A Track Tracking Control Method for Subsea Tracked Vehicles Based on Adaptive Backstepping Control

Abstract

This invention discloses a trajectory tracking control method for a subsea tracked vehicle based on adaptive backstepping control. The method includes the following steps: First, based on the Newton-Euler principle, a mathematical model of the subsea tracked vehicle under external disturbances is established; then, based on the mathematical model and expected value of the subsea tracked vehicle system under external disturbances, the tracking error function of the subsea tracked vehicle is obtained; subsequently, using the backstepping control method and combining the tracking error function, an adaptive backstepping controller for the subsea tracked vehicle is designed; finally, the external disturbance is estimated using a radial basis function neural network, and the external disturbance term in the adaptive backstepping controller is replaced with the output value of the radial basis function neural network to obtain the adaptive anti-interference controller and the actual control quantity, thereby realizing the tracking control of the subsea tracked vehicle.

Description

Technical Field

[0001] This invention relates to the field of underwater tracked vehicle control, specifically to a method for tracking and controlling the trajectory of an underwater tracked vehicle based on adaptive backstepping control. Background Technology

[0002] In the 21st century, with the gradual depletion of terrestrial mineral resources, the abundant metallic mineral resources hidden on the seabed have become particularly crucial. Against this backdrop, the technological development and innovation of seabed mining machines, as a core component of deep-sea mining systems, are of paramount importance. For deep-sea mining operations, especially in seabed environments covered by soft sediments, tracked seabed production tools are highly favored due to their superior adaptability and stability.

[0003] In these deep-sea operational scenarios, the mobility of tracked vehicles is a key factor determining their work efficiency. Specifically, the vehicle's traction primarily originates from the shear stress between the tracks and the seabed. However, during seabed movement, SPTs not only face compaction and bulldozing resistance from seabed sediments but also must contend with the hydrodynamic effects of complex and variable ocean currents. These complex environmental factors must be fully considered when constructing the dynamic model of seabed tracked mining vehicles.

[0004] These complex environmental factors lead to problems such as low accuracy, slow response, and poor stability in existing traditional PID tracked vehicle control methods. Summary of the Invention

[0005] This invention provides a trajectory tracking control method for a subsea tracked vehicle based on adaptive backstepping control to solve the aforementioned technical problems. First, a mathematical model of the subsea tracked vehicle system under external disturbances is established based on Newton's principle. Next, based on the mathematical model and expected value of the subsea tracked vehicle system under external disturbances, the tracking error function of the subsea tracked vehicle is obtained. This tracking error function is then transformed using the adaptive backstepping function to obtain the transformed error function. An adaptive backstepping controller for the subsea tracked vehicle is designed. Finally, a radial basis function neural network is used to estimate the external disturbances. The external disturbance term in the adaptive backstepping controller is replaced with the output value of the radial basis function neural network, resulting in the adaptive anti-interference controller and the actual control quantity, thus realizing the trajectory tracking control of the subsea tracked vehicle.

[0006] This invention specifically provides: a method for tracking and controlling the trajectory of a tracked vehicle on the seabed based on adaptive backstepping control, comprising the following steps:

[0007] S1. Based on the Newton-Euler principle, establish a mathematical model of the underwater tracked vehicle system under external disturbances;

[0008] S2. Based on the mathematical model and expected value of the underwater tracked vehicle system under external disturbances, the tracking error function of the underwater tracked vehicle is obtained.

[0009] S3. Using the backstepping control method and combining the tracking error function, design an adaptive backstepping controller for the underwater tracked vehicle under external disturbances.

[0010] S4. Using a radial basis function neural network to estimate external disturbances, the external disturbance term in the adaptive backstepping controller is replaced with the output value of the radial basis function neural network to obtain the adaptive anti-interference controller and the actual control quantity, thereby realizing the trajectory tracking control of the underwater tracked vehicle under external disturbances.

[0011] First, based on Newton's principles, the position state equation of the underwater tracked vehicle is established as follows:

[0012]

[0013] The motion state of the underwater tracked vehicle is determined by its position (x, y) in the inertial coordinate system. p ,y p ) and direction of motion θ p To describe; the distance between the two tracks is L; the width of the tracks is d; x p ,y p Let x and y be the coordinates of the underwater tracked vehicle in the reference coordinate system; For x p ,y p The first derivative; v p θ represents the speed at the center of mass C of the underwater tracked vehicle. p The angle between the direction of travel of the underwater tracked vehicle and the positive x-axis; For θ p The first derivative; ω p Let be the turning angular velocity of the underwater tracked vehicle.

[0014] Based on Newton's principles and the position state equation of the underwater tracked vehicle, the mathematical model of the underwater tracked vehicle under external disturbances is established as follows:

[0015]

[0016] Wherein, U1 is the control input of the system, that is, the driving force of the tracked vehicle; U2 is also the control input of the system, that is, the rotational torque of the tracked vehicle; For v p ,ω p The first derivative; d1, d2 represent uncertain external disturbances; m is the mass; I is the moment of inertia.

[0017] The position tracking error is defined as:

[0018]

[0019] Among them, e x and e y These are the x-axis and y-axis errors of the actual position of the underwater tracked vehicle relative to the reference position, namely, the longitudinal displacement error and the lateral displacement error; e θ For heading angle error; x b and y b θ represents the coordinates of the reference position of the underwater tracked vehicle on the x-axis and y-axis, respectively; b Using the reference heading angle, the tracking error function is obtained as follows:

[0020]

[0021] in For e B First derivative; For e x First derivative; For e y First derivative; For e θ First derivative.

[0022] Based on the mathematical model of the underwater tracked vehicle, the expected input is:

[0023]

[0024] Where, η=(v p ,ω p ) T v b and ω b These are the reference driving speed and turning angular velocity of the underwater tracked vehicle, respectively; K1, K2, K3 > 0 are adjustment parameters.

[0025] Taking the derivative with respect to η, we obtain the first-order time derivative of η. for:

[0026]

[0027] Assuming that the linear velocity and angular velocity remain constant, the above equation can be rewritten as:

[0028]

[0029] The torque tracking error e is obtained. η =η d -η.

[0030] Construct the Lyapunov function V(e η ):

[0031]

[0032] For V(e) η Take the derivative, and obtain the first derivative. for:

[0033]

[0034] By Lyapunov's stability theorem, It should be half negative, that is

[0035]

[0036]

[0037] Make The backstep controller of the underwater tracked vehicle is obtained as follows:

[0038] U1=m[e v +K1(v p cose θ -v b +e y ω p )-e ω v b sine θ ];

[0039] U2=I[e ω +K2v b (v b sine θ -e x ω p )+K3v b cose θ e ω ].

[0040] Utilizing the universal approximation property of radial basis function neural networks, the external disturbances d1 and d2 are approximated using the following algorithm:

[0041] d1 = W1 T h(e v )+ε1;

[0042]

[0043] Among them, e v It is the speed error, e ω The angular velocity error is both an input to the radial basis function neural network, h(e v ), h(e ω) is the Gausky function output of the radial basis function neural network, W1 and W2 are the ideal weights of the radial basis function neural network, and ε1 and ε2 are the approximation errors of the radial basis function neural network. The estimated value of the external disturbance is obtained as follows:

[0044]

[0045] in, The output values ​​of d1 and d2, For the output values ​​of W1 and W2, the adaptive law is designed as follows:

[0046]

[0047] in, for The first derivative; α 11 α 21 α 12 α 22 For the parameters of the controller to be designed,

[0048] M1 and M2 are positive constants; M1 and M2 are the weights of the radial basis function neural network.

[0049] By replacing the external disturbance term in the adaptive backstepping controller with the output value of the radial basis neural network, the adaptive anti-interference controller is obtained as follows:

[0050]

[0051]

[0052] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0053] 1. By employing a backstepping control method, the system can set performance indicators based on diverse marine environmental conditions, ensuring that the subsea tracked vehicle maintains predetermined performance standards under various dynamic environments. Compared to traditional sliding mode control methods, this method has a faster convergence speed, effectively preventing accidents caused by large overshoot of the subsea tracked vehicle. Furthermore, its rapid convergence characteristics significantly improve the response speed of trajectory tracking, thereby enhancing the overall performance of the subsea tracked vehicle system.

[0054] 2. An adaptive adjustment method is adopted. Referring to the navigation system and the actual sea environment, the trajectory of the underwater tracked vehicle is planned. The actual heading signal received by the heading adaptive device is compared with the planned heading of the underwater tracked vehicle to obtain the error. The adaptive backstepping controller system sends the heading error to the underwater tracked vehicle's servo motor, and then the automatic steering control system adjusts the servo motor. This adjustment is a continuous cyclical process, requiring continuous acquisition of information on the underwater tracked vehicle's travel direction and feedback to the heading controller system, while the error continues to change. When the heading error of the underwater tracked vehicle approaches zero, the actual heading of the underwater tracked vehicle is almost consistent with the theoretical travel. Compared with the existing traditional PID tracked vehicle control methods, which suffer from low accuracy, slow response, and poor stability, the adaptive backstepping control system designed in this invention has the advantages of high sensitivity, stable performance, and high accuracy.

[0055] 3. A backstepping method is used to derive the adaptive weight update law for radial basis function (RBF) neural networks. RBF neural networks can estimate unmodeled parts of the system, modeling errors, and external disturbances, thereby compensating for the dynamic controller. Compared to general backpropagation (BP) feedforward neural networks, which suffer from sensitivity to initial parameters, overfitting, complex structure, lack of unified guiding theory, and local minima during training, RBF neural networks use radial basis functions in the data space to describe the relationships between samples. This distance-based representation makes them robust to outliers or noise. Therefore, even with noise or outliers in the input data, RBF neural networks can still produce relatively stable outputs. Attached Figure Description

[0056] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0057] Figure 2 This is a mechanical model of the underwater tracked vehicle according to an embodiment of the present invention;

[0058] Figure 3 This is the underwater track tracking error model of an embodiment of the present invention;

[0059] Figure 4 This is a schematic diagram of the control system according to an embodiment of the present invention. Detailed Implementation

[0060] In the embodiments of the present invention, the technical solutions will be clearly and completely described in conjunction with the accompanying drawings. It is worth noting that the embodiments described represent only a portion of the application of the present invention, and not all of it. Based on the principles of the present invention, those skilled in the art can obtain all other embodiments without inventive work, and these embodiments are also protected by the present invention. In the following description, two specific embodiments will be elaborated in detail to demonstrate the feasibility and application potential of the present invention.

[0061] Current control methods for underwater tracked vehicles primarily focus on static performance indicators, such as steady-state error, while giving less consideration to dynamic performance indicators, such as settling time and overshoot. This control strategy, which emphasizes static performance, faces challenges in dealing with sudden changes in the marine environment, such as drastic fluctuations in waves, wind, and current. Furthermore, existing technologies are insufficient in handling these external disturbances, affecting the trajectory stability and control accuracy of underwater tracked vehicles in complex dynamic environments. In addition, existing control methods often rely on precise mathematical models; however, obtaining accurate physical models of the underwater tracked vehicle and its environment is difficult in practice, thus limiting the adaptability and effectiveness of control strategies in variable marine environments. To improve the operational performance and tracking accuracy of underwater tracked vehicles in complex marine environments, this invention proposes an underwater tracked vehicle tracking control scheme based on adaptive backstepping anti-interference control. To demonstrate the feasibility of this invention, three specific embodiments will be described below.

[0062] Example 1

[0063] Please see Figure 1-4 This invention proposes a trajectory tracking control strategy based on adaptive backstepping control, specifically for the precise control of underwater tracked vehicles. First, based on Newton's laws of motion, a dynamic mathematical model of the underwater tracked vehicle system, incorporating external disturbances, is constructed. Second, combining this model with a preset expected value, the trajectory tracking error function of the underwater tracked vehicle is obtained. This error function is then transformed using an adaptive backstepping method to obtain a more accurate transformation error function. Adopting backstepping control theory and integrating the transformation error function, an adaptive backstepping controller for the underwater tracked vehicle is designed. To further enhance the controller's anti-interference capability, a radial basis function neural network is introduced to estimate external disturbances. The estimated value from the neural network is then used to replace the original external disturbance term in the adaptive backstepping controller, ultimately constructing an adaptive backstepping controller with strong anti-interference capabilities and outputting the actual control quantity, thereby achieving high-precision trajectory tracking control of the underwater tracked vehicle.

[0064] Furthermore, the specific implementation process of this application embodiment is as follows: In this application embodiment, the parameters of the underwater tracked vehicle system are selected as follows: m = 200 kg, I = 0.5 kg·m 2, k1=0.93, k2=0.95, k3=1, α 11 =20, α 21 =0.5, α 12 =15, α 22 =0.8; where m is the mass of the underwater tracked vehicle, I is the moment of inertia of the underwater tracked vehicle; k1, k2, k3 are the coefficients of the underwater tracked vehicle trajectory tracker; α 11 ,α 12 ,α 21 ,α 22 These are the radial basis vector neural network adjustment coefficients; the initial coordinates and orientation angle of the referenced underwater tracked vehicle are (3 - 1 0.25π), and the initial coordinates and orientation angle of the actual tracked vehicle are (110.5π); the reference speed is set to v = 0.5 m / s, the reference angular velocity is set to ω = 0 rad / s, the initial speed is set to v = 0 m / s, and the initial angular velocity is set to ω = 0 rad / s; the predetermined tracking trajectory of the tracked vehicle is a straight line with a starting point of (3 0) and an angle of π / 4 with the positive x-axis.

[0065] First, based on Newton's principles, the position state equation of the underwater tracked vehicle is established as follows:

[0066]

[0067] The motion state of the underwater tracked vehicle is determined by its position (x, y) in the inertial coordinate system. p ,y p ) and direction of motion θ p To describe; the distance between the two tracks is L; the width of the tracks is d; x p ,y p Let x and y be the coordinates of the underwater tracked vehicle in the reference coordinate system; For x p ,y p The first derivative; v p θ represents the speed at the center of mass C of the underwater tracked vehicle. p The angle between the direction of travel of the underwater tracked vehicle and the positive x-axis; For θ p The first derivative; ω p Let be the turning angular velocity of the underwater tracked vehicle.

[0068] Based on Newton's principles and the position state equation of the underwater tracked vehicle, the mathematical model of the underwater tracked vehicle under external disturbances is established as follows:

[0069]

[0070] Wherein, U1 is the control input of the system, that is, the driving force of the tracked vehicle; U2 is also the control input of the system, that is, the rotational torque of the tracked vehicle; For v p ,ω p The first derivative; d1, d2 represent uncertain external disturbances; m is the mass; I is the moment of inertia.

[0071] In the embodiments of this application, a mathematical model of the underwater tracked vehicle is constructed based on the principles of Newtonian mechanics to describe its dynamic characteristics in a complex underwater environment. This model reflects the motion laws of the underwater tracked vehicle to optimize and ensure its stability and handling performance under complex conditions.

[0072] Furthermore, based on the mathematical model and expected value of the underwater tracked vehicle system under external disturbances, the tracking error function of the underwater tracked vehicle is obtained, and the tracking error function is transformed according to the adaptive backstepping function to obtain the transformed error function.

[0073] The trajectory tracking process refers to the underwater tracked vehicle starting from a given initial position and tracking the trajectory based on the trajectory error (e). x ,e y ,e θ ) T and control output (v,ω) T , making e x →0,e y →0,e θ →0, the process of finally reaching and continuing to travel along the desired trajectory.

[0074]

[0075] Among them, e x and e y These are the x-axis and y-axis errors of the tracked vehicle's actual position relative to the reference position, i.e., longitudinal displacement error and lateral displacement error; e θ For heading angle error; x b and y b θ represents the coordinates of the tracked vehicle's reference position on the x-axis and y-axis, respectively; b Using the reference heading angle, the dynamic error model is obtained by differentiating the tracking error formula:

[0076]

[0077] In the embodiments of this application, in order to meet the requirements of high-precision trajectory tracking control, an error model is constructed. By controlling the tracking error, the deviation between the expected tracking trajectory and the actual motion trajectory of the underwater tracked vehicle is reduced, thereby realizing the tracking control of the underwater tracked vehicle trajectory.

[0078] Based on the mathematical model of the subsea tracked vehicle with mobile tracks, the output control input is obtained as follows:

[0079]

[0080] Among them, v b and ω b These are the reference travel speed and steering angular velocity of the tracked vehicle, respectively; K1, K2, K3 > 0.

[0081] In the embodiments of this application, based on a pre-established mathematical model of the underwater tracked vehicle and under the condition of no slippage assumption, control input parameters are derived. By adjusting these control input parameters, it is ensured that the underwater tracked vehicle can follow the preset desired trajectory.

[0082] Taking the derivative with respect to η, we obtain the first-order time derivative of η. for:

[0083]

[0084] Assuming that the linear velocity and angular velocity remain constant, the above equation can be rewritten as:

[0085]

[0086] The torque tracking error e is obtained. η =η d -η.

[0087] In the embodiments of this application, we first calculate the torque tracking error of the underwater tracked vehicle based on the derived control input parameters and the expected value. This error index is used in the subsequent controller design. By applying the backstepping method to mathematically derive the torque tracking error, we minimize the torque tracking error and thus calculate the control law of the underwater tracked vehicle, ensuring the stability and performance optimization of the underwater tracked vehicle in actual operation.

[0088] According to Lyapunov theory, assuming the height subsystem is at point e η Equilibrium is reached at (e = e) d Construct the Lyapunov function V(e) η ):

[0089]

[0090] Along the trajectory V(e) of the system η The time derivative of ) is:

[0091]

[0092] According to Lyapunov's stability theorem, it should be Negative half-definite, that is

[0093]

[0094] Therefore, using the backstepping control method and combining it with the aforementioned conversion error function, the underwater tracked vehicle trajectory tracking controller U1 is designed as follows:

[0095] Position controller: U1 = m[e v +K1(v p cose θ -v b +e y ω p )-e ω v b sine θ ];

[0096] Angle controller: U2 = I[e ω +K2v b (v b sine θ -e x ω p )+K3v b cose θ e ω ];

[0097] Make

[0098] In the embodiments of this application, a backstepping control method is employed, which significantly improves the convergence speed of the control system. This optimization not only effectively prevents accidents that may be caused by excessive overshoot of the underwater tracked vehicle, but also enhances the real-time responsiveness of trajectory tracking with a faster convergence rate, thereby improving the overall performance of the underwater tracked vehicle system.

[0099] Furthermore, by using a radial basis function neural network to estimate external disturbances, the external disturbance term in the adaptive backstepping controller is replaced with the output value of the radial basis function neural network, thus obtaining the adaptive anti-interference controller and the actual control quantity, and realizing the tracking control of the underwater tracked vehicle.

[0100] Utilizing the universal approximation property of radial basis function neural networks, the external disturbances d1 and d2 are approximated using the following algorithm:

[0101] d1 = W1 T h(e v )+ε1;

[0102]

[0103] Among them, e v It is the speed error, e ω The angular velocity error is both an input to the radial basis function neural network, h(ev ), h(e ω ) is the Gausky function output of the radial basis function neural network, W1 and W2 are the ideal weights of the radial basis function neural network, and ε1 and ε2 are the approximation errors of the radial basis function neural network. The estimated value of the external disturbance is obtained as follows:

[0104]

[0105] in, The output values ​​of d1 and d2, For the output values ​​of W1 and W2, the adaptive law is designed as follows:

[0106]

[0107] in, for The first derivative; α 11 α 21 α 12 α 22 The parameters to be designed are positive constants; M1 and M2 are the weights of the radial basis function neural network.

[0108] In this embodiment, radial basis function (RBF) neural networks are used to estimate external disturbances due to their universal approximation properties. Introducing RBF improves the system's rapid response and adaptability to external disturbances, enabling real-time learning and dynamic adjustment of control strategies to accurately estimate the impact of external disturbances. This enhances the robustness of the control system and effectively reduces tracking errors, allowing the underwater tracked vehicle to perform tasks more stably and cope with complex changes in the marine environment.

[0109] By replacing the external disturbance term in the adaptive backstepping controller with the output value of the radial basis neural network, the adaptive anti-interference controller is obtained as follows:

[0110]

[0111] In this embodiment, the external disturbance term in the adaptive backstepping controller is replaced with the output value of the radial basis function neural network to obtain the adaptive anti-interference controller. This controller combines the estimation capabilities of adaptive backstepping control and radial basis function neural networks, and employs an adaptive law, reducing the dependence on precise mathematical models and achieving effective adaptation and stable control in complex dynamic environments.

[0112] Example 2: In this embodiment of the application, the parameters of the underwater tracked vehicle system are selected as follows: m = 200 kg, I = 0.5 kg·m 2 , k1=0.856, k2=0.862, k3=0.893, α11 =30, α 21 =1.25, α 12 =18, α 22 =1.3; where m is the mass of the underwater tracked vehicle, I is the moment of inertia of the underwater tracked vehicle; k1, k2, k3 are the coefficients of the underwater tracked vehicle trajectory tracker; α 11 ,α 12 ,α 21 ,α 22 These are the adjustment coefficients of the radial basis vector neural network; the starting coordinates and orientation angle of the reference tracked vehicle are (11 0.66π), and the starting coordinates and orientation angle of the actual underwater tracked vehicle are (0 0 0.66π); the reference speed is set to v = 0.5 m / s, the reference angular velocity is set to ω = 0.5 rad / s, the reference angular velocity at the turning point is set to ω = 0.33π rad / s, the starting speed is set to v = 0 m / s, and the starting angular velocity is set to ω = 0 rad / s; the tracking trajectory is a broken line trajectory with (1 1) as the starting point and (3.7 6.2) as the turning point, and the ray after the turning point is parallel to the x-axis.

[0113] First, based on Newton's principles, the position state equation of the underwater tracked vehicle is established as follows:

[0114]

[0115] The motion state of the underwater tracked vehicle is determined by its position (x, y) in the inertial coordinate system. p ,y p ) and direction of motion θ p To describe; the distance between the two tracks is L; the width of the tracks is d; x p ,y p Let x and y be the coordinates of the underwater tracked vehicle in the reference coordinate system; For x p ,y p The first derivative; v p θ represents the speed at the center of mass C of the underwater tracked vehicle. p The angle between the direction of travel of the underwater tracked vehicle and the positive x-axis; For θ p The first derivative; ω p Let be the turning angular velocity of the underwater tracked vehicle.

[0116] Based on Newton's principles and the position state equation of the underwater tracked vehicle, the mathematical model of the underwater tracked vehicle under external disturbances is established as follows:

[0117]

[0118] Wherein, U1 is the control input of the system, that is, the driving force of the tracked vehicle; U2 is also the control input of the system, that is, the rotational torque of the tracked vehicle; For v p ,ω p The first derivative; d1, d2 represent uncertain external disturbances; m is the mass; I is the moment of inertia.

[0119] The position tracking error is defined as:

[0120]

[0121] Among them, e x and e y These are the x-axis and y-axis errors of the actual position of the underwater tracked vehicle relative to the reference position, namely, the longitudinal displacement error and the lateral displacement error; e θ For heading angle error; x b and y b θ represents the coordinates of the reference position of the underwater tracked vehicle on the x-axis and y-axis, respectively; b Using the reference heading angle, the tracking error function is obtained as follows:

[0122]

[0123] in For e B First derivative; For e x First derivative; For e y First derivative; For e θ First derivative.

[0124] Based on the mathematical model of the underwater tracked vehicle, the expected input is:

[0125]

[0126] Where, η=(v p ,ω p ) T v b and ω b These are the reference driving speed and turning angular velocity of the underwater tracked vehicle, respectively; K1, K2, K3 > 0 are adjustment parameters.

[0127] Taking the derivative with respect to η, we obtain the first-order time derivative of η. for:

[0128]

[0129] Assuming that the linear velocity and angular velocity remain constant, the above equation can be rewritten as:

[0130]

[0131] The torque tracking error e is obtained. η =η d -η.

[0132] Construct the Lyapunov function V(e η ):

[0133]

[0134] For V(e) η Take the derivative, and obtain the first derivative. for:

[0135]

[0136] By Lyapunov's stability theorem, It should be half negative, that is

[0137]

[0138] Make The backstep controller of the underwater tracked vehicle is obtained as follows:

[0139] U1=m[e v +K1(v p cose θ -v b +e y ω p )-e ω v b sine θ ];

[0140] U2=I[e ω +K2v b (v b sine θ -e x ω p )+K3v b cose θ e ω ].

[0141] Utilizing the universal approximation property of radial basis function neural networks, the external disturbances d1 and d2 are approximated using the following algorithm:

[0142] d1 = W1 T h(e v )+ε1;

[0143]

[0144] Among them, e vIt is the speed error, e ω The angular velocity error is both an input to the radial basis function neural network, h(e v ), h(e ω ) is the Gausky function output of the radial basis function neural network, W1 and W2 are the ideal weights of the radial basis function neural network, and ε1 and ε2 are the approximation errors of the radial basis function neural network. The estimated value of the external disturbance is obtained as follows:

[0145]

[0146] in, The output values ​​of d1 and d2, For the output values ​​of W1 and W2, the adaptive law is designed as follows:

[0147]

[0148] in, for The first derivative; α 11 α 21 α 12 α 22 The parameters to be designed are positive constants; M1 and M2 are the weights of the radial basis function neural network.

[0149] By replacing the external disturbance term in the adaptive backstepping controller with the output value of the radial basis neural network, the adaptive anti-interference controller is obtained as follows:

[0150]

[0151] The adaptive anti-interference controller is obtained by replacing the external disturbance term in the adaptive backstepping controller with the output value of the radial basis neural network.

[0152] The examples described herein are merely preferred embodiments of the invention and are not intended to limit the concept and scope of the invention. Any modifications and improvements made by those skilled in the art to the technical solutions of the invention without departing from the design concept of the invention should fall within the protection scope of the invention.

Claims

1. A method for tracking and controlling the trajectory of a tracked vehicle on the seabed based on adaptive backstepping control, characterized in that, Includes the following steps: S1. Based on the Newton-Euler equations, a mathematical model is constructed for an underwater tracked vehicle system subject to external disturbances. The construction of the mathematical model includes: establishing the position state equation of the underwater tracked vehicle, which describes the kinematic relationship between the position, heading, linear velocity, and angular velocity of its center of mass C; and establishing a dynamic equation containing external disturbance terms based on the Newton-Euler equations, which reflects the relationship between the linear acceleration and angular acceleration of the underwater tracked vehicle and the driving force, rotational torque, and external disturbances, wherein external disturbances d1 and d2 act on the linear acceleration and angular acceleration channels, respectively. S2. Based on the mathematical model and the desired trajectory state, obtain the position tracking error function and torque tracking error of the underwater tracked vehicle; S3. Combining the backstepping control strategy, and integrating the position tracking error function and the torque tracking error, design an adaptive backstepping controller for the underwater tracked vehicle. S4. Introduce a radial basis function neural network to estimate external disturbances, and replace the external disturbance term in the adaptive backstepping controller with the output value of the radial basis function neural network to obtain an adaptive anti-interference controller.

2. The method for tracking and controlling the trajectory of a tracked vehicle on the seabed based on adaptive backstepping control according to claim 1, wherein the process of obtaining the mathematical model includes: The first step, based on Newton's principles, is to establish the position and state equations of the underwater tracked vehicle as follows: The motion state of the underwater tracked vehicle is determined by its position in the inertial coordinate system. and direction of movement To describe; the distance between the two tracks is The width of the track is ; The underwater tracked vehicle in the reference coordinate system axis, Axis coordinates; for The first derivative; The center of gravity of the underwater tracked vehicle The speed at that location; The direction of travel of the underwater tracked vehicle is... The angle between the positive axis and the axis; for The first derivative; The turning angular velocity of the underwater tracked vehicle; The second step involves establishing a mathematical model of the underwater tracked vehicle under external disturbances, based on its position and state equations: in, This is the control input to the system, i.e., the driving force of the tracked vehicle; Similarly, the control input of the system is the rotational torque of the tracked vehicle; for The first derivative; Due to uncertain external interference; For quality; Let be the moment of inertia.

3. The method for tracking and controlling the trajectory of a tracked vehicle under external disturbances based on adaptive backstepping control according to claim 2, wherein the process of obtaining the tracking error function includes: The first step is to define the position tracking error as: in, and These are the actual positions of the underwater tracked vehicle relative to the reference positions. axis, Shaft error, namely longitudinal displacement error and lateral displacement error; This refers to the heading angle error; and The reference positions of the underwater tracked vehicle are respectively at axis, The coordinates of the axis; For reference heading angle; The second step is... Taking the derivative, we obtain the tracking error function as follows: in for First derivative; for First derivative; for First derivative; for First derivative.

4. According to the method for trajectory tracking control of an underwater tracked vehicle based on adaptive backstepping control as described in claim 3, the desired input is obtained based on the mathematical model of the underwater tracked vehicle: in, , and These are the reference driving speed and steering angular velocity of the underwater tracked vehicle, respectively. To adjust the parameters.

5. The method for tracking and controlling the trajectory of a tracked vehicle on the seabed based on adaptive backstepping control according to claim 4, wherein the torque tracking error is obtained according to the desired input. The acquisition process includes: Step 1: Knowing the expected input Assuming that the linear velocity and angular velocity remain constant, for Taking the derivative, we get First time derivative ; The second step is to denote the expected input as The actual input is The torque tracking error is obtained. : 。 6. The method for tracking and controlling the trajectory of a tracked vehicle on the seabed based on adaptive backstepping control according to claim 5, wherein the process of acquiring the backstepping controller includes: The first step is to construct the Lyapunov function. The second step is... Taking the derivative, we obtain the first derivative. According to Lyapunov's stability theorem, It should be semi-negative constant, meaning the backstepping controller should be designed to ensure that... Therefore, the backstepping controller of the underwater tracked vehicle is as follows:

7. The underwater tracked vehicle trajectory tracking control method based on adaptive backstepping control according to claim 4 utilizes the universal approximation characteristic of radial basis function neural networks to approximate external disturbances. , ; The first step is to establish external interference in the algorithm. , The radial basis function neural network model is as follows: in, It's a speed error. Both angular velocity errors are inputs to the radial basis function neural network. , It is the Gausky function output of the radial basis function neural network. These are the ideal weights for the radial basis function neural network. , It is the approximation error of the radial basis neural network; The second step, based on the radial basis function neural network model, yields the estimated value of the external disturbance: in, , for , The output value, , for , The output value; Based on this, the adaptive law is designed as follows: in, , for , The first derivative; , , , These are the parameters of the controller to be designed, and they are positive values. , These are the weights of the radial basis function neural network; The third step involves updating the iterative parameter weights using a radial basis function network to approximate external disturbances. , .

8. The method for tracking and controlling the trajectory of a tracked vehicle on the seabed based on adaptive backstepping control according to claim 7, characterized in that, By replacing the external disturbance term in the adaptive backstepping controller with the output value of the radial basis neural network, the adaptive anti-interference controller is obtained as follows:

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