Method for constructing human-machine collaborative steering framework based on lqr and feedforward control

Abstract

This invention relates to the field of driver assistance technology, and in particular to a method for constructing a human-machine cooperative steering framework based on LQR and feedforward control. It includes proposing a second-order driver model describing the steering maneuver process based on a two-point preview model and a driver neuromuscular model. Based on this, key parameters in the driver model are obtained online through data acquisition from a driving simulator and feature parameter identification based on the least squares method. Then, a shared steering control behavior model of the driver-road-vehicle system is constructed by combining a two-degree-of-freedom vehicle dynamics model. Finally, a shared controller based on LQR and feedforward control is derived, the feedback and feedforward control quantities are solved, and the stiffness parameters of the shared controller are defined. Human-machine cooperative driving experiments were conducted on a driving simulator. This invention integrates driver characteristics into the design of the shared controller, improving the comfort of driver-controller cooperation while ensuring vehicle stability and path tracking capabilities, effectively enhancing human-machine trust.

Description

Technical Field

[0001] This invention relates to the field of driver assistance technology, and in particular to a method for constructing a human-machine cooperative steering framework based on LQR and feedforward control. Background Technology

[0002] In recent years, autonomous driving technology has become increasingly mature, not only improving the driving experience but also mitigating some of the drawbacks of manual driving. Studies have shown that the introduction of advanced driver assistance systems during the application of autonomous driving technology can effectively improve driving safety and passenger comfort, reduce the number of accidents caused by drivers, and reduce driver workload.

[0003] Academics and industry are working to design human-machine shared control strategies that keep drivers within the control loop and engage in a game-like interaction with the automated system regarding control authority. Compared to traditional single-task control and transactional control, the novelty of this system lies in its high degree of synergy, achieved by simultaneously combining driver control actions with the automation of vehicle guidance.

[0004] However, effectively combining the skills of drivers and autonomous vehicles to achieve optimal shared cooperative control remains a huge challenge. Summary of the Invention

[0005] The purpose of this invention is to address the problems existing in the background technology by proposing a human-machine cooperative steering framework construction method based on LQR and feedforward control. This method combines driver characteristics with a two-degree-of-freedom vehicle dynamics model, derives and designs algorithms for solving the LQR feedback gain matrix and the feedforward control input, and couples the shared controller stiffness parameters with the actual driver input.

[0006] The technical solution of this invention, a method for constructing a human-machine collaborative steering framework based on LQR and feedforward control, includes the following specific steps:

[0007] S1. Based on the two-point preview model and the driver neuromuscular model, a second-order driver model describing the steering operation process is established.

[0008] S2. Based on the second-order driver model in S1, the parameters in the driver model are obtained online through data collection from the driving simulator and feature parameter identification based on the least squares method.

[0009] S3. A driver-road-vehicle system shared steering control behavior model was constructed by combining a two-degree-of-freedom vehicle dynamics model.

[0010] S4. Derive the shared controller based on LQR and feedforward control, solve for the feedback and feedforward control quantities, and define the stiffness parameters of the shared controller.

[0011] S5. A human-machine co-driving experiment was conducted on a driving simulator to verify the results.

[0012] Preferably, S1 employs a two-point preview strategy to describe the driver's preprocessing of the road ahead, and introduces a second-order response process to describe the driver's neural and muscular decision-making and reaction processes; the s-domain expression of the second-order driver model is:

[0013]

[0014] In the formula, Kp and Kc represent the driver's aiming gain and compensation gain, respectively; θ f θ n τ1 and τ2 represent the near and far visual angles in the driver's two-point preview model, respectively; τ1 and τ2 represent the driver's brain decision-making delay and muscle information transmission delay, respectively; δ d This indicates the actual steering wheel angle turned by the driver.

[0015] Preferably, step S2 further includes the following steps:

[0016] S21. The s-domain expression of the second-order driver model is transformed to the z-plane using a bilinear transformation, thereby obtaining the time-domain discrete difference equation:

[0017] δ d (k)=ψ T θ

[0018]

[0019] ψ=[δ d (k-1),δ d (k-2),θ f (k)+2θ f (k-1)+θ f (k-2),θ n (k)+2θ n (k-1)+θ n (k-2)] T

[0020]

[0021]

[0022]

[0023] In the formula, Ts is the sampling period, and k represents the current discrete time;

[0024] S22. Construct the recurrence relation of the online recursive least squares identification algorithm with a forgetting factor, and identify the parameters for solving each time step:

[0025]

[0026] In the formula, G and P are intermediate variables, I represents the identity matrix, and α is the forgetting factor. Based on the functional mapping relationship between each element of θ and the driver feature parameters Kp, Kc, τ1, and τ2, the driver model parameters are obtained online.

[0027] S23. Obtain parameters online in real time through an identification algorithm, and apply the parameters directly to the controller.

[0028] Preferably, in S3, the driver model is combined with the two-degree-of-freedom vehicle dynamics model to obtain the following state-space expression:

[0029]

[0030]

[0031]

[0032]

[0033] In the formula, C αf C αr These represent the side plate stiffness of the front and rear wheels, respectively; a and b represent the distances from the front and rear axles to the center of mass, respectively; v x I represents the longitudinal speed; m represents the vehicle mass; I represents the longitudinal speed. z The vehicle's moment of inertia; l f and l n These represent the driver's long and short aiming distances, respectively; δ fd and δ fc These are the front wheel steering angles input by the driver and the controller, respectively; e d and These are the vehicle's lateral position error and heading error, respectively; R g For steering ratio, δ d =R g *δ fd .

[0034] Preferably, S4 includes the following steps:

[0035] S41. Construct LQR state-space feedback and design feedforward control to eliminate the steady-state error caused by the third term of the driver-road-vehicle state-space equation; the objective function for LQR state-space feedback optimization is:

[0036] J=∑(x T Qx+δ fc T Rδ fc )

[0037] R = [r]

[0038] In the formula, Q and R are the weight matrices of the state variables and control variables in the optimization objective of LQR, respectively, and q1, q2, q3, q4 and r are the weight values;

[0039] S42. Constructing the recursive formula of the Riccati equation based on LQR state-space feedback:

[0040] P k-1 =Q+A T P k (I+BR -1 B T P k ) -1 A

[0041] Further, the state feedback gain is obtained:

[0042] K = (R + B) T PB) -1 B T PA

[0043] S43. Combine the state feedback -Kx obtained from LQR with the feedforward control quantity δ f The sum is used as the control quantity δ fc =-Kx+δ f Substitute the error state space equations of the two-degree-of-freedom vehicle dynamics model and solve for the feedforward control quantity.

[0044] Substituting the control variables into the driver-road-vehicle state-space equations, we obtain:

[0045]

[0046]

[0047]

[0048]

[0049] Preferably, once the vehicle system is stable, there are then:

[0050]

[0051] In the formula, K k Let K1 and K3 be the one-dimensional column vector formed by rows 1-4 of the LQR state feedback matrix. k The first and third rows of elements.

[0052] Preferably, the lateral error after vehicle stabilization is 0, and the calculation formula for the feedforward control quantity is obtained, namely:

[0053]

[0054] Preferably, the controller stiffness parameter λ characterizes the proportion of the driver's and controller's inputs acting on the vehicle's steering system, i.e., the actual control angle input of the vehicle is:

[0055] δ=λδ fc +(1-λ)δ fd =λ(-Kx+δ) f )+(1-λ)δ fd .

[0056] Compared with the prior art, the present invention has the following beneficial technical effects:

[0057] 1. This invention combines driver characteristics with a two-degree-of-freedom vehicle dynamics model, derives and designs algorithms for solving the LQR feedback gain matrix and the feedforward control input, couples the stiffness parameters of the shared controller with the actual input of the driver, and comprehensively considers the integration of human behavior factors with the controller in the shared controller. It uses a low-computational-cost control method for shared control design, which has broad prospects and practicality in the research and application of personalized auxiliary control systems that consider driver steering behavior.

[0058] 2. This invention comprehensively considers the LQR algorithm and feedforward control algorithm and incorporates driver characteristics into the controller design, enabling human-machine cooperative interaction in shared steering control. It has significant advantages in the design of personalized controllers, offering clear logic, high flexibility, and good versatility. Attached Figure Description

[0059] Figure 1 This is a structural diagram of the human-machine cooperative steering framework based on LQR and feedforward control of the present invention.

[0060] Figure 2 In a driving simulator, the driver does not operate the controls; only the controller outputs the actual position and the desired trajectory.

[0061] Figure 3 The diagram shows the actual position and the desired trajectory when the driver and controller work together on a driving simulator and the controller stiffness is 0.8.

[0062] Figure 4 This is a diagram showing the driver, controller, and final actual steering wheel angle on a driving simulator, where the driver and controller work together, and the controller stiffness is 0.8.

[0063] Figure 5 This is a diagram of a two-degree-of-freedom vehicle dynamics model in the human-machine cooperative steering framework construction method based on LQR and feedforward control of this invention.

[0064] Figure 6 This is a structural diagram of the LQR controller in the human-machine collaborative steering framework construction method based on LQR and feedforward control of the present invention. Detailed Implementation

[0065] Example 1

[0066] like Figure 1 As shown, the human-machine cooperative steering framework construction method based on LQR and feedforward control proposed in this invention includes the following steps:

[0067] A two-point preview strategy is employed to describe the driver's preprocessing of the road ahead, and a second-order response process is introduced to describe the driver's neural and muscular decision-making and reaction processes. The s-domain expression of the second-order driver model is:

[0068]

[0069] In the formula, K p K c These represent the driver's aiming gain and compensation gain, respectively; θ f θ n τ1 and τ2 represent the near and far visual angles in the driver's two-point preview model, respectively; τ1 and τ2 represent the driver's brain decision-making delay and muscle information transmission delay, respectively; δ d This indicates the actual steering wheel angle turned by the driver.

[0070] Using least squares with a forgetting factor to evaluate the parameter K in the second-order driver model. p K c Identify τ1 and τ2.

[0071] The s-domain expression of the second-order driver model is transformed to the z-plane using a bilinear transformation, thus obtaining the time-domain discrete-difference equation:

[0072] δ d (k)=ψ T θ

[0073]

[0074] ψ=[δ d (k-1),δ d (k-2),θ f (k)+2θ f (k-1)+θ f (k-2),θ n (k)+2θ n (k-1)+θ n (k-2)] T

[0075]

[0076]

[0077]

[0078] In the formula, T s The sampling period is k, which represents the current discrete time.

[0079] Construct the recurrence relation of an online recursive least squares identification algorithm with a forgetting factor to identify the parameters at each time step:

[0080]

[0081] In the formula, G and P are intermediate variables, I represents the identity matrix, and α is the forgetting factor.

[0082] Based on each element of θ and the driver characteristic parameter K p K c The function mapping relationship of τ1 and τ2 is used to obtain the driver model parameters online and apply them to the subsequent control model.

[0083] By combining the driver model with the two-degree-of-freedom vehicle dynamics model, a shared steering control behavior model for the driver-road-vehicle system is obtained. The state-space expression of the model is as follows:

[0084]

[0085]

[0086]

[0087]

[0088] In the formula, C αf C αr These represent the side plate stiffness of the front and rear wheels, respectively; a and b represent the distances from the front and rear axles to the center of mass, respectively; v x I represents the longitudinal speed; m represents the vehicle mass; I represents the longitudinal speed. z The vehicle's moment of inertia; l f and l n These represent the driver's long and short aiming distances, respectively; δ fd and δ fc These are the front wheel steering angles input by the driver and the controller, respectively; e d and These are the vehicle's lateral position error and heading error, respectively; R g For steering ratio, δ d =R g *δ fd .

[0089] Considering the first two terms of the driver-road-vehicle state-space equation, construct the LQR state-space feedback and design feedforward control to eliminate the steady-state error caused by the third term of the driver-road-vehicle state-space equation.

[0090] The optimization objective of LQR is:

[0091] J=∑(x T Qx+δ fc T Rδ fc )

[0092] R = [r]

[0093] In the formula, Q and R are the weight matrices of the state variables and control variables in the optimization objective of LQR, respectively, and q1, q2, q3, q4 and r are the weight values.

[0094] Constructing the recurrence relation for the Riccati equation:

[0095] P k-1 =Q+A T P k (I+BR -1 B T P k ) -1 A

[0096] Further, the state feedback gain is obtained:

[0097] K = (R + B) T PB) -1 B T PA

[0098] The state feedback -Kx obtained from LQR is combined with the feedforward control quantity δ f The sum is used as the control quantity δ fc =-Kx+δ f Substituting the error state-space equations of the two-degree-of-freedom vehicle dynamics model, we obtain:

[0099]

[0100]

[0101]

[0102]

[0103] Once the vehicle system stabilizes, there is then:

[0104]

[0105] In the formula, K k Let K1 and K3 be the one-dimensional column vector formed by rows 1-4 of the LQR state feedback matrix. k The first and third rows of elements.

[0106] At this point, e represents the current steady-state error of the system. To eliminate the steady-state error, the feedforward input δ must be... f satisfy:

[0107]

[0108] The controller stiffness parameter λ characterizes the proportion of the driver's and controller's inputs acting on the vehicle's steering system, i.e., the actual control angle input of the vehicle is:

[0109] δ=λδ fc +(1-λ)δ fd =λ(-Kx+δ) f )+(1-λ)δ fd

[0110] Finally, experiments were conducted on a driver-in-the-loop semi-physical simulation platform to build a model identification algorithm. During the driver's driving process, the time-varying characteristic parameters of the driver were identified online, and the obtained parameters were substituted into the model to build a shared control algorithm model of LQR and feedforward control.

[0111] Two tests were conducted in Prescan with a U-turn test condition of 100m radius: (1) The driver did not perform steering operations, and the vehicle was controlled by the controller. The actual vehicle trajectory and the expected trajectory were as follows. Figure 2 As shown; (2) The driver and controller perform control operations simultaneously, and the controller stiffness is 0.8, i.e., δ=0.8×δ fc +0.2×δ fd The obtained actual vehicle trajectory and the expected trajectory are as follows: Figure 2 As shown, the driver's steering angle input, controller's steering angle input, and total steering wheel angle results are as follows: Figure 3 As shown.

[0112] Analyze the results: Figure 2 and Figure 3 Both demonstrate the reliability of the pure controller and the shared controller. In experiment (2), the driver input an inaccurate steering wheel angle and exhibited abnormal operating behavior at the 15th and 26th seconds. However, the shared controller was able to offset the driver's inaccurate input and respond quickly to the abnormal operation, ensuring the stable and safe driving of the vehicle.

[0113] This invention combines driver characteristics with a two-degree-of-freedom vehicle dynamics model, derives and designs algorithms for solving the LQR feedback gain matrix and the feedforward control input, couples the stiffness parameters of the shared controller with the actual input of the driver, and comprehensively considers the integration of human behavior factors with the controller in the shared controller. It uses a low-computational-cost control method for shared control design, which has broad prospects and practicality in the research and application of personalized auxiliary control systems that consider driver steering behavior.

[0114] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. A method for constructing a human-machine cooperative steering framework based on LQR and feedforward control, characterized in that, The specific steps include the following: S1. Based on the two-point preview model and the driver neuromuscular model, a second-order driver model describing the steering operation process is established. S2. Based on the second-order driver model in S1, the parameters in the driver model are obtained online through data collection from the driving simulator and feature parameter identification based on the least squares method. S21. The s-domain expression of the second-order driver model is transformed to the z-plane using a bilinear transformation, thereby obtaining the time-domain discrete difference equation: ； In the formula, Ts The sampling period is k Indicates the current discrete time; S22. Construct the recurrence relation of the online recursive least squares identification algorithm with a forgetting factor, and identify the parameters for solving each time step: In the formula, G and P As an intermediate variable, I Represents the identity matrix. α Forgetting factor; according to θ Each element is related to the driver's characteristic parameters Kp , Kc , The function mapping relationship allows for the online acquisition of driver model parameters; These represent the delay in the driver's brain decision-making and the delay in muscle information transmission, respectively. δ d This indicates the actual steering wheel angle turned by the driver; S23. Obtain parameters online in real time through an identification algorithm and apply the parameters directly to the controller; S3. A driver-road-vehicle system shared steering control behavior model was constructed by combining a two-degree-of-freedom vehicle dynamics model. In S3, the driver model is combined with the two-degree-of-freedom vehicle dynamics model to obtain the following state-space expression: In the formula, C αf , C αr These refer to the stiffness of the side plates of the front and rear wheels, respectively. a、b These are the distances from the front axle and rear axle to the center of mass, respectively. v x This refers to the longitudinal speed of the vehicle. m For vehicle quality; I z The vehicle's moment of inertia; l f and l n These are the driver's long and short aiming distances, respectively. δ fd and δ fc These are the front wheel steering angles input by the driver and the controller, respectively. e d and e φ These are the vehicle's lateral position error and heading error, respectively. R g For steering ratio, δ d =R g *δ fd ; S4. Derive the shared controller based on LQR and feedforward control, solve for the feedback and feedforward control quantities, and define the stiffness parameters of the shared controller. S41. Construct LQR state-space feedback and design feedforward control to eliminate the steady-state error caused by the third term of the driver-road-vehicle state-space equation; the objective function for LQR state-space feedback optimization is: In the formula, Q and R are the weight matrices of the state variables and control variables in the optimization objective of LQR, respectively. q 1 、q 2 、q 3 、q 4 and r These are weight values; S42. Constructing the recursive formula of the Riccati equation based on LQR state-space feedback: Further, the state feedback gain is obtained: S43. Feedback the state obtained from LQR. -Kx With feedforward control quantity δ f Added as control quantity δ fc =-Kx+δ f Substitute the error state space equations of the two-degree-of-freedom vehicle dynamics model and solve for the feedforward control quantity. Substituting the control variables into the driver-road-vehicle state-space equations, we obtain: Once the vehicle system stabilizes, there is ,then: In the formula, K k This is a one-dimensional column vector composed of rows 1-4 of the LQR state feedback matrix. K 1 、K 3 For K k The first and third row elements; S5. A human-machine co-driving experiment was conducted on a driving simulator to verify the results.

2. The method for constructing a human-machine collaborative steering framework based on LQR and feedforward control according to claim 1, characterized in that, S1 employs a two-point preview strategy to describe the driver's preprocessing of the road ahead, and introduces a second-order response process to describe the driver's neural and muscular decision-making and reaction processes; the s-domain expression of the second-order driver model is: ； In the formula, Kp , Kc These represent the driver's aiming gain and compensation gain, respectively. θ f , θ n These represent the near and far visual angles in the driver's dual-point preview model, respectively. τ 1 , τ 2 These represent the delay in the driver's brain decision-making and the delay in muscle information transmission, respectively. δ d This indicates the actual steering wheel angle turned by the driver.

3. The method for constructing a human-machine cooperative steering framework based on LQR and feedforward control according to claim 1, characterized in that, To ensure the lateral error of the vehicle is zero after stabilization, the formula for calculating the feedforward control quantity is obtained, namely: 。 4. The method for constructing a human-machine cooperative steering framework based on LQR and feedforward control according to claim 1, characterized in that, The controller stiffness parameter λ characterizes the proportion of the driver's and controller's inputs acting on the vehicle's steering system, i.e., the actual control angle input of the vehicle is: 。

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