A neural network adaptive multi-axis vehicle tracking control method and system based on obstacle function

Abstract

The present invention relates to a neural network adaptive multi-axis vehicle tracking control method and system based on an obstacle function. The system comprises a data acquisition module, an ideal state calculation module, a vehicle motion control module and a neural network approximation module. The method collects vehicle state and position information according to vehicle sensors through the data acquisition module, and then establishes a multi-axis steering vehicle system dynamics model and a state tracking control model that take into account system parameter uncertainty, road roughness and unknown external disturbances through the vehicle motion control module. Based on the established state tracking control model, an adaptive integral sliding mode anti-interference controller based on the obstacle function is constructed to avoid the influence of unknown interference on control performance and weaken the sliding mode chattering phenomenon. Finally, the neural network approximation module is used to approximate the unknown part of the system to improve the robustness of the controller. At the same time, an online network weight adaptive law is designed taking into account network efficiency to improve the tracking performance of the multi-axis steering vehicle.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-axis vehicle control, in particular to a neural network adaptive multi-axis vehicle tracking control method and system based on an obstacle function. Background Art

[0002] As an indispensable core equipment in modern engineering construction and economic development, multi-axle steering vehicles are widely used in many fields such as large-scale wind power equipment installation, resource mining and transportation in harsh environments, and emergency rescue material transfer, and are developing towards electrification and intelligence. However, due to the increase in the number of axles, more complex structure, and more severe and changeable driving environment of multi-axle steering vehicles, the changes in vehicle parameters lead to inaccurate dynamic modeling and susceptibility to external unknown disturbances. Traditional tracking control methods are difficult to achieve excellent control performance under these conditions, resulting in poor vehicle tracking performance. Therefore, it is urgent to design a path tracking control system and method with strong robustness and high tracking accuracy, which can resist the influence of changes in internal system parameters and unknown external disturbances, achieve high-precision trajectory tracking of multi-axle steering vehicles while ensuring their driving stability, so as to meet the requirements of flexible and efficient modern transportation. There are existing issues regarding achieving anti-interference and precise tracking motion control of vehicles. For example, reference patent CN117369287A proposes a robust super-helical sliding mode control method for multi-axis vehicles. It constructs a robust super-helical mode controller consisting of a nominal control law and a switching control law. The nominal control law is designed based on model predictive control to achieve system stability control, and the switching control law is designed based on super-helical sliding mode control. A variable gain function is constructed to suppress internal and external disturbances in the system, weaken the sliding mode control chattering, and improve the multi-axis vehicle trajectory tracking performance. For example, reference patent CN116679571A proposes a multi-axis vehicle tracking control method based on a dual-loop neural network. By designing the optimal nominal control law and the switching control law, the robustness of the entire tracking control system is improved. The dual-feedback loop neural network is also applied to the optimal integral sliding mode controller to approximate the unknown part of the multi-axis vehicle dynamics system and improve the multi-axis vehicle tracking performance. Although these control methods have good anti-interference performance and good tracking performance, they still have some shortcomings and limitations, which are mainly manifested as follows:

[0003] (1) Traditional tracking control methods often rely too much on accurate dynamic models, but multi-axis steering vehicles have strong nonlinear characteristics, and the relationships between various subsystems are more coupled and complex. In addition, there are factors such as parameter changes and external disturbances during actual driving, which increase the uncertainty of the multi-axis steering vehicle system, resulting in a decrease in the control performance of the traditional tracking controller, and thus causing the multi-axis steering vehicle's driving trajectory to shift. Although neural networks are currently commonly used to approximate nonlinear system uncertainties and address the impact of nonlinear system uncertainties on controller performance, for closed-loop systems, the traditional method of using gradient descent to obtain neural network weights can often only guarantee local optimality, but cannot guarantee global asymptotic stability, and is prone to divergence.

[0004] (2) Neural networks can address the impact of system uncertainties on controller performance. However, due to the complex and changeable driving environment of multi-axis steering vehicles, they are easily affected by external unknown disturbances, making it difficult to determine the control parameters. Although traditional adaptive control methods have a certain degree of robustness to external unknown disturbances, they often require the prediction of the upper bound of external unknown disturbances in advance. Due to the structural characteristics of the multi-axis steering vehicle itself and the driving environment factors, external unknown disturbances are always difficult to accurately estimate, resulting in poor control performance of the adaptive controller and poor multi-axis steering vehicle trajectory tracking accuracy. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a neural network adaptive multi-axis vehicle tracking control method and system based on obstacle function, which is beneficial to improving the trajectory tracking performance of multi-axis steering vehicles under time-varying system parameters and external unknown disturbances.

[0006] To achieve the above object, the present invention adopts the following technical solution: a neural network adaptive multi-axis vehicle tracking control method based on an obstacle function, comprising the following steps:

[0007] Step S1: A driver model is established in the ideal state calculation module. Based on the desired path information, real-time vehicle position information, and vehicle state information collected by the data acquisition module, the ideal yaw rate and sideslip angle required for the multi-axis steering vehicle to track the desired path are calculated, and the state error is obtained and sent to the vehicle motion control module.

[0008] Step S2: In the vehicle motion control module, the system parameter uncertainty, road irregularities, and unknown external disturbances of the multi-axis steering vehicle model are considered to establish a multi-axis steering vehicle dynamics model and a tracking control model;

[0009] Step S3: In the vehicle motion control module, an adaptive integral sliding mode controller based on a barrier function is constructed according to the tracking control model established in step S2 to suppress the influence of unknown disturbances on the system control performance and reduce the chattering phenomenon that occurs during the sliding mode control process;

[0010] Step S4: In the neural network approximation module, a three-layer neural network is established to approximate the unknown parts of the multi-axis steering vehicle dynamics system. The Lyapunove stability theory is used to design an online network weight adaptation law to enhance the tracking control performance of the multi-axis steering vehicle and ensure the stability and convergence of the closed-loop system.

[0011] Step S5: Based on the stability theory, it is proved that the designed controller can ensure the stability and convergence of the entire closed-loop system and enhance the tracking performance of the multi-axis steering vehicle;

[0012] Step S6: Based on the turning angle signal of the multi-axis steering vehicle obtained by the motion controller, a command is sent to the actuator to adjust the turning angle of each axis to the required angle, change the vehicle motion state, and realize tracking control.

[0013] In a preferred embodiment, the method for obtaining the ideal state required for multi-axis steering vehicle trajectory tracking in step S1 is:

[0014]

[0015] Where, γ pre is the vehicle yaw rate obtained by preview, Δy is the vertical distance between the vehicle center of mass and the preview point, v x is the vehicle longitudinal velocity, t p is the preview time, β is the vehicle's center of mass side slip angle, θ is the center angle of the vehicle's current trajectory, and x GC is the longitudinal distance between the vehicle's center of mass and the preview point, γ z is the actual yaw rate of the vehicle, γ d is the ideal yaw rate of the vehicle, μ max is the maximum adhesion coefficient that the ground can provide, and g is the acceleration due to gravity;

[0016] The ideal center of mass sideslip angle β is required during vehicle driving d is 0°, that is:

[0017] β d =0.

[0018] In a preferred embodiment, the method for establishing the multi-axis steering vehicle dynamics model and tracking control model in step S2 is as follows:

[0019]

[0020] Where, FX and F Y are the resultant forces of the vehicle along the X-axis and Y-axis, M Z is the yaw moment of the vehicle around the Z axis, m is the vehicle mass, v x and v y are the vehicle longitudinal velocity and lateral velocity, is the vehicle longitudinal acceleration, is the rate of change of the sideslip angle of the center of mass, γ is the yaw angle of the vehicle, is the vehicle yaw angular acceleration, I z is the moment of inertia of the vehicle around the Z axis, F xil and F xir are the longitudinal forces of the i-th tire on the left and right sides, respectively, F yil and F yir are the lateral forces of the i-th tire on the left and right sides, δ il and δ ir Divided into the turning angle of the i-th tire on the left and right sides, L i represents the distance from the center of mass of the vehicle to the i-th axle, where the axle in front of the center of mass is positive and the axle behind the center of mass is negative, n is the number of axles of the vehicle, and b is the vehicle wheelbase;

[0021] The expression of the vehicle lateral force is:

[0022] F yi =k i α i

[0023]

[0024] Where k i is the cornering stiffness of the vehicle tire, α i is the side slip angle of the vehicle tire; δ i is the tire turning angle;

[0025] The tracking control problem of the multi-axle steering vehicle is transformed into a state tracking control problem, and accurate trajectory tracking control is achieved by independently controlling the steering of each axle of the multi-axle steering vehicle. According to the above multi-axle steering vehicle dynamics model, the system state tracking control model is derived:

[0026]

[0027] Where β is the sideslip angle of the center of mass, d1 and d2 are unknown disturbances, It is a custom function and can be obtained as follows:

[0028]

[0029]

[0030] To further reflect the influence of wheel angle on the motion characteristics of multi-axle steering vehicles, the first and last axle angles are controlled, and the remaining wheel angles are obtained using the following Ackerman steering relationship:

[0031]

[0032]

[0033]

[0034] Where x0 and y0 are the coordinates of the instantaneous steering center; let the state variable x = [γ, β] T , is the first-order derivative of the state variable, and the system state tracking control model is reconstructed as:

[0035]

[0036] in,

[0037]

[0038] Where y is the output of the system, u is the control input of the system and u=[δ1,…,δ n ] T , d(t) is the external unknown disturbance, including road disturbance, and the system is not modeled dynamics. Let F = Ax + d(t) represent the uncertainty term of the system function.

[0039] In a preferred embodiment, the implementation method of designing the adaptive integral sliding mode controller based on the barrier function in step S3 is:

[0040] According to the multi-axis steering vehicle tracking control model, the nonlinear dynamic equations of the control-oriented multi-axis steering vehicle system can be reformulated as:

[0041]

[0042] F=Ax+D+d(t)

[0043] in,

[0044]

[0045] The state tracking error of the multi-axis steering vehicle is selected to construct the integral sliding membrane surface S, which is expressed as follows:

[0046]

[0047] x e =xx d

[0048] Where xe is the system state tracking error, x d =[γ d ,β d ] T is the ideal state vector of the system, λ and P(t) are controller parameters and satisfy P(t) = exp(-ρt), where ρ is a positive number; combined with the state tracking error equation, the differential expression of the integral sliding surface S is as follows:

[0049]

[0050] make Integral sliding mode equivalent control law u eq The expression is as follows:

[0051]

[0052] Construct robust control law u according to the exponential convergence law rc As shown below:

[0053] u rc (t) = B -1 (-Ksat(S)-η(ε 2 -S 2 )S)

[0054] Where K = diag(K1, K2) > 0 is a custom parameter, η = diag(η1, η2) > 0 is a custom parameter, ε is the boundary value of the custom sliding surface, and satisfies |S| ≤ ε, sat(S) is the saturation function instead of the sign function sat(S), and its expression is:

[0055]

[0056] The integral sliding mode control law u is further obtained as follows:

[0057]

[0058] Based on the barrier function, the adaptive gain control law is constructed as follows:

[0059]

[0060]

[0061] Where, is the adaptive control parameter, t a is the minimum time that the sliding surface satisfies |S|<(ε / 2) during the control process.

[0062] In a preferred embodiment, the method for implementing the use of a neural network to approximate the unknown part of the multi-axis steering vehicle dynamics system in step S4 is as follows:

[0063] The approximate function of the neural network is used to approximate the unknown nonlinear function in the system. The neural network structure used is divided into three layers: input layer, hidden layer, and output layer, as shown below:

[0064]

[0065]

[0066] F=ω *T H i (x j )+ε e

[0067] Where x j is the network input vector, j is the number of input networks, i is the number of hidden layer nodes, H i (x j ) is the Gaussian basis function in the hidden layer, c ij and b i are the center vector and width of the Gaussian basis function, F is the network output, ω * is the optimal weight vector of the network, ε e is the network approximation error, and satisfies |ε e |≤ε N , ε N is the maximum error;

[0068] The function uncertainty F = Ax + d(t) is reconstructed as:

[0069]

[0070] Where, is the network output approximation; then the control law u is redefined as:

[0071]

[0072] In a preferred embodiment, the method for designing the online network weight adaptation law based on the Lyapunov theory in step S4 is:

[0073] According to the reconstructed control law u, the differential expression of the integral sliding surface S is as follows:

[0074]

[0075] in,

[0076]

[0077] Where, is the network approximation error, is the network weight error. In addition, there is an upper bound θ on the error that satisfies

[0078] According to Lyapunov's stability theorem, the system state quickly converges to the sliding surface S, and the network error To converge to zero in a finite time and be in a globally stable state, the neural network weight adaptation law should meet the following conditions:

[0079]

[0080] Where Γ is a positive matrix and tr(·) represents the trace of the matrix.

[0081] In a preferred embodiment, the stability proof in step S5 is implemented as follows:

[0082] The proof consists of the following two steps:

[0083] Proof: Step 51, when 0≤t≤t a , controller gain K = K a , the selected Lyapunov function is expressed as follows:

[0084]

[0085] Where, K * is a custom parameter and satisfies and ε N <θ<K a <K * ; The differential expression of the Lyapunov function V1 is as follows:

[0086]

[0087] Prove the stability of the system. In addition, S, K a -K * 、 are all bounded; further proof is as follows: Select Lyapunov function to express as follows:

[0088]

[0089] The differential expression of the Lyapunov function V2 is obtained as follows:

[0090]

[0091] According to 0<H i (x j )<1, Conclusion Thus we get Therefore, it is inferred and Right now:

[0092]

[0093] According to the above proof, it can be concluded that the sliding surface S will converge to This proves that step 51 is completed;

[0094] Step 52, when t≥t a , controller gain K = K b , the selected Lyapunov function is expressed as follows:

[0095]

[0096] The differential expression of the Lyapunov function V3 is obtained as follows:

[0097]

[0098] Where, is a custom parameter, and the custom parameter S a satisfy:

[0099]

[0100] For any |ζ|, there always exists S a <ε; In addition, for |S|>S a , there exists K b (S)>K(S a )=|ζ|≥ε N >ε e , we get (K b2 -ε e )|S T |>0 and (K b2 -|ξ|)|K b2 |>0; thus it is proved that the sliding surface S can be a It converges asymptotically under the condition; it is further proved that the sliding surface S converges to |S|≤S in a finite time. a <ε, as shown below:

[0101] The Lyapunov function is chosen to be expressed as follows:

[0102]

[0103] The differential expression of the Lyapunov function V4 is obtained as follows:

[0104]

[0105] According to K b (S)>K(Sa )=|ζ|≥ε N >ε e ,get and Right now:

[0106]

[0107] Therefore, for t ≥ t a , the sliding surface S can converge to |S|≤S a <ε and ensure system stability.

[0108] The present invention also provides a neural network adaptive multi-axis vehicle tracking control system based on an obstacle function, and the operation of the neural network adaptive multi-axis vehicle tracking control method based on an obstacle function includes:

[0109] Data acquisition module, including wheel angle sensor, wheel speed sensor, vehicle speed sensor, yaw rate sensor, and lidar sensor;

[0110] An ideal state calculation module is used to calculate the ideal yaw rate and sideslip angle required for the multi-axis steering vehicle to track the desired path based on the desired path information and the real-time vehicle position and state information obtained by the data acquisition module, and send this information to the vehicle motion control module;

[0111] The vehicle motion control module includes establishing a multi-axle steering vehicle dynamics model and a state tracking control model that take into account the uncertainty of the multi-axle steering vehicle model system parameters, road roughness, and unknown external disturbances. An adaptive integral sliding mode anti-interference controller based on the barrier function is designed based on the state error to control the wheel angles of each axle of the multi-axle steering vehicle and avoid the influence of external unknown disturbances on the controller.

[0112] The neural network approximation module applies neural networks to the adaptive controller to approximate the unknown parts of the multi-axis steering vehicle dynamics system, improving the robustness of system control under model parameter uncertainty. It also uses Lyapunov stability theory to design an online network weight adaptation law to update the network weights in real time, avoiding the local optimality defects of the traditional gradient descent method.

[0113] Compared with the prior art, the present invention has the following beneficial effects:

[0114] 1) This invention addresses the issues of trajectory tracking controller performance degradation and vehicle trajectory deviation during the actual operation of multi-axle steering vehicles, which are caused by factors such as strong dynamic nonlinear interference in the system, changes in the driving environment, and external unknown disturbances. By combining the characteristics of the barrier function with the integral sliding mode control method, an adaptive integral sliding mode controller based on the barrier function is designed to control the rotation angles of each axle of the multi-axle steering vehicle for trajectory tracking. This controller overcomes the shortcomings of traditional adaptive methods and eliminates the need for accurate information on the upper bound of external disturbances, ensuring that system variables converge to a preset range within a finite time. Simultaneously, it reduces chattering in the sliding mode control, improves controller performance, and thus enhances vehicle trajectory tracking accuracy.

[0115] 2) The present invention addresses the problem that the time-varying problem of model parameters of multi-axis steering vehicles leads to poor controller performance and makes it difficult to further improve tracking accuracy. A neural network is used to approximate the unknown nonlinear function of the system and is applied to an obstacle adaptive integral sliding mode controller to improve the robustness of the controller. An online network weight adaptation law is designed based on the Lyapunov stability theory to overcome the defects of the traditional gradient descent method for obtaining network weights, which can only guarantee local optimality and is prone to divergence. This allows the controller to obtain good approximate performance even under arbitrary initial value conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Figure 1 This is a block diagram of the control flow principle of an embodiment of the present invention;

[0117] Figure 2 The plane dynamics model of the multi-axle steering vehicle in the embodiment of the present invention;

[0118] Figure 3 Schematic diagram of the Ackerman steering principle of each axle of a multi-axle steering vehicle in an embodiment of the present invention;

[0119] Figure 4 1 is an overall architecture diagram of a neural network adaptive integral sliding mode control method based on a barrier function in an embodiment of the present invention;

[0120] Figure 5 2 is a schematic diagram of a preview reference trajectory in an embodiment of the present invention;

[0121] Figure 6 is a schematic diagram of an obstacle function in an embodiment of the present invention;

[0122] Figure 7 Schematic diagram of the neural network structure in an embodiment of the present invention;

[0123] Figure 8: These are trajectory tracking effect diagrams of a multi-axle steering vehicle under the designed control system and method in an embodiment of the present invention, where (a) is the desired trajectory tracking effect diagram, (b) is the lateral tracking error, (c) is the ideal yaw rate tracking effect, (d) is the error in tracking the ideal yaw rate, (e) is the error in tracking the ideal center of mass sideslip angle, and (f) is the neural network approximation effect diagram. DETAILED DESCRIPTION

[0124] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0125] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present application belongs.

[0126] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form, and it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0127] like Figure 1-8 As described above, this embodiment provides a neural network adaptive multi-axis vehicle tracking control method based on an obstacle function, which includes a data acquisition module, an ideal state calculation module, a vehicle motion control module, and a neural network approximation module.

[0128] The data acquisition module includes a wheel angle sensor, a wheel speed sensor, a vehicle speed sensor, a yaw rate sensor, a lidar sensor, etc.

[0129] The ideal state calculation module is used to calculate the ideal yaw rate and sideslip angle required for the multi-axis steering vehicle to track the desired path based on the desired path information and the real-time vehicle position and state information obtained by the data acquisition module, and send the information to the vehicle motion control module;

[0130] The vehicle motion control module includes a multi-axle steering vehicle dynamics model and a state tracking control model that take into account the uncertainty of the multi-axle steering vehicle model system parameters, road irregularities, and unknown external disturbances. An adaptive integral sliding mode anti-interference controller based on the obstacle function is designed based on the state error to control the wheel angles of each axle of the multi-axle steering vehicle and avoid the influence of external unknown disturbances on the controller.

[0131] The neural network approximation module applies a neural network to an adaptive controller to approximate the unknown parts of the multi-axis steering vehicle dynamics system, improving the robustness of system control under model parameter uncertainty. It also uses Lyapunov stability theory to design an online network weight adaptation law to update the network weights in real time, avoiding the local optimality defects of the traditional gradient descent method.

[0132] Figure 2 For the multi-axis steering vehicle planar dynamics model and Ackerman steering principle schematic diagram in this embodiment, a lateral dynamics model including the lateral motion and yaw motion of the multi-axis steering vehicle system is established.

[0133] Figure 3 This is a geometric diagram of various turning angle relationships determined based on the Ackerman steering principle for a multi-axle steering vehicle in this embodiment. The turning angle geometric relationship of each axle is determined by the turning angles of the first and last axles to achieve all-wheel steering of the vehicle.

[0134] Figure 4 The overall architecture of the neural network adaptive integral sliding mode control method based on the obstacle function in this embodiment is as follows: First, the ideal yaw rate γ of the vehicle under the desired trajectory is obtained through the preview path tracking control model. d Side slip angle β from the ideal center of mass d ; Then, an adaptive integral sliding mode control law u based on the barrier function is designed to control the steering angle of each axle of the vehicle, so as to realize automatic adjustment of the control gain without predicting the upper limit of the external unknown disturbance of the control state variable, and ensure that the system converges to the preset range within a finite time, while reducing the chattering in the sliding mode control; finally, the neural network is applied to the adaptive controller to approximate the unknown part of the multi-axis steering vehicle dynamics system, and an online network weight adaptive law is designed based on the Lyapunov stability theory to update the network weight in real time, avoiding the local optimal defect of the traditional gradient descent method, and realizing high-precision trajectory tracking control of the multi-axis steering vehicle while ensuring driving stability.

[0135] Figure 5 This is a schematic diagram of the preview reference trajectory in this embodiment. The longitudinal distance from the current position of the multi-axis steering vehicle through the preview is x GC , the point with a horizontal distance of Δy is calculated at the set preview time t p The center angle θ of the trajectory taken by the inner vehicle to reach the preview point is used to obtain the ideal yaw rate γ of the vehicle d .

[0136] In this embodiment, a three-axle steering test vehicle built in the laboratory is taken as an example, and its vehicle parameters are as follows:

[0137]

[0138]

[0139] The following is a further detailed explanation of the relevant contents involved in this method.

[0140] In step S1, a driver model is established in the ideal state calculation module. Based on the desired path information, real-time vehicle position information, and vehicle state information collected by the data acquisition module, the ideal yaw rate and sideslip angle required for the multi-axis steering vehicle to track the desired path are calculated. The state error is then obtained and sent to the vehicle motion control module. The expression describing the driver model is as follows:

[0141]

[0142] Where, γ pre is the vehicle yaw rate obtained by preview, Δy is the vertical distance between the vehicle center of mass and the preview point, v x is the vehicle longitudinal velocity, t p is the preview time and t p =2, β is the vehicle's center of mass side slip angle, θ is the center angle of the vehicle's current trajectory, x GC is the longitudinal distance between the vehicle's center of mass and the preview point, γ z is the actual yaw rate of the vehicle, γ d is the ideal yaw rate of the vehicle, μ max is the maximum adhesion coefficient that the ground can provide, g is the acceleration due to gravity and g=9.8.

[0143] In order to ensure the tracking stability of multi-axis steering vehicles, it is generally required that the ideal center of mass side slip angle β d is 0°, that is:

[0144] β d =0

[0145] In step S2, the vehicle motion control module establishes a 2-DOF lateral dynamics model of the multi-axis steering vehicle, taking into account the system parameter uncertainty, road irregularities, and unknown external disturbances of the multi-axis steering vehicle model to reduce modeling complexity. The expressions describing the vehicle's lateral and yaw motions are as follows:

[0146]

[0147]

[0148] Where, F Y is the resultant force of the vehicle along the X-axis and Y-axis, M Z is the yaw moment of the vehicle around the Z axis, m is the vehicle mass, v x is the longitudinal velocity of the vehicle, is the rate of change of the sideslip angle of the center of mass, γ is the yaw angle of the vehicle, is the vehicle yaw angular acceleration, I z is the moment of inertia of the vehicle around the Z axis, F xil and F xir are the longitudinal forces of the i-th tire on the left and right sides, respectively, F yil and F yir are the lateral forces of the i-th tire on the left and right sides, δ il and δ ir Divided into the turning angle of the i-th tire on the left and right sides, L i It represents the distance from the center of mass of the vehicle to the i-th axle, where the axle in front of the center of mass is positive and the axle behind the center of mass is negative, n is the number of axles of the vehicle, and b is the vehicle wheelbase.

[0149] Generally speaking, the tire slip angle is always assumed to be within a small area, and the lateral force on the left and right wheels is assumed to be the same. Therefore, by assuming a linear relationship between the lateral force and the slip angle of each wheel of a multi-axle steering vehicle, the expression is as follows:

[0150] F yil =F yir =F yi =k i α i

[0151]

[0152] Where k i is the cornering stiffness of the vehicle tire, α i is the side slip angle of the vehicle tire.

[0153] Furthermore, the lateral dynamics equation of the multi-axle steering vehicle can be reconstructed as:

[0154]

[0155]

[0156] Where d1 and d2 represent unknown disturbances in the system. The above equation can be rewritten as:

[0157]

[0158] Where, It is a custom function and can be obtained as follows:

[0159]

[0160]

[0161] To further reflect the influence of wheel angles on the motion characteristics of multi-axle steering vehicles, by controlling the first and last axle angles, the remaining wheel angles can be obtained through the following Ackerman steering relationship:

[0162] according to Figure 3 As shown, the wheel center coordinates x1 of the first axis are (L1,0), and the wheel center coordinates x n (L n ,0), the instantaneous steering center coordinate o of the vehicle is expressed as (x0,y0). According to the geometric relationship, we can derive the following equation:

[0163]

[0164] According to the above equation, the instantaneous steering center coordinates can be calculated as:

[0165]

[0166] Therefore, the wheel steering of the remaining axles of the vehicle can be expressed by the Ackermann steering relationship as follows:

[0167]

[0168]

[0169]

[0170] Let the state variable x = [γ, β] T , The tracking control problem of a multi-axle steering vehicle is transformed into a state tracking control problem, and dynamic tracking is achieved by controlling the wheel angles of each axle of the multi-axle steering vehicle. Therefore, the nonlinear dynamic equation of the control-oriented multi-axle steering vehicle system can be expressed as:

[0171]

[0172] in,

[0173]

[0174] Where y is the output of the system, u is the control input of the system and u=[δ1,…,δ n ] T , d(t) is the external unknown disturbance, including road interference, unmodeled system dynamics, etc. Let F = Ax + d(t) represent the uncertainty term of the system function.

[0175] In step S3, an adaptive integral sliding mode controller based on a barrier function is constructed in the vehicle motion control module to suppress the impact of unknown disturbances on the system control performance and weaken the chattering phenomenon that occurs during the sliding mode control process. The novel adaptive controller is designed as follows:

[0176] According to the multi-axis steering vehicle tracking control model, the nonlinear dynamic equations of the control-oriented multi-axis steering vehicle system can be reformulated as:

[0177]

[0178] F=Ax+D+d(t)

[0179] in,

[0180] u=[δ1,δ n ] T ,

[0181] In order to ensure that the system state tracking error converges quickly in a finite time, the state tracking error of the multi-axis steering vehicle is selected to construct the integral sliding membrane surface S, which is expressed as follows:

[0182]

[0183] x e =xx d

[0184] Where x e is the system state tracking error, x d =[γ d ,β d ] T is the ideal state vector of the system, λ and P(t) are controller parameters and satisfy P(t) = exp(-ρt), where ρ is a positive number. Combined with the state tracking error equation, the differential expression of the integral sliding surface S is as follows:

[0185]

[0186] make Integral sliding mode equivalent control law u eq The expression is as follows:

[0187]

[0188] In order to ensure the stability of the system state on the sliding surface, ensure that the system converges to the sliding surface quickly within a limited time, and reduce system chattering, a robust control law u is constructed according to the exponential convergence law. rc As shown below:

[0189] u rc (t) = B -1 (-Ksat(S)-η(ε 2 -S 2 )S)

[0190] Where K = diag(K1, K2) > 0 is a custom parameter, η = diag(η1, η2) > 0 is a custom parameter, ε is the boundary value of the custom sliding surface, and satisfies |S| ≤ ε, sat(S) is the saturation function instead of the sign function sat(S), and its expression is:

[0191]

[0192] The integral sliding mode control law u is further obtained as follows:

[0193]

[0194] Since multi-axis steering vehicles are easily affected by unknown external disturbances during driving, the control gain K of the integral sliding mode changes dynamically and is difficult to determine. In order to ensure the selection of appropriate control gain under unknown external disturbances, based on the barrier function, its structure is as follows Figure 6 As shown, the adaptive gain control law is constructed as follows:

[0195]

[0196]

[0197] Where, is the adaptive control parameter, t a is the minimum time that the sliding surface satisfies |S|<(ε / 2) during the control process.

[0198] In step S4, the neural network is used to approximate the unknown parts of the multi-axis steering vehicle dynamics system, and the Lyapunov stability theory is used to design an online network weight adaptation law to enhance the tracking control performance of the multi-axis steering vehicle and ensure the stability and convergence of the closed-loop system. The structure of the neural network is as follows: Figure 7 As shown, it is divided into three layers: input layer, hidden layer, and output layer, as shown below:

[0199]

[0200]

[0201] F=ω *T H i (x j )+ε e

[0202] Where x j is the network input vector, j is the number of input networks, i is the number of hidden layer nodes, H i (x j ) is the Gaussian basis function in the hidden layer, c ij and b iare the center vector and width of the Gaussian basis function, F is the network output, ω * is the optimal weight vector of the network, ε e is the network approximation error, and satisfies |ε e |≤ε N , ε N is the maximum error value.

[0203] Therefore, the function uncertainty F = Ax + d(t) can be reconstructed as:

[0204]

[0205] Where, is the network output approximation. Then the control law u can be redefined as:

[0206]

[0207] Among them, the implementation method of designing the online network weight adaptation law based on Lyapunov theory is:

[0208] According to the reconstructed control law u, the differential expression of the integral sliding surface S is as follows:

[0209]

[0210] in,

[0211]

[0212] Where, is the network approximation error, is the network weight error. In addition, there is an upper bound θ on the error that satisfies

[0213] In order to avoid the divergence phenomenon that the traditional gradient descent method can only guarantee the local optimum and cannot guarantee the global asymptotic stability, the system state is quickly converged to the sliding surface S according to the Lyapunov stability theorem. Converging to zero in a finite time and being in a globally stable state, the neural network weight adaptive law acquisition process is as follows:

[0214] First, the chosen Lyapunov function is expressed as follows:

[0215]

[0216] Where Γ is a positive matrix and tr(·) represents the trace of the matrix. The differential expression of the Lyapunov function V is as follows:

[0217]

[0218] To meet the requirements of Lyapunov's stability theorem Design the following adaptive law:

[0219]

[0220] therefore, Can be refactored as:

[0221]

[0222] In the formula, since there are always positive numbers K and η, and satisfy K>>|ε e |, thus we can get:

[0223]

[0224] In step S5, the stability of the designed neural network adaptive integral sliding mode controller based on the barrier function is proved as follows:

[0225] The proof consists of the following two steps:

[0226] Proof: Step 1, when 0≤t≤t a , controller gain K = K a , the selected Lyapunov function is expressed as follows:

[0227]

[0228] Where, K * is a custom parameter and satisfies and ε N <θ<K a <K * The differential expression of the Lyapunov function V1 is as follows:

[0229]

[0230] Therefore, the above proves the stability of the system. In addition, S, K a -K * 、 are bounded. However, this is not a necessary condition to ensure that the system converges under any initial conditions, so further proof is as follows:

[0231] The Lyapunov function is chosen to be expressed as follows:

[0232]

[0233] The differential expression of the Lyapunov function V2 is obtained as follows:

[0234]

[0235] According to 0<H i (x j )<1, We can conclude that Thus we can get Therefore, it can be inferred that and Right now:

[0236]

[0237] According to the above proof, it can be concluded that the sliding surface S will converge to This proves that step 1 is completed.

[0238] Step 2: When t≥t a , controller gain K = K b , the selected Lyapunov function is expressed as follows:

[0239]

[0240] The differential expression of the Lyapunov function V3 is obtained as follows:

[0241]

[0242] Where, is a custom parameter, and the custom parameter S a satisfy:

[0243]

[0244] For any |ζ|, there always exists S a <ε. In addition, for |S|>S a , there exists K b (S)>K(S a )=|ζ|≥ε N >ε e , so we can get (K b2 -ε e )|S T |>0 and (K b2 -|ξ|)|K b2 |>0. This proves that the sliding surface S can be a To further prove that the sliding surface S can converge to |S|≤S in a finite time, a <ε, as shown below:

[0245] The Lyapunov function is chosen to be expressed as follows:

[0246]

[0247] The differential expression of the Lyapunov function V4 is obtained as follows:

[0248]

[0249] According to K b (S)>K(S a )=|ζ|≥ε N >ε e ,available and Right now:

[0250]

[0251] Therefore, for t ≥ t a , the sliding surface S can converge to |S|≤S a <ε and ensure system stability.

[0252] The present invention provides a neural network adaptive multi-axis vehicle tracking control method based on an obstacle function. This method addresses the problem of multi-axis steering vehicle tracking control under time-varying system parameters and unpredictable external unknown disturbances. A neural network adaptive integral sliding mode control method based on an obstacle function is proposed to ensure that the multi-axis steering vehicle can avoid the degradation of tracking control performance and driving trajectory deviation caused by the influence of unknown disturbances inside and outside the system during actual driving, and the problem that traditional adaptive control methods are limited by the upper bound of external unknown disturbances and the traditional gradient descent method for obtaining network weights can only ensure local optimality and the tracking accuracy is difficult to further improve.

[0253] Figure 8 The figure shows the trajectory tracking effect comparison between the multi-axle steering vehicle under the designed controller in this embodiment and other controllers. According to the neural network adaptive integral sliding mode control method based on the obstacle function of the present invention, the three-axle steering experimental vehicle can achieve accurate trajectory tracking under time-varying system parameters and external unknown disturbances, while ensuring vehicle driving stability. Figure 8 shown.

[0254] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0255] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0256] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0257] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0258] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other manner. Any person skilled in the art may utilize the above-disclosed technical content to modify or modify the present invention into equivalent embodiments. However, any simple modifications, equivalent variations, and modifications to the above embodiments that do not depart from the technical content of the present invention and are based on the technical essence of the present invention remain within the scope of protection of the present invention.

Claims

1. A neural network adaptive multi-axis vehicle tracking control method based on obstacle function, characterized in that: The following steps are involved: Step S1: A driver model is established in the ideal state calculation module. Based on the desired path information, real-time vehicle position information, and vehicle state information collected by the data acquisition module, the ideal yaw rate and sideslip angle required for the multi-axis steering vehicle to track the desired path are calculated, and the state error is obtained and sent to the vehicle motion control module. Step S2: In the vehicle motion control module, the system parameter uncertainty, road irregularities, and unknown external disturbances of the multi-axis steering vehicle model are considered to establish a multi-axis steering vehicle dynamics model and a tracking control model; Step S3: In the vehicle motion control module, an adaptive integral sliding mode controller based on a barrier function is constructed according to the tracking control model established in step S2 to suppress the influence of unknown disturbances on the system control performance and reduce the chattering phenomenon that occurs during the sliding mode control process; Step S4: In the neural network approximation module, a three-layer neural network is established to approximate the unknown parts of the multi-axis steering vehicle dynamics system. The Lyapunove stability theory is used to design an online network weight adaptation law to enhance the tracking control performance of the multi-axis steering vehicle and ensure the stability and convergence of the closed-loop system. Step S5: Based on the stability theory, it is proved that the designed controller can ensure the stability and convergence of the entire closed-loop system and enhance the tracking performance of the multi-axis steering vehicle; Step S6: Based on the turning angle signal of the multi-axis steering vehicle obtained by the motion controller, a command is sent to the actuator to adjust the turning angle of each axis to the required angle, change the vehicle motion state, and realize tracking control.

2. The neural network adaptive multi-axis vehicle tracking control method based on obstacle function according to claim 1 is characterized in that: The method for obtaining the ideal state required for multi-axis steering vehicle trajectory tracking in step S1 is: Where, γ pre is the vehicle yaw rate obtained by preview, Δy is the vertical distance between the vehicle center of mass and the preview point, v x is the vehicle longitudinal velocity, t p is the preview time, β is the vehicle's center of mass side slip angle, θ is the center angle of the vehicle's current trajectory, and x GC is the longitudinal distance between the vehicle's center of mass and the preview point, γ z is the actual yaw rate of the vehicle, γ d is the ideal yaw rate of the vehicle, μ max is the maximum adhesion coefficient that the ground can provide, and g is the acceleration due to gravity; The ideal center of mass sideslip angle β is required during vehicle driving d is 0°, that is: β d ＝0。 3. The neural network adaptive multi-axis vehicle tracking control method based on obstacle function according to claim 1 is characterized in that: The method for establishing the multi-axis steering vehicle dynamics model and tracking control model in step S2 is as follows: Where, F X and F Y are the resultant forces of the vehicle along the X-axis and Y-axis, M Z is the yaw moment of the vehicle around the Z axis, m is the vehicle mass, v x and v y are the vehicle longitudinal velocity and lateral velocity, is the vehicle longitudinal acceleration, is the rate of change of the sideslip angle of the center of mass, γ is the yaw angle of the vehicle, is the vehicle yaw angular acceleration, I z is the moment of inertia of the vehicle around the Z axis, F xil and F xir are the longitudinal forces of the i-th tire on the left and right sides, respectively, F yil and F yir are the lateral forces of the left and right tires, δ il and δ ir Divided into the turning angle of the i-th tire on the left and right sides, L i represents the distance from the center of mass of the vehicle to the i-th axle, where the axle in front of the center of mass is positive and the axle behind the center of mass is negative, n is the number of axles of the vehicle, and b is the vehicle wheelbase; The expression of the vehicle lateral force is: F yi =k i a i Where k i is the cornering stiffness of the vehicle tire, α i is the side slip angle of the vehicle tire, δ i is the tire turning angle; The tracking control problem of the multi-axle steering vehicle is transformed into a state tracking control problem, and accurate trajectory tracking control is achieved by independently controlling the steering of each axle of the multi-axle steering vehicle. According to the above multi-axle steering vehicle dynamics model, the system state tracking control model is derived: Where β is the sideslip angle of the center of mass, d1 and d2 are unknown disturbances, It is a custom function and can be obtained as follows: To further reflect the influence of wheel angle on the motion characteristics of multi-axle steering vehicles, the first and last axle angles are controlled, and the remaining wheel angles are obtained using the following Ackerman steering relationship: Where x0 and y0 are the coordinates of the instantaneous steering center; let the state variable x = [γ, β] T , is the first-order derivative of the state variable; The system state tracking control model is reconstructed as: in, Where y is the output of the system, u is the control input of the system and u=[δ1,…,δ n ] T , d(t) is the external unknown disturbance, including road disturbance, and the system is not modeled dynamics. Let F = Ax + d(t) represent the uncertainty term of the system function.

4. The neural network adaptive multi-axis vehicle tracking control method based on obstacle function according to claim 1 is characterized in that: The implementation method of designing the adaptive integral sliding mode controller based on the barrier function in step S3 is: According to the multi-axis steering vehicle tracking control model, the nonlinear dynamic equations of the control-oriented multi-axis steering vehicle system can be reformulated as: F=Ax+D+d(t) in, The state tracking error of the multi-axis steering vehicle is selected to construct the integral sliding membrane surface S, which is expressed as follows: x e =x-x d Where x e is the system state tracking error, x d =[γ d ,β d ] T is the ideal state vector of the system, λ and P(t) are controller parameters and satisfy P(t) = exp(-ρt), where ρ is a positive number; combined with the state tracking error equation, the differential expression of the integral sliding surface S is as follows: make Integral sliding mode equivalent control law u eq The expression is as follows: Construct robust control law u according to the exponential convergence law rc As shown below: you rc (t)=B -1 (-Ksat(S)-η(ε 2 -S 2 )S) Where K = diag(K1, K2) > 0 is a custom parameter, η = diag(η1, η2) > 0 is a custom parameter, ε is the boundary value of the custom sliding surface, and satisfies S ≤ ε, sat(S) is the saturation function instead of the sign function sat(S), and its expression is: The integral sliding mode control law u is further obtained as follows: Based on the barrier function, the adaptive gain control law is constructed as follows: Where, is the adaptive control parameter, t a It is the minimum time for the sliding surface to satisfy S<(ε / 2) during the control process.

5. The neural network adaptive multi-axis vehicle tracking control method based on obstacle function according to claim 1 is characterized in that: The implementation method of using a neural network to approximate the unknown part of the multi-axis steering vehicle dynamics system in step S4 is as follows: The approximate function of the neural network is used to approximate the unknown nonlinear function in the system. The neural network structure used is divided into three layers: input layer, hidden layer, and output layer, as shown below: F=ω *T H i (x j )+e e Where x j is the network input vector, j is the number of input networks, i is the number of hidden layer nodes, H i (x j ) is the Gaussian basis function in the hidden layer, c ij and b i are the center vector and width of the Gaussian basis function, F is the network output, ω * is the optimal weight vector of the network, ε e is the network approximation error, and satisfies ε e ≤ε N , ε N is the maximum error; The function uncertainty F = Ax + d(t) is reconstructed as: Where, is the network output approximation; then the control law u is redefined as:

6. The neural network adaptive multi-axis vehicle tracking control method based on obstacle function according to claim 1 is characterized in that: The implementation method of designing the online network weight adaptation law based on Lyapunov theory in step S4 is: According to the reconstructed control law u, the differential expression of the integral sliding surface S is as follows: in, Where, is the network approximation error, is the network weight error. In addition, there is an upper bound θ on the error that satisfies According to Lyapunov's stability theorem, the system state quickly converges to the sliding surface S, and the network error To converge to zero in a finite time and be in a globally stable state, the neural network weight adaptation law should meet the following conditions: Where Γ is a positive matrix and tr(·) represents the trace of the matrix.

7. The neural network adaptive multi-axis vehicle tracking control method based on obstacle function according to claim 1 is characterized in that: The implementation method of the stability proof in step S5 is: The proof consists of the following two steps: Proof: Step 51, when 0≤t≤t a , controller gain K = K a , the selected Lyapunov function is expressed as follows: Where, K * is a custom parameter and satisfies and ε N <θ<K a <K * ; The differential expression of the Lyapunov function V1 is as follows: Prove the stability of the system. In addition, S, K a -K * 、 are all bounded; further proof is as follows: The Lyapunov function is chosen to be expressed as follows: The differential expression of the Lyapunov function V2 is obtained as follows: According to 0<H i (x j )<1, Conclusion Thus we get Therefore, it is inferred and Right now: According to the above proof, it can be concluded that the sliding surface S will converge to This proves that step 51 is completed; Step 52, when t≥t a , controller gain K = K b , the selected Lyapunov function is expressed as follows: The differential expression of the Lyapunov function V3 is obtained as follows: Where, is a custom parameter, and the custom parameter Sa satisfies: For any ζ, there always exists S a <ε; In addition, for S>S a , there exists K b (S)>K(S a )=ζ≥ε N >ε e , we get (K b2 -ε e )S T >0 and (K b2 -ξ)K b2 >0; thus it is proved that the sliding surface S can be a It converges asymptotically under the condition; it is further proved that the sliding surface S converges to S≤S in a finite time. a <ε, as shown below: The Lyapunov function is chosen to be expressed as follows: The differential expression of the Lyapunov function V4 is obtained as follows: According to K b (S)>K(S a )=ζ≥ε N >ε e ,get and Right now: Therefore, for t ≥ t a , the sliding surface S can converge to S≤S a <ε and ensure system stability.

8. A neural network adaptive multi-axis vehicle tracking control system based on obstacle function, characterized in that: Running a neural network adaptive multi-axis vehicle tracking control method based on an obstacle function according to any one of claims 1 to 7, comprising: Data acquisition module, including wheel angle sensor, wheel speed sensor, vehicle speed sensor, yaw rate sensor, and lidar sensor; An ideal state calculation module is used to calculate the ideal yaw rate and sideslip angle required for the multi-axis steering vehicle to track the desired path based on the desired path information and the real-time vehicle position and state information obtained by the data acquisition module, and send this information to the vehicle motion control module; The vehicle motion control module includes establishing a multi-axle steering vehicle dynamics model and a state tracking control model that take into account the uncertainty of the multi-axle steering vehicle model system parameters, road roughness, and unknown external disturbances. An adaptive integral sliding mode anti-interference controller based on the barrier function is designed based on the state error to control the wheel angles of each axle of the multi-axle steering vehicle and avoid the influence of external unknown disturbances on the controller. The neural network approximation module applies neural networks to the adaptive controller to approximate the unknown parts of the multi-axis steering vehicle dynamics system, improving the robustness of system control under model parameter uncertainty. It also uses Lyapunov stability theory to design an online network weight adaptation law to update the network weights in real time, avoiding the local optimality defects of the traditional gradient descent method.

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