The estimated values ​​and estimated errors of the second set of front wheel steering angles are respectively used.

[0090] 7. Perform weighted fusion on the front wheel steering angle estimation value obtained in the above step 6.

[0091] The above is only a specific implementation of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial changes to the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention.

Claims

1. A wheel angle estimation method based on multi-model adaptive law, characterized in that: The following steps are involved: S1. Establish vehicle dynamics model and steering actuator model; S2. According to the accessibility of the magic tire model in Carsim under several relatively extreme working conditions, N groups of cornering stiffness are selected as the cornering stiffness of the vertex model; S3, based on the convex inclusion property, the corresponding multi-model adaptive law is introduced, and the weight of each vertex model is allocated through the multi-model adaptive law, which specifically includes: 1) designing the index function l according to the specific situation i ′(t); 2) Compare the index functions and select the minimum performance function value l at the current moment min ′(t); 3) According to the error at the current moment, a weight iteration index is obtained by a step-by-step iterative multiplication method; 4) Finally, the corresponding weight is obtained by the overall proportion of the weight iteration index; S4, estimating the front wheel angle according to the selected N groups of cornering stiffnesses through the vehicle dynamics model and the steering actuator model of step S1; S5. Perform weighted fusion on the N front wheel steering angle estimation values ​​obtained in step S4.

2. A wheel angle estimation method based on multi-model adaptive law as claimed in claim 1, characterized in that: The vehicle dynamics model is as follows: where k f and k r are the equivalent cornering stiffness of the front and rear axles, β is the sideslip angle of the center of mass, γ is the yaw rate of the vehicle, a and b are the distances from the center of mass of the vehicle to the front and rear axles, m is the vehicle mass, and v x is the vehicle speed, δ is the front wheel turning angle of the vehicle, I z is the moment of inertia of the vehicle around the oz axis.

3. The wheel angle estimation method based on multi-model adaptive law as claimed in claim 2, characterized in that: The steering actuator model is specifically as follows: Among them, M r is the rack mass, B r is the rack damping coefficient, F R is the front wheel steering resistance acting on the rack, k i is the steering actuator motor reduction ratio, k m is the electromagnetic torque coefficient of the steering actuator motor, k z is the angular transmission ratio of the wire-controlled steering system, η is the total efficiency of the steering actuator motor and its reduction mechanism, I m is the total current of the redundant dual-winding motor, r p is the radius of the pinion, t p is the tire trail, t m is the kingpin drag.

4. The wheel angle estimation method based on multi-model adaptive law as claimed in claim 3, characterized in that: The step S2 uses a two-degree-of-freedom vehicle model as a vertex model, and the specific formula is as follows: Among them A s (k f , k r ) and B s (k f , k r ) is the uncertain state matrix, whose uncertainty depends on the parameters.

5. The wheel angle estimation method based on multi-model adaptive law as claimed in claim 4, characterized in that: Using N groups of cornering stiffness (k f1 , k r1 ), (k f2 , k r2 ),...,(k fn , k rn ) is used as the cornering stiffness of the vertex model, and the uncertainty matrix is ​​expressed as: [A s (k f , k r )B s (k f , k r )]∈Co{[A i B i ]: i=1,...,N}(5); Co{[A in formula (6) i B i ]: i = 1, ..., N} represents the convex inclusion of the matrix set. For each vertex i∈{1, ..., N} of the convex inclusion in equation (5), its fixed parameter dynamic model is as follows:

6. The wheel angle estimation method based on multi-model adaptive law as claimed in claim 5, characterized in that: Based on the convex inclusion property, the corresponding multi-model adaptive law is introduced as follows: where w i (t) represents the weight of each vertex model at time t.

7. The wheel angle estimation method based on multi-model adaptive law as claimed in claim 1, characterized in that: When weight allocation is performed in step S3, at the initial moment of the weighted algorithm, the weight w i (0) and weight iteration index l i (0) The initial value is averaged with probability 1, i = 1, ..., N: The indicator function l i ′(t) is expressed as follows: where e i (t) is the error between the output of each local model and the real system output. i ′(t)=0 occurs, it is necessary that α>0 and be a smaller value; the minimum performance function value l min ′(t) is expressed as follows: min ′(t)=min{l i '(t)}, i = 1, ..., n. (11); The specific formula of the weight iteration index is as shown in formula (12) and (13): Where ceil(x) is the upper limit function that generates the smallest integer not less than x, that is, ceil(x)=min{n∈Z|x≤n}(16); the overall proportion of the weight iteration index is obtained by the corresponding weight as follows:

8. The wheel angle estimation method based on multi-model adaptive law as claimed in claim 7, characterized in that: The model weight of each vertex must satisfy: Considering that the above algorithm is difficult to meet the requirements after the local model converges to 0, it is necessary to limit the threshold of weight convergence to ensure that the weight is not 0; therefore, the limiting condition is: when w i When (t)<0.001, Guaranteed weight w i (t), i=1, ..., N. are not less than 0.

001.

9. The wheel angle estimation method based on multi-model adaptive law as claimed in claim 7, characterized in that: The step S4 specifically includes: 1) The established vehicle dynamics model is combined with the steering actuator model to obtain a joint dynamics model for state estimation: in As a state variable, y = [a y ] is the observed value, [I m ] is the input of the system; 2) Given the following initial parameters: sampling time T = 0.001s, initial error covariance matrix P0 = [I 4×4 ], initial state variable x0 = [0 0 0 0] T , the process excitation noise covariance Q = diag[1×10 -1 1×10 -1 5×10 -5 4×10 -4 ], the measurement noise covariance R = [1 × 10 -4 };get: 3) Adoption As a state variable, [I m ] as input, y = [γ] as the measurement value, and estimate another set of front wheel steering angle signals through the above algorithm.

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