Submarine crawler trajectory tracking control method based on adaptive backstepping control

Abstract

The invention discloses a seabed crawler trajectory tracking control method based on adaptive backstepping control. The method comprises the following steps: firstly, according to the Newton-Euler principle, establishing a mathematical model of the seabed crawler under external interference; then, according to the mathematical model and the expected value of the seabed crawler system under the external interference, a tracking error function of the seabed crawler is obtained; then, a backstepping control method is used, and the tracking error function is combined to design a self-adaptive backstepping controller of the seabed crawler; and finally, estimating external interference by using the radial basis function neural network, replacing an external interference item in the self-adaptive backstepping controller with an output value of the radial basis function neural network, obtaining the self-adaptive anti-interference controller and an actual control quantity of self-adaptive backstepping, and realizing tracking control of the seabed crawler.

Description

Technical Field

[0001] The invention relates to the field of submarine crawler vehicle control, and in particular to a submarine crawler vehicle trajectory tracking control method based on adaptive backstepping control. Background Art

[0002] In the 21st century, as land-based mineral resources are becoming increasingly depleted, the rich metal mineral resources on the seafloor have become particularly critical. In this context, the technological development and innovation of seafloor miners, as the core component of deep-sea mining systems, are particularly important. For deep-sea mining tasks, especially in seafloor environments covered with soft sediments, seafloor production tools equipped with tracks are highly favored due to their excellent adaptability and stability.

[0003] In these deep-sea operation scenarios, the walking performance of the tracked vehicle is a key factor in determining its working efficiency. Specifically, the traction of the vehicle mainly comes from the shear stress between the track and the seabed. However, during the seabed walking process, the SPT not only faces the compaction and bulldozing resistance from the seabed sediments, but also needs to deal with the hydrodynamic effects brought by the complex and changeable seabed currents. These complex environmental factors must be fully considered when constructing the dynamic model of the seabed tracked mining vehicle.

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

[0005] The present invention provides a submarine tracked vehicle trajectory tracking control method based on adaptive backstepping control, which is used to solve the above technical problems. First, according to Newton's principle, a mathematical model of the submarine tracked vehicle system under external interference is established; then, according to the mathematical model and expected value of the submarine tracked vehicle system under external interference, the tracking error function of the submarine tracked vehicle is obtained, and the tracking error function is converted according to the adaptive backstepping function to obtain the conversion error function; the adaptive backstepping controller of the submarine tracked vehicle is designed; finally, the external interference is estimated by using a radial basis function neural network, and the external interference term in the adaptive backstepping controller is replaced by the output value of the radial basis function neural network, and the adaptive anti-interference controller and the actual control quantity of the adaptive backstepping are obtained to realize the trajectory tracking control of the submarine tracked vehicle.

[0006] The present invention specifically provides: a submarine crawler vehicle trajectory tracking control method based on adaptive backstepping control, comprising the following steps:

[0007] S1. According to the Newton-Euler principle, a mathematical model of the submarine crawler system under external interference is established;

[0008] S2. Obtaining a tracking error function of the submarine crawler vehicle according to a mathematical model and an expected value of the submarine crawler vehicle system under external interference;

[0009] S3, using a backstepping control method and combining the tracking error function to design an adaptive backstepping controller for the submarine crawler vehicle under external disturbance;

[0010] S4. Use radial basis function neural network to estimate external disturbance, replace the external disturbance term in the adaptive backstepping controller with the output value of radial basis function neural network, obtain the adaptive anti-interference controller and the actual control quantity of adaptive backstepping, and realize the trajectory tracking control of the submarine crawler vehicle under external disturbance.

[0011] First, according to Newton's principle, the position state equation of the submarine crawler is established as follows:

[0012]

[0013] The motion state of the submarine crawler is determined by its position in the inertial coordinate system (x p ,y p ) and the direction of motion θ p to describe; the distance between the two tracks is L; the width of the track is d; x p ,y p are the x-axis and y-axis coordinates of the submarine crawler in the reference coordinate system; For x p ,y p The first derivative of v p is the travel speed of the submarine crawler at the center of mass C; θ p is the angle between the driving direction of the submarine crawler and the positive direction of the x-axis; is θ p The first derivative of p is the steering angular velocity of the submarine crawler.

[0014] According to Newton's principle and combined with the position state equation of the submarine crawler, the mathematical model of the submarine crawler under external interference is established as follows:

[0015]

[0016] Among them, U1 is the control input of the system, that is, the driving force of the crawler vehicle; U2 is also the control input of the system, that is, the rotational torque of the crawler vehicle; v p ,ω p The first-order derivative of ; d1, d2 are uncertain external disturbances; m is the mass; I is the moment of inertia.

[0017] Define the position tracking error as:

[0018]

[0019] Among them, e x and e y are the x-axis and y-axis errors of the actual position of the submarine crawler relative to the reference position, i.e., the longitudinal displacement error and the lateral displacement error; e θ is the heading angle error; x b and b are the coordinates of the reference position of the submarine crawler on the x-axis and y-axis respectively; θ b As the reference heading angle, the tracking error function is obtained as:

[0020]

[0021] in for e B First-order derivative; for e x First-order derivative; for e y First-order derivative; for e θ First-order derivative.

[0022] According to the mathematical model of the submarine crawler, the expected input is:

[0023]

[0024] Where η=(v p ,ω p ) T , v b and ω b They are respectively the reference driving speed and steering angular velocity of the submarine crawler; K1, K2, K3>0 are adjustment parameters.

[0025] Taking the derivative of η, we get 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 Lyapunov function V(e η ):

[0031]

[0032] V(e η ) to obtain the first-order derivative for:

[0033]

[0034] According to the Lyapunov stability theorem, should be semi-negative definite, that is

[0035]

[0036]

[0037] Make The backstepping controller of the submarine crawler vehicle is obtained as:

[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] Using the universal approximation characteristics of radial basis neural network, the external interference d1 and d2 are approximated. The algorithm is:

[0041] d1=W1 T h(e v )+ε1;

[0042]

[0043] Among them, e v is the velocity error, e ω is the angular velocity error, both of which are inputs of the radial basis neural network, h(e v ), h(e ω) is the Gaussian basis function output of the radial basis neural network, W1, W2 are the ideal weights of the radial basis neural network, ε1, ε2 are the approximation errors of the radial basis neural network, and the estimated value of the external interference is:

[0044]

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

[0046]

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

[0048] is a positive constant; M1 and M2 are the weights of the radial basis neural network.

[0049] The external disturbance term in the adaptive backstepping controller is replaced by the output value of the radial basis neural network, and the adaptive anti-interference controller is obtained as follows:

[0050]

[0051]

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1. The backstepping control method is adopted, and the system can set performance indicators based on diverse marine environmental conditions to ensure that the submarine crawler can maintain the predetermined performance standards in various dynamic environments. Compared with the traditional sliding mode control method, the method has a faster convergence speed, effectively preventing accidents caused by large overshoot of the submarine crawler, and its fast convergence characteristics significantly improve the response speed of trajectory tracking, thereby enhancing the overall performance of the submarine crawler system.

[0054] 2. An adaptive adjustment method is adopted. The navigation system and the actual sea environment are referred to to plan the track of the submarine tracked vehicle. The actual heading signal received by the heading adaptive device is compared with the proposed heading of the submarine tracked vehicle to obtain the error. The adaptive backstepping controller system sends the heading error to the submarine tracked vehicle steering gear, and then the automatic rudder control system adjusts the steering gear. This adjustment is a continuous cycle. It is necessary to continuously collect information on the navigation direction of the submarine tracked vehicle and feed it back to the heading controller system. The error is also constantly changing. When the heading error of the submarine tracked vehicle approaches 0, the actual heading of the submarine tracked vehicle is almost consistent with the theoretical navigation. Compared with the existing traditional PID tracked vehicle control method with problems such as low precision, slow response and poor stability, the adaptive backstepping control system designed by the present invention has the advantages of high sensitivity, stable performance and high accuracy.

[0055] 3. The backstepping method is used to give the weight adaptive update law of the radial basis neural network. The weight adaptive update radial basis neural network can estimate the unmodeled part of the system, the modeling error and the external disturbance, so as to compensate the dynamic controller. Compared with the general BP feedforward neural network, there are problems including sensitivity to initial parameters, overfitting, complex structure and lack of unified guidance theory, and local minimization problems in the training process. The radial basis neural network uses radial basis functions in the data space to describe the relationship between samples. This distance-based representation makes them robust to abnormal data or noise. Therefore, even if there are some noise or outliers in the input data, the radial basis neural network can still produce relatively stable outputs. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a schematic diagram of a flow chart of an embodiment of the present invention;

[0057] Figure 2 is a mechanical model of the submarine crawler vehicle according to an embodiment of the present invention;

[0058] Figure 3 is a submarine crawler vehicle trajectory tracking error model of an embodiment of the present invention;

[0059] Figure 4 Schematic diagram of a control system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0060] In the embodiments of the present invention, the technical solutions will be described clearly and completely in conjunction with the accompanying drawings. It is worth noting that the embodiments only represent some applications of the present invention, not all of them. According to the principles of the present invention, ordinary technicians in this field can obtain all other embodiments without performing creative 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] At present, the control method of submarine crawler vehicles mainly focuses on static performance indicators, such as steady-state errors, and less consideration is given to dynamic performance indicators, such as adjustment time and overshoot. This control strategy that focuses on static performance is challenging when dealing with sudden changes in the marine environment, such as drastic fluctuations in waves, wind and flow rate. At the same time, the existing technology has deficiencies in dealing with these external interferences, resulting in the track stability and control accuracy of submarine crawler vehicles in complex dynamic environments being affected. In addition, the existing control methods mostly rely on accurate mathematical models. However, it is difficult to obtain accurate physical models of submarine crawler vehicles and environments in actual situations, thereby limiting the adaptability and effectiveness of control strategies in changeable marine environments. In order to improve the operating performance and tracking accuracy of submarine crawler vehicles in complex marine environments, the present invention proposes a submarine crawler vehicle tracking control scheme based on adaptive backstepping anti-interference control. In order to demonstrate the feasibility of the present invention, three specific embodiments will be described below.

[0062] Embodiment 1

[0063] See also Figure 1-4 , the present invention proposes a trajectory tracking control strategy based on adaptive backstepping control, which is specially used for the precise control of submarine tracked vehicles. First, according to Newton's laws of motion, a dynamic mathematical model of the submarine tracked vehicle system including external interference factors is constructed. Secondly, by combining this model with the preset expected value, the trajectory tracking error function of the submarine tracked vehicle is obtained, and this error function is transformed by the adaptive backstepping method to obtain a more accurate conversion error function. The backstepping control theory is adopted, the conversion error function is integrated, and the adaptive backstepping controller of the submarine tracked vehicle is designed. In order to further improve the anti-interference ability of the controller, a radial basis neural network is introduced to estimate the external interference, and then the estimated value of the neural network is used to replace the original external interference term in the adaptive backstepping controller, and finally an adaptive backstepping controller with strong anti-interference ability is constructed, and the actual control quantity is output, thereby realizing high-precision trajectory tracking control of the submarine tracked vehicle.

[0064] Further, the specific implementation process of the embodiment of the present application is as follows: In the embodiment of the present application, the parameters of the submarine crawler 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 submarine crawler, I is the moment of inertia of the submarine crawler; k1, k2, k3 are the coefficients of the submarine crawler trajectory tracker respectively; α 11 ,α 12 ,α 21 ,α 22 are the radial basis vector neural network adjustment coefficients respectively; the starting coordinates and direction angles of the reference submarine crawler are (3 -1 0.25π), and the starting coordinates and direction angles of the actual crawler are (110.5π); the reference speed v=0.5m / s, the reference angular velocity ω=0rad / s, the starting speed v=0m / s, and the starting angular velocity ω=0rad / s are set; the predetermined tracking trajectory of the crawler is the expected trajectory is a straight line with a starting point of (3 0) and an angle of π / 4 with the positive direction of the x-axis.

[0065] First, according to Newton's principle, the position state equation of the submarine crawler is established as follows:

[0066]

[0067] The motion state of the submarine crawler is determined by its position in the inertial coordinate system (x p ,y p ) and the direction of motion θ p to describe; the distance between the two tracks is L; the width of the track is d; x p ,y p are the x-axis and y-axis coordinates of the submarine crawler in the reference coordinate system; For x p ,y p The first derivative of v p is the travel speed of the submarine crawler at the center of mass C; θ p is the angle between the driving direction of the submarine crawler and the positive direction of the x-axis; is θ p The first derivative of p is the steering angular velocity of the submarine crawler.

[0068] According to Newton's principle and combined with the position state equation of the submarine crawler vehicle, the mathematical model of the submarine crawler vehicle under external interference is established as follows:

[0069]

[0070] Among them, U1 is the control input of the system, that is, the driving force of the crawler vehicle; U2 is also the control input of the system, that is, the rotational torque of the crawler vehicle; v p ,ω p The first-order derivative of ; d1, d2 are uncertain external disturbances; m is the mass; I is the moment of inertia.

[0071] In the embodiment of the present application, a mathematical model of the submarine crawler is constructed based on the principles of Newtonian mechanics to describe the dynamic characteristics of the submarine crawler in a complex submarine environment. This model reflects the motion law of the submarine crawler to optimize and ensure the stability and control performance of the submarine crawler under complex conditions.

[0072] Further, according to the mathematical model and expected value of the submarine crawler system under external interference, the tracking error function of the submarine crawler is obtained, and the tracking error function is converted according to the adaptive backstepping function to obtain the conversion error function;

[0073] The trajectory tracking process is that the submarine crawler starts from a given initial position and tracks the trajectory error (e x ,e y ,e θ ) T and control output (v,ω) T , so that e x →0,e y →0,e θ →0, and finally arrive at and continue to drive along the desired trajectory.

[0074]

[0075] Among them, e x and e y are the x-axis and y-axis errors of the actual position of the crawler relative to the reference position, namely the longitudinal displacement error and the lateral displacement error; e θ is the heading angle error; x b and b are the coordinates of the tracked vehicle reference position on the x-axis and y-axis respectively; θ b is the reference heading angle. Differentiating the tracking error formula gives the error dynamic model:

[0076]

[0077] In an embodiment of the present 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 of the submarine crawler vehicle and the actual motion trajectory is reduced, thereby achieving tracking control of the submarine crawler vehicle trajectory.

[0078] According to the mathematical model of the submarine crawler vehicle described in the mobile crawler, the control input is obtained as:

[0079]

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

[0081] In an embodiment of the present application, based on a pre-established mathematical model of a submarine crawler and under the assumption of no slip, control input parameters are derived, and by adjusting these control input parameters, it is ensured that the submarine crawler can follow the preset desired trajectory.

[0082] Taking the derivative of η, we get 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 embodiment of the present application, we first calculated the torque tracking error of the submarine crawler 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, the torque tracking error is minimized, and the control law of the submarine crawler is calculated to ensure the stability and performance optimization of the submarine crawler in actual operation.

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

[0089]

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

[0091]

[0092] According to the Lyapunov stability theorem, it should be Negative semidefinite, that is

[0093]

[0094] Therefore, using the backstepping control method and combining the conversion error function, the submarine crawler 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 embodiment of the present application, a backstepping control method is used, 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 submarine crawler, but also the faster convergence rate enhances the real-time responsiveness of the trajectory tracking, thereby improving the overall performance of the submarine crawler system.

[0099] Furthermore, the radial basis function neural network is used to estimate the external disturbance, and the external disturbance term in the adaptive backstepping controller is replaced by the output value of the radial basis function neural network, so as to obtain the adaptive anti-interference controller and the actual control quantity of the adaptive backstepping controller, and realize the tracking control of the submarine crawler vehicle;

[0100] Using the universal approximation characteristics of radial basis neural network, the external interference d1 and d2 are approximated. The algorithm is:

[0101] d1=W1 T h(e v )+ε1;

[0102]

[0103] Among them, e v is the velocity error, e ω is the angular velocity error, both of which are inputs of the radial basis neural network, h(ev ), h(e ω ) is the Gaussian basis function output of the radial basis neural network, W1, W2 are the ideal weights of the radial basis neural network, ε1, ε2 are the approximation errors of the radial basis neural network, and the estimated value of the external interference is:

[0104]

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

[0106]

[0107] in, for The first derivative of 11 , α 21 , α 12 , α 22 is the controller parameter to be designed, which is a positive constant; M1 and M2 are the weights of the radial basis neural network.

[0108] In the embodiment of the present application, a radial basis function neural network is used to estimate external interference because of its universal approximation characteristics. The introduction of a radial basis function neural network improves the system's ability to respond quickly and adapt to external interference, and can accurately estimate the impact of external interference by real-time learning and dynamic adjustment of control strategies through a radial basis function neural network. The robustness of the control system is improved, and the tracking error is effectively reduced, so that the submarine crawler can perform tasks more stably and cope with complex changes in the marine environment.

[0109] The external disturbance term in the adaptive backstepping controller is replaced by the output value of the radial basis neural network, and the adaptive anti-interference controller is obtained as follows:

[0110]

[0111] In the embodiment of the present application, the external interference term in the adaptive backstepping controller is replaced by the output value of the radial basis neural network to obtain the adaptive anti-interference controller. This controller combines the estimation capabilities of the adaptive backstepping control and the radial basis neural network, and adopts the adaptive law, which reduces the dependence on the precise mathematical model and realizes effective adaptation and stable control of complex dynamic environments.

[0112] Embodiment 2 In the embodiment of the present application, the parameters of the submarine crawler system are 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. ; Wherein, m is the mass of the submarine crawler, I is the moment of inertia of the submarine crawler; k1, k2, k3 are the coefficients of the submarine crawler tracker respectively; α 11 ,α 12 ,α 21 ,α 22 are the radial basis vector neural network adjustment coefficients respectively; the starting coordinates and direction angles of the reference tracked vehicle are (11 0.66π), and the actual starting coordinates and direction angles of the submarine tracked vehicle are (0 0 0.66π); set the reference speed v=0.5m / s, the reference angular velocity ω=0.5rad / s, the reference angular velocity ω=0.33πrad / s at the turning point, the starting speed v=0m / s, and the starting angular velocity ω=0rad / 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 is parallel to the x-axis.

[0113] First, according to Newton's principle, the position state equation of the submarine crawler is established as follows:

[0114]

[0115] The motion state of the submarine crawler is determined by its position in the inertial coordinate system (x p ,y p ) and the direction of motion θ p to describe; the distance between the two tracks is L; the width of the track is d; x p ,y p are the x-axis and y-axis coordinates of the submarine crawler in the reference coordinate system; For x p ,y p The first derivative of v p is the travel speed of the submarine crawler at the center of mass C; θ p is the angle between the driving direction of the submarine crawler and the positive direction of the x-axis; is θ p The first derivative of p is the steering angular velocity of the submarine crawler.

[0116] According to Newton's principle and combined with the position state equation of the submarine crawler vehicle, the mathematical model of the submarine crawler vehicle under external interference is established as follows:

[0117]

[0118] Among them, U1 is the control input of the system, that is, the driving force of the crawler vehicle; U2 is also the control input of the system, that is, the rotational torque of the crawler vehicle; v p ,ω p The first-order derivative of ; d1, d2 are uncertain external disturbances; m is the mass; I is the moment of inertia.

[0119] Define the position tracking error as:

[0120]

[0121] Among them, e x and e y are the x-axis and y-axis errors of the actual position of the submarine crawler relative to the reference position, i.e., the longitudinal displacement error and the lateral displacement error; e θ is the heading angle error; x b and b are the coordinates of the reference position of the submarine crawler on the x-axis and y-axis respectively; θ b As the reference heading angle, the tracking error function is obtained as:

[0122]

[0123] in for e B First-order derivative; for e x First-order derivative; for e y First-order derivative; for e θ First-order derivative.

[0124] According to the mathematical model of the submarine crawler, the expected input is:

[0125]

[0126] Where η=(v p ,ω p ) T , v b and ω b They are respectively the reference driving speed and steering angular velocity of the submarine crawler; K1, K2, K3>0 are adjustment parameters.

[0127] Taking the derivative of η, we get 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 Lyapunov function V(e η ):

[0133]

[0134] V(e η ) to obtain the first-order derivative for:

[0135]

[0136] According to the Lyapunov stability theorem, should be semi-negative definite, that is

[0137]

[0138] Make The backstepping controller of the submarine crawler vehicle is obtained as:

[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] Using the universal approximation characteristics of radial basis neural network, the external interference d1 and d2 are approximated. The algorithm is:

[0142] d1=W1 T h(e v )+ε1;

[0143]

[0144] Among them, e vis the velocity error, e ω is the angular velocity error, both of which are inputs of the radial basis neural network, h(e v ), h(e ω ) is the Gaussian basis function output of the radial basis neural network, W1, W2 are the ideal weights of the radial basis neural network, ε1, ε2 are the approximation errors of the radial basis neural network, and the estimated value of the external interference is:

[0145]

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

[0147]

[0148] in, for The first derivative of 11 , α 21 , α 12 , α 22 is the controller parameter to be designed, which is a positive constant; M1 and M2 are the weights of the radial basis neural network.

[0149] The external disturbance term in the adaptive backstepping controller is replaced by the output value of the radial basis neural network, and the adaptive anti-interference controller is obtained as follows:

[0150]

[0151] The external disturbance term in the adaptive backstepping controller is replaced by the output value of the radial basis neural network to obtain the adaptive anti-disturbance controller.

[0152] The examples described in the present invention are merely descriptions of the preferred implementation modes of the present invention, and are not intended to limit the concept and scope of the present invention. Without departing from the design concept of the present invention, various modifications and improvements made to the technical solutions of the present invention by engineers and technicians in this field should all fall within the protection scope of the present invention.

Claims

1. A submarine crawler vehicle trajectory tracking control method based on adaptive backstepping control, characterized in that: The following steps are involved: S1. Based on the Newton-Euler equation, a mathematical model is constructed for the submarine crawler system with external interference; S2. According to the mathematical model and the expected trajectory state, a position tracking error function and a torque tracking error of the submarine crawler vehicle are obtained; S3, combining the backstepping control strategy, integrating the position tracking error function and the torque tracking error, and designing an adaptive backstepping controller for the submarine crawler vehicle; S4. Introduce a radial basis function neural network to estimate external interference, replace the external interference term in the adaptive backstepping controller with the output value of the radial basis function neural network, and obtain an adaptive anti-interference controller.

2. According to the method for tracking and controlling a submarine crawler vehicle trajectory based on adaptive backstepping control according to claim 1, the process of acquiring the mathematical model comprises: The first step is to establish the position state equation of the submarine crawler according to Newton's principle as follows: The motion state of the submarine crawler is determined by its position in the inertial coordinate system (x p ,y p ) and the direction of motion θ p to describe; the distance between the two tracks is L; the width of the track is d; x p ,y p are the x-axis and y-axis coordinates of the submarine crawler in the reference coordinate system; For x p ,y p The first derivative of v p is the travel speed of the submarine crawler at the center of mass C; θ p is the angle between the driving direction of the submarine crawler and the positive direction of the x-axis; is θ p The first derivative of p is the steering angular velocity of the submarine crawler; In the second step, combined with the position state equation of the submarine crawler, the mathematical model of the submarine crawler under external interference is established as follows: Among them, U1 is the control input of the system, which is the driving force of the crawler vehicle; U2 is the control input of the system, which is the rotational torque of the crawler vehicle; v p ,ω p The first-order derivative of ; d1, d2 are uncertain external disturbances; m is the mass; I is the moment of inertia.

3. According to the method for tracking and controlling a submarine crawler vehicle under external disturbance based on adaptive backstepping control according to claim 2, the process of obtaining the tracking error function comprises: The first step is to define the position tracking error as: Among them, e x and e y are the x-axis and y-axis errors of the actual position of the submarine crawler relative to the reference position, i.e., the longitudinal displacement error and the lateral displacement error; e θ is the heading angle error; x b and b are the coordinates of the reference position of the submarine crawler on the x-axis and y-axis respectively; θ b is the reference heading angle; The second step is to B Taking the derivative, we get the tracking error function as: in for e B First-order derivative; for e x First-order derivative; for e y First-order derivative; for e θ First-order derivative.

4. According to the method for tracking and controlling a submarine crawler vehicle trajectory based on adaptive backstepping control as claimed in claim 3, according to the mathematical model of the submarine crawler vehicle, the expected input is: in, η=(v p ,ω p ) T , v b and ω b They are respectively the reference driving speed and steering angular velocity of the submarine crawler; K1, K2, K3>0 are adjustment parameters.

5. According to the method for tracking the trajectory of a submarine crawler vehicle based on adaptive backstepping control in claim 4, the torque tracking error e is obtained according to the expected input. η , the acquisition process includes: The first step is to know the expected input η, assume that the linear velocity and angular velocity remain constant, and take the derivative of η to obtain the first-order time derivative of η The second step is to denote the expected input as η d , the actual input is η, and the torque tracking error e is obtained η :

6. According to the method for tracking the trajectory of a submarine crawler vehicle based on adaptive backstepping control according to claim 5, the backstepping controller of the submarine crawler vehicle is designed by the Lyapunov method, and the acquisition process of the backstepping controller includes: The first step is to construct the Lyapunov function The second step is to calculate V(e η ) to obtain the first-order derivative According to the Lyapunov stability theorem, Should be semi-negative, that is, the backstepping controller should be designed so that The backstepping controller of the submarine crawler vehicle is obtained as follows: U1=m[e v +K1(in p something θ -v b +e y ω p )-e ω in b blue θ ]; U2=I[e ω +K2v b (v b son θ -e x ω p )+K3v b things θ yes ω ]。 7. According to claim 6, a submarine crawler vehicle trajectory tracking control method based on adaptive backstepping control uses the universal approximation characteristics of radial basis neural network to approximate external disturbances d1 and d2; In the first step, the algorithm establishes the radial basis neural network model of external interference d1 and d2 as follows: d1=W1 T h(e v )+ε1; in, e v is the velocity error, e ω is the angular velocity error, both of which are inputs of the radial basis neural network, h(e v ), h(e ω ) is the Gaussian basis function output of the radial basis neural network, W1, W2 are the ideal weights of the radial basis neural network, ε1, ε2 are the approximation errors of the radial basis neural network; In the second step, according to the radial basis neural network model, the estimated value of the external interference is: in, is the output value of d1 and d2, is the output value of W1 and W2; On this basis, the design adaptation law is: in, for The first derivative of 11 , α 21 , α 12 , α 22 is the controller parameter to be designed, which is a positive constant; M1 and M2 are the weights of the radial basis neural network; In the third step, the iterative parameter weights are updated through the radial basis network to approximate the external interferences d1 and d2.

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

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