Automobile trajectory tracking robust control method

Abstract

The invention discloses an automobile trajectory tracking robust control method, which comprises the following steps that: a controller Ks calculates a required front wheel turning angle according to a lateral deviation yr and a deflection state of a real-time measured automobile centroid and a trajectory route, and the controller Ks determines the following steps: establishing a state space expression containing a generalized controlled object based on an automobile linear two-degree-of-freedom model; a transfer function G0 (s) from a front wheel steering angle to lateral deviation yr and a transfer function W (s) from a deviation state as interference input to the lateral deviation yr are derived based on state space expression, a generalized interference control system is expressed based on the two transfer functions, u (s) = Ks (s) y (s) in the system, w (s) is interference, u (s) is the feedback control rate of a controller Ks (s), and the controller Ks (s) is determined through an H infinity loop forming method. Accurate control over automobile trajectory tracking is achieved, and the lateral deviation between the automobile and the preset trajectory can be smaller than 0.2 m.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of automobile trajectory tracking control method. BACKGROUND

[0002] At present, automatic driving car develops rapidly, and the research on automobile trajectory tracking control is significantly increased, but the vehicle control problem under complex conditions is insufficient, and the development of some control algorithms is limited to medium and low speed, and the design parameters need to be re-adjusted when exceeding the speed limit. Robust control has good effect when dealing with complex problems with external disturbance and parameter disturbance.

[0003] For the problem of automobile trajectory tracking, the automobile dynamics model in ground coordinate system is first converted into a generalized disturbance control system type, and "lateral deviation" is directly used as output variable. Although this model is more intuitive, the dynamic equation has high order and many variables, and the operation is complex. SUMMARY

[0004] In view of the defects of the above prior art, the purpose of the present application is to provide a kind of automobile trajectory tracking robust control method, to solve the problem of trajectory tracking control when automobile drives at high speed on the curve with variable curvature.

[0005] The technical scheme of the present application is as follows: a kind of automobile trajectory tracking robust control method, including the controller K s According to the lateral deviation y r of real-time measurement automobile mass center and trajectory route s , the required front wheel steering angle is calculated by the controller K r , which is determined by the following steps:

[0006] Based on the linear two-degree-of-freedom model of automobile, the state space expression of the generalized controlled object is established;

[0007] Based on the state space expression, the transfer function G0(s) of the front wheel steering angle to the lateral deviation y r and the transfer function W(s) of the steering state as disturbance input to the lateral deviation y s are derived.

[0008] The generalized disturbance control system is represented as:

[0009]

[0010] w(s) is disturbance, u(s) is the feedback control rate of controller K ∞ (s), and the controller K s (s) is determined by H ∞ loop shaping method.

[0011] Further, the controller K ∞ is determined by Hs (s) comprises the steps of:

[0012] Taking G0(s) as the controlled object, setting the weighting functions W1 and W2, and obtaining the total controlled object with compensator:

[0013]

[0014] Based on the coefficients A s , B s , C s and D s , the robust stabilization index formula is solved by Riccati equation:

[0015]

[0016] , X and Z, and ρ is the spectral radius of the maximum eigenvalue, and ε max is the maximum stability margin;

[0017] The value range of γ is set, and when γ min is greater than the upper limit of the value range of γ, the weighting functions W1 and W2 are re-set and the robust stabilization index formula is solved until γ min falls within the value range of γ;

[0018] Select γ min greater than γ, and based on the coefficients A s , B s , C s and D s , the controller K

[0019]

[0020] is obtained. k , B k , C k and D k , and determine the controller K ∞ , and finally obtain K s = W1K ∞ W2.

[0021] Further, the solving formula of X and Z is:

[0022] (A s -B s C -1 D s T C s ) T X+X(A s -B s S -1 D s T Cs ) - XB s S -1 B s T X + C s T R -1 C s = 0,

[0023] (A s - B s S -1 D s T C s ) Z + Z (A s - B s S -1 D s T C s ) T - ZC s T R -1 C s Z + B s S -1 B s T = 0,

[0024] R = I + D s D s T , S = I + D s T D s .

[0025] Further, the calculation formulas of the coefficients A k , B k , C k and D k are as follows:

[0026] B K = γ 2 (L T ) -1 ZC s T , F = - S -1 (D s T C s + B s T X), L = (1 - γ 2 ) I + XZ.

[0027] Further, the state space expression of the generalized controlled object is

[0028]

[0029] wherein the system state variable z and y are controllable output and measured output respectively, control signal u = front wheel steering angle, external disturbance C 11 , C 21 , D 11 , D 12 , D 21 , D 22 Depending on the required output variable,

[0030]

[0031] wherein u is the component of vehicle mass center speed on the x-axis of the vehicle coordinate system, v is the component of vehicle mass center speed on the y-axis of the vehicle coordinate system, r is the yaw rate, m is the total mass, a and b are the distances from the mass center to the front axle and the mass center to the rear axle respectively, k1 and k2 are the total front wheel cornering stiffness and the total rear wheel cornering stiffness respectively, I z is the moment of inertia around the z-axis, ψ r represents the angle between the predetermined trajectory coordinate axis and the absolute coordinate axis of the ground, ψ s respectively represent the angle between the vehicle and the predetermined trajectory coordinate X r axis in the current cornering state.

[0032] Further, the transfer function G0(s) is

[0033]

[0034] wherein A(1) represents the 1st row of matrix A, B2(1) represents the 1st row of matrix B2, C = [0 1], s represents the Laplace transform complex variable, and I represents the unit matrix.

[0035] Further, the transfer function W(s) is

[0036]

[0037] wherein A(1) represents the 1st row of matrix A, B1(1) represents the 1st row of matrix B1, and C = [0 1].

[0038] Compared with the prior art, the technical scheme provided by the present application has the advantages that:

[0039] A new method is used in model processing, and the angle relationship between the vehicle coordinate axis fixed on the car and the road coordinate axis is analyzed to express the car dynamics equation as a state space equation containing a generalized controlled object. ∞ The required controllable output transfer function matrix is obtained indirectly by using transfer function operation, and the car trajectory tracking problem is converted into a standard H ∞ loop shaping method to design a robust controller. The index gamma is used to measure the robust stability of the closed loop system and to determine whether the loop shaping is successful. The requirement of 1<gamma<10 is met. The designed controller can test the trajectory tracking ability of the car on the variable curvature trajectory route. When the vehicle drives at different speeds, different masses and different curvatures, the change of system parameters is equivalent to the disturbance perturbation applied to the controller. The controller designed in the application can make the vehicle maintain good tracking performance on any road section, and the deviation between the car and the road is kept within a small range, which shows that the controller has strong anti-interference ability and makes the car have good tracking performance on all target trajectories under complex working conditions. In addition, for intelligent cars, navigation deviation can be added as a disturbance factor on this basis, and the control logic is the same. Therefore, the application has wide applicability. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 is a schematic diagram of the motion of the vehicle in the absolute coordinate system of the ground.

[0041] Figure 2 is a schematic diagram of the generalized disturbance control system module.

[0042] Figure 3 is a H ∞ loop shaping design flowchart.

[0043] Figure 4 is a car trajectory tracking robust control block diagram. DETAILED DESCRIPTION

[0044] The application will be further described below in conjunction with the embodiments, and it should be understood that these embodiments are only used to illustrate the application and not to limit the scope of the application. After reading the description, those skilled in the art can make various modifications to the description, and all modifications fall within the scope defined by the claims attached hereto.

[0045] The present embodiment proposes a car trajectory tracking robust control method. A new analysis method is used for the car model. The model still has the form of a generalized disturbance control system, but the output variable is no longer the lateral deviation of the car. Instead, the most basic simplified two-degree-of-freedom car model is used, and the required controllable output can be obtained by transfer function operation of the output variable. The method is simple and the data is easy to process. The main contents include:

[0046] (1) The motion relationship when the vehicle deviates from the track is shown in Fig. 1 Figure 1 , where x-y is a vehicle coordinate system, u is a component of the mass center velocity of the vehicle on the x-axis, v is a component on the y-axis, r is a yaw rate, δ is a front wheel steering angle, and a linear two-degree-of-freedom model of the vehicle is shown in Equation (1).

[0047]

[0048] In the equations, m is a total mass, a and b are distances from the mass center to the front and rear axles, respectively, k1 and k2 are total cornering stiffnesses of the front and rear wheels, respectively, I z is a moment of inertia about the z-axis.

[0049] (2) X-Y is a ground absolute coordinate system, and the X r axis indicates a road tangent direction, the Y r axis is perpendicular to the X r axis through the mass center of the vehicle, ψ and ψ s indicate angles between the vehicle and the ground absolute coordinate X r axis and the predetermined track coordinate X r axis in the current deviation state, respectively, and ψ s indicates an angle between the predetermined track coordinate axis and the ground absolute coordinate axis, and the three angle relationships are ψ = ψ r + ψ.

[0050] (3) The yaw rate and angular acceleration relationships are obtained from the angular velocity relationships.

[0051]

[0052] In the equations, indicate yaw rates of the vehicle with respect to the ground absolute coordinate and the track coordinate in the current deviation state, respectively, and can be regarded as a yaw rate of the vehicle with respect to the ground absolute coordinate when the vehicle does not deviate from the track.

[0053] (4) Equations (2) and (3) are substituted into Equation (1).

[0054]

[0055] In the equations,

[0056] (5) In order to design a robust controller, Equation (4) is converted into a state space form including a generalized controlled object.

[0057]

[0058] In the equations, the system state variables z and y are controllable output and measured output, control signal u = δ, external disturbance C 11 , C 21 , D 11 , D 12 , D 21 , D 22 Depending on the desired output variable.

[0059] (6) The lateral deviation of the mass center of the car is selected as the output variable, and the controllable output is obtained by using the transfer function operation.

[0060] (7) The lateral deviation of the mass center of the car in the Y r axis direction and the track line is y r , the angle between the mass center velocity U and the X r axis is γ, and the mass center side slip angle is It is assumed that the forward vehicle speed u is constant.

[0061]

[0062] (8) The transfer function from δ to y r without disturbance is obtained by using formula (7), and then the transfer function G0(s) from the front wheel steering angle δ to the mass center lateral deviation y .

[0063]

[0064] In the formula: A(1), A(2), B(1), B(2) represent the 1st, 2nd rows of matrix A and the 1st, 2nd rows of matrix B respectively, C = [0 1], s represents the Laplace transform complex variable, and I represents the unit matrix.

[0065] (9) Similarly, the transfer function W(s) from the disturbance input to y r without steering angle δ input.

[0066]

[0067] (10) The two transfer functions in formula (8) and formula (9) are described by a generalized disturbance control system, as shown in Figure 2 , in which G0(s) is the nominal controlled object, the disturbance w forms the disturbance input of the system through the transfer function W(s), K s is the controller, and the control output z is the same as the measured output y of the system.

[0068]

[0069] (11) A feedback control law is sought for the system represented by formula (10) so that z(s) has the desired performance, K s(s) represents the required controller.

[0070] y(s)=K s (s)y(s) (11) (12) Substituting equation (11) into equation (10), we obtain the transfer function matrix from the disturbance w(s) to the controllable output z(s), thus transforming the disturbance suppression or route tracking problem into a standard H function. ∞ Control issues.

[0071] (13) It is expected that under the action of the controller, the car will have strong trajectory tracking performance, and even when driving at high speed on curves with varying curvature, the lateral deviation y between the car and the predetermined trajectory will be minimized. r It can still be kept within 0.2 meters, therefore this invention proposes a method based on H ∞ A loop-forming robust control method for vehicle trajectory tracking is proposed to achieve this objective.

[0072] (14) Using H ∞ The controller K in the design formula (11) of the loop forming method s (s), the controlled object is G0 obtained in step (8). By determining the weighting functions W1 and W2, the total controlled object G after the compensator is made... s =

[0073] W2G0W1, see Figure 3 As shown in (a), the controller K is finally calculated. s =W1K ∞ W2, see Figure 3 As shown in (b).

[0074] (15) The total controlled object G after adding the compensator s It can be represented in state-space form.

[0075]

[0076] (16) Initially select W1 and W2, and G0 is known. The coefficient A in formula (12) can be obtained. s B s C s and D s .

[0077] (17) The basis for judging whether the circuit formation is successful is that the coefficient γ must satisfy formula (13).

[0078]

[0079] In the formula: γ ranges from 1 to 10, ε represents the robust stabilization index (stability margin), and M... s For G s The normalized left coprime decomposition.

[0080] (18) Equation (13) can be expressed by equation (14).

[0081]

[0082] where: maximum stability margin ε max <1, p is the spectral radius of the largest eigenvalue.

[0083] (19) X and Z in equation (14) can be solved by using Riccati equation, in which other parameters are calculated in step (16).

[0084] (A s -B s C -1 D s T C s ) T X + X(A s -B s S -1 D s T C s )-SB s S -1 B s T X + C s T R -1 C s = 0 (15)

[0085] (A s -B s S -1 D s T C s )Z + Z(A s -B s S -1 D s T C s ) T -ZC s T R -1 C s Z + B s S -1 B s T = (16)

[0086] where: R = I + D s D s T , S = I + D s T Ds .

[0087] (20) If the obtained γ min If the value is greater than 10, it means that W1 and W2 are not suitable choices. Return to step (16) to reselect until a suitable γ is found. min The final value was chosen to be slightly larger than γ. min It can meet the performance requirements of formula (13).

[0088] (21) Obtain the controller K ∞ State-space form.

[0089]

[0090] In the formula: B K =γ 2 (L T ) -1 ZC s T , F = -S -1 (D s T C s +B s T X), L=(1-γ) 2 )I+XZ.

[0091] (22) The controller K is finally calculated s =W1K ∞ W2, makes the open-loop transfer function G0K S The shape in the low-frequency and high-frequency bands meets the requirements of the system's performance and stability boundaries, so that the singular values ​​of the controlled object are shaped into the desired open-loop shape, and the closed-loop system target meets the desired performance indicators.

[0092] This controller design can be implemented using the MATLAB software toolbox, making it convenient to debug controller parameters, providing rapid computation, and applicable to a wide range of vehicle speeds. Its control process is as follows: Figure 4 As shown, the method of this invention solves the problem of insufficient anti-interference capability of conventional controllers when a car is traveling at high speed. When a car is traveling at high speed on a curve, the change in road curvature is considered as interference. The designed controller has good robustness, enabling the car to have strong trajectory tracking performance.

Claims

1. A robust control method for vehicle trajectory tracking, characterized by, comprises a controller K s According to real-time measurement of the lateral deviation y of the vehicle's center of mass from the trajectory course r and the required front wheel steering angle for the yawing state, the controller K s is determined by the following steps: The state space expression of the generalized controlled object is established based on a linear two-degree-of-freedom model of an automobile; Based on the state space representation, the transfer function G0(s) from front wheel steering angle to lateral deviation y r and the transfer function W(s) from sideslip state as disturbance input to lateral deviation y r ​ The generalized disturbance control system is expressed as: u(s) = K s (s)y(s), w(s) is the disturbance, u(s) is the controller K s (s) feedback control rate, through H ∞ Loop shaping method determines the controller K s (s).

2. The robust control method for trajectory tracking of an automobile according to claim 1, characterized by, The passage H ∞ Loop forming method determines controller K s (s) includes the step of: With the controlled object G0(s), the weighting functions W1 and W2 are set to obtain the total controlled object with a compensator: Based on the coefficients A s , B s , C s , and D s , the formula for the robust stabilization index is solved by the Riccati equation: X and Z in the above equation, p is the spectral radius of the largest eigenvalue, and ε max is the maximum stability margin; The range of values of γ is set, when γ min The weighting functions W1 and W2 are re-set and the robust stabilization index formula is solved until γ min falls within the range of values of γ; Selecting a gamma greater than gamma min and calculating a controller based on coefficients A s , B s , C s , and D s : coefficients A k , B k , C k , and D k , and determines the controller K ∞ , ultimately obtaining K s = W1K ∞ W2.

3. The robust control method for trajectory tracking of an automobile according to claim 2, wherein, The value range of γ is 1-10.

4. The robust control method for trajectory tracking of an automobile according to claim 2, wherein, The solving formula of X and Z is: (A s -B s S -1 D s T C s ) T X+X(A s -B s S -1 D s T C s )-XB s S -1 B s T X+C s T R -1 C s =0, (A s -B s S -1 D s T C s )Z+Z(A s -B s S -1 D s T C s ) T -ZC s T R -1 C s Z+B s S -1 B s T =0, R = I + D s D s T S = I + D s T D s .

5. The robust control method for trajectory tracking of an automobile according to claim 2, wherein, The coefficients A k , B k , C k , and D k are calculated as follows: B K = γ 2 (L T ) -1 ZC s T , F = -S -1 (D s T C s + B s T X), L = (1 - γ 2 )I + XZ.

6. The robust control method for trajectory tracking of an automobile according to claim 1, wherein, The state space expression of the generalized controlled object is where the system state variable z and y are the controllable output and measured output, respectively, the control signal u = front wheel steering angle, the external disturbance C 11 , C 21 , D 11 , D 12 , D 21 , D 22 Depending on the desired output variable, where u is the component of the vehicle mass center velocity on the x-axis of the vehicle coordinate system, v is the component of the vehicle mass center velocity on the y-axis of the vehicle coordinate system, r is the yaw rate, m is the total mass, a and b are the distances from the mass center to the front axle and the rear axle respectively, k1 and k2 are the total side slip stiffness of the front wheel and the rear wheel respectively, I z is the moment of inertia about the z-axis, ψ r represents the angle between the predetermined trajectory coordinate axis and the ground absolute coordinate axis, ψ s respectively represent the angle between the vehicle and the predetermined trajectory coordinate X r axis in the current steering state.

7. The robust control method for trajectory tracking of an automobile according to claim 6, wherein, The transfer function G0(s) is Wherein, A(1) represents the first row of the matrix A, b2(1) represents the first row of the matrix b2, C=[0 1], s represents a Laplace transform complex variable, and I represents a unit matrix.

8. The robust control method for vehicle trajectory tracking according to claim 6, wherein, The transfer function W(s) is Wherein, A(1) represents the first row of the matrix A, B1(1) represents the first row of the matrix B1, C=[0 1], s represents a Laplace transform complex variable, and I represents a unit matrix.

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