Underwater mechanical arm trajectory tracking control method based on RBF neural network and sliding mode surface

Abstract

The invention provides an underwater mechanical arm trajectory tracking control method based on an RBF neural network and a sliding mode surface. The underwater mechanical arm trajectory tracking control method comprises the following steps that an underwater dynamic model and an electric drive mathematical model are established; constructing a cascade dynamic equation set; setting an expected input signal and defining a related error; designing a sliding mode function of a fast terminal sliding mode surface, defining a Lyapunov equation expression and deriving the Lyapunov equation expression; designing a singular point eliminating function according to the singular point problem existing in the sliding mode function, and updating a derivation function of the Lyapunov equation; and designing an RBF neural network and a weight to carry out neural network approximation on a nonlinear term of a derivation function of the Lyapunov equation, and designing an electric drive auxiliary controller and a dynamics auxiliary controller. On the basis of considering the auxiliary control of the electric driving force, the rapid terminal sliding mode control method is improved, the stability and the convergence speed of the trajectory tracking control method of the underwater mechanical arm are improved, and specific requirements of different application occasions can be met.

Description

Technical Field

[0001] The invention relates to an underwater vehicle-manipulator system (UVMS), and in particular to an underwater manipulator trajectory tracking control method based on RBF neural network and sliding surface. Background Art

[0002] The underwater vehicle manipulator system (UVMS) can control the underwater manipulator to complete underwater tasks instead of humans, and is currently an effective means of developing underwater ocean energy. Usually, when the manipulator is connected to the underwater vehicle, a UVMS is formed. As an important tool for underwater vehicles, UVMS is of great significance for underwater real-time photography, underwater target reconnaissance and monitoring, marine resource development, marine biological exploration and other tasks. UVMS plays an important role in various marine underwater tasks and has become the research focus of many scholars.

[0003] Due to the strong robustness of sliding mode control, corresponding control methods have been proposed at home and abroad for underwater manipulator trajectory tracking. For example, sliding mode control is used to design the controller, and non-singular terminal sliding mode control methods are used. On the one hand, it does not have a fast convergence speed, and on the other hand, it does not consider the influence of electric drive. If the influence of electric drive is not considered, the tracking accuracy of underwater manipulator trajectory tracking control will be low. Summary of the invention

[0004] The purpose of the present invention is to propose a trajectory tracking control method for an underwater manipulator based on an RBF neural network and a sliding surface, wherein the trajectory tracking control is more stable and converges faster under consideration of electric drive motion.

[0005] To achieve the above object, the technical solution of the present invention is: a method for tracking and controlling the trajectory of an underwater manipulator based on an RBF neural network and a sliding surface, comprising the following steps:

[0006] Step 1: Establish an underwater dynamics model and an electric drive mathematical model to provide a theoretical basis for the construction of the cascade dynamics equations in step 2;

[0007] Step 2: Construct the cascade dynamics equations to provide a more detailed and reliable mathematical model for the design of the control method;

[0008] Step 3: Set the expected input signal and substitute it into the cascade dynamic equations, thereby introducing the electric drive auxiliary controller and the dynamic auxiliary controller, and defining the related errors;

[0009] Step 4: Design the sliding function of the fast terminal sliding surface, define the Lyapunov equation expression and derive it;

[0010] Step 5: According to the singular point problem of the sliding mode function, a function to eliminate the singular point is designed, and the derivative function of the Lyapunov equation is updated;

[0011] Step 6: Design RBF neural network and weights to perform neural network approximation on the nonlinear terms of the derivative functions of the Lyapunov equation in steps 4 and 5;

[0012] Step 7: Design the electric drive auxiliary controller and dynamic auxiliary controller to realize the trajectory tracking control of the underwater manipulator.

[0013] Furthermore, in step 1, the mathematical model of the underwater manipulator and electric drive is established as follows:

[0014]

[0015] In the formula, q, They represent the joint angle, the first-order derivative of the joint angle, and the second-order derivative of the joint angle respectively. M(q) is the inertia matrix. is the centripetal force and Coriolis force coefficient matrix, is the water resistance coefficient matrix, G(q) is the equivalent gravity vector matrix, τ ms is the dynamic control input, Δ represents the uncertain disturbance, including the influence of the underwater robot body on the underwater manipulator, I is the current, K me is the conversion matrix between torques, τ me Indicates the motor driving force.

[0016] Furthermore, the cascade kinetic equations are:

[0017]

[0018] Where L e Represents inductance, R e Represents resistance, K e represents capacitance, τ e represents a voltage source, Represents the first derivative of the current.

[0019] Furthermore, the step 3 is specifically as follows:

[0020] Set the expected input signal I d , and introduce the dynamic auxiliary controller τ1:

[0021]

[0022] Utilize I d The cascade dynamics equations are updated and the electric drive auxiliary controller τ2 is introduced:

[0023]

[0024] Define the current error η and the tracking error e of the joint:

[0025] η=I d -I

[0026] e=q d -q

[0027] Among them, M, C, D, and G are M(q), Simplification of G(q), q d is the expected current, is the second-order derivative of the desired current.

[0028] Furthermore, the function of the fast terminal sliding surface is:

[0029]

[0030] Among them, γ1 and γ2 represent positive numbers, and γ1≥1, 0≤γ2≤1, α1 and α2 are positive gain matrices, is the first-order derivative of the joint tracking error;

[0031] The first derivative of the function of the fast terminal sliding surface is:

[0032]

[0033] Introducing auxiliary variables and μ:

[0034]

[0035] The specific expression of the Lyapunov equation is:

[0036]

[0037] Where L represents the inductance matrix, and the derivative of the Lyapunov equation is:

[0038]

[0039] in, is the first-order derivative of the desired input signal.

[0040] Furthermore, the step 5 is specifically: for the singular point phenomenon in the derivative function of the Lyapunov equation in step 4 Perform saturation processing and design the saturation function as follows:

[0041]

[0042] in, is a positive number, use sat(vz ) instead

[0043] The first-order derivative of the improved sliding surface is defined as First-order derivative based on improved sliding surface Inversely infer the new sliding surface s2 and update the Lyapunov function to:

[0044]

[0045] And update the derivative function of the Lyapunov equation:

[0046]

[0047] Furthermore, the step 6 is specifically to define f1 and f2 as nonlinear terms of the derivative function of the Lyapunov equation in step 4, and perform RBF neural network approximation on the nonlinear terms f1 and f2. The specific expression is:

[0048]

[0049] Among them, W1 and W2 represent the ideal weights of the neural network, h1(x) and h2(x) represent the Gaussian function output vectors, ε1 and ε2 represent the approximation errors of the network unknown to the nonlinear function,

[0050] Replace f1 with f3, and define f3 as the nonlinear term of the derivative function of the Lyapunov equation in step 5. Perform RBF neural network approximation on the nonlinear term f3. The specific expression is:

[0051]

[0052] Among them, W 1N represents the ideal weights of the improved neural network,

[0053] Furthermore, the design of the electric drive auxiliary controller and the dynamic auxiliary controller in step 7 is specifically as follows:

[0054]

[0055] Among them, τ1 represents the dynamic auxiliary controller and τ2 represents the electric drive auxiliary controller.

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

[0057] The present invention provides a cascade sliding mode underwater manipulator trajectory tracking control method based on RBF neural network, so as to enable the underwater manipulator to maintain a stable trajectory tracking control effect in a complex underwater environment, and consider the influence of electric drive to form cascade control. Compared with the traditional non-singular fast terminal sliding mode control method, it can more stably complete the work requirements and ensure that the control system has good performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a spatial motion diagram of the underwater mechanical arm implemented by the present invention carried by the underwater robot;

[0059] Figure 2 It is a rendering of the spatial trajectory tracking effect of the underwater manipulator implemented by the present invention;

[0060] Figure 3 This is the trajectory tracking effect of the underwater manipulator joint 1, joint 2, and joint 3 in the embodiment of the present invention;

[0061] Figure 4 It is the tracking effect of the underwater manipulator in the x-direction, y-direction and z-direction in the embodiment of the present invention;

[0062] Figure 5 are the tracking errors of the underwater manipulator in the x-, y- and z-directions according to the embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following is combined with Figure 1-5 , the technical solution of the present invention is specifically described.

[0064] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0065] 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. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0066] The present invention proposes a trajectory tracking control method for an underwater manipulator based on an RBF neural network and a sliding surface. On the basis of fast terminal sliding mode control, a saturation function is eliminated for singular points, and an RBF neural network is used to approximate nonlinear terms. Furthermore, considering the influence of electric drive, a trajectory tracking control method of cascade control is proposed. By comparing the tracking effects of the underwater manipulator under ordinary sliding mode control and PD control, the superiority of the control method proposed in this patent is verified.

[0067] The present invention proposes a method for tracking and controlling underwater manipulator trajectory based on RBF neural network and sliding surface, and the specific steps are as follows:

[0068] Establish mathematical models of underwater manipulator and electric drive:

[0069]

[0070] In the formula, q, They represent the joint angle, the first-order derivative of the joint angle, and the second-order derivative of the joint angle respectively. M(q) is the inertia matrix. is the centripetal force and Coriolis force coefficient matrix, is the water resistance coefficient matrix, G(q) is the equivalent gravity vector matrix, τ ms is the dynamic control input, Δ represents the uncertain disturbance, including the influence of the underwater robot body on the underwater manipulator, I is the current, K me is the conversion matrix between torques, τ me Indicates the motor driving force.

[0071] Construct the cascade kinetic equations:

[0072]

[0073] Where L e Represents inductance, R e Represents resistance, K e represents capacitance, τ e represents a voltage source, Represents the first derivative of the current.

[0074] Set the expected input signal:

[0075]

[0076] Among them, M, C, D, and G are M(q), Simplification of G(q), q d is the expected current, is the second-order derivative of the desired current, and τ1 is the auxiliary controller of the underwater manipulator dynamics.

[0077] Utilize Id Update the cascade dynamics equations:

[0078]

[0079] Among them, τ2 is the auxiliary controller of the electrical system.

[0080] The tracking error of the joint is defined as follows:

[0081] e=q d -q

[0082] The current tracking error is defined as follows:

[0083] η=I d -I

[0084] To ensure the convergence quality, the fast terminal sliding surface is selected as:

[0085]

[0086] Among them, γ1 and γ2 represent positive integers, γ1≥1, 0≤γ2≤1, and α1 and α2 are positive gain matrices.

[0087] The first-order derivative of the sliding surface is further obtained as:

[0088]

[0089] To facilitate calculation, auxiliary variables are introduced and μ, are expressed as follows:

[0090]

[0091] To ensure the stability of the system, we can define the Lyapunov function for the error, mechanical subsystem, and electrical signal flux system as:

[0092]

[0093] Further obtain the derivative function of the Lyapunov equation:

[0094]

[0095] This function contains nonlinear terms. For the trajectory tracking control of the underwater manipulator, the nonlinear term has a certain influence on the control result, so the RBF neural network is used to approximate the nonlinear term:

[0096]

[0097] Among them, weight, hidden layer input and approximation error are represented by W i 、h iand ε i To express.

[0098] When e→0, the There will be a singular point phenomenon, which will cause the controller to have a fault phenomenon. Singular point phenomenon will occur for saturation processing, and the fast terminal sliding surface will be modified to a non-singular fast terminal sliding surface. The saturation function is designed as:

[0099]

[0100] in, Is a positive number.

[0101] Use sat(v z ) instead The first-order derivative of the improved sliding surface is defined as:

[0102]

[0103] First-order derivative based on improved sliding surface The new sliding surface s2 is inversely deduced, thereby improving the fast terminal sliding mode controller s1 to a non-singular fast terminal sliding surface s2.

[0104] In order to ensure the stability of the system, its Lyapunov function is defined as:

[0105]

[0106] Taking the derivative of the Lyapunov function,

[0107]

[0108] Apply neural network to approximate the nonlinear terms:

[0109]

[0110] Among them, W 1N represents the ideal weights of the improved neural network,

[0111] Therefore, the auxiliary controllers τ1 and τ2 can be designed as:

[0112]

[0113] Among them, τ1 represents the dynamic auxiliary controller and τ2 represents the electric drive auxiliary controller.

[0114] Finally, the Lyapunov function is set to verify the stability of the embodiment of the present invention:

[0115]

[0116] Further we can get:

[0117]

[0118] In order to ensure the robustness of the neural network controller, in terms of weight adjustment, it is defined as follows:

[0119]

[0120] in, represents the adjusted weight derivative, Represents the adjusted weight derivative, W 1e represents the ideal weight of the neural network, W 2e represents the ideal weights of the neural network, k1 and k2 represent constants, which are positive, and h1(X1) and h2(X2) represent the outputs of the updated Gaussian function.

[0121] Obviously, the system error is asymptotically stable. This verifies that the non-singular fast terminal sliding mode cascade controller based on the RBF neural network proposed in the present invention has good stability and can ensure that the UVMS has good stability and tracking accuracy when tracking underwater trajectories.

[0122] Figure 2 This is the effect diagram of the underwater manipulator space trajectory tracking implemented by the present invention. By comparing with the RBF neural network (NN) and PD control, it can be seen that the control algorithm proposed by the present invention has a significantly better tracking effect than the other two control methods.

[0123] Figure 3 This is the trajectory tracking effect of the underwater manipulator joints 1-3 in the embodiment of the present invention. By comparing with the RBF neural network (NN) and PD control, it can be seen that the non-singular fast terminal sliding surface based on the neural network and the sliding mode controller based on the neural network proposed in this patent have higher tracking stability than the PD control.

[0124] Figure 4 This is the tracking effect of the underwater manipulator in the x, y, and z directions under the embodiment of the present invention. By comparing with the RBF neural network (NN) and PD control, it can be seen that in the method with neural network control, the tracking effect of x can be stable. As for the RBF-based non-singular fast terminal sliding mode control method proposed in this patent, it can track the desired trajectory faster and more stably.

[0125] Figure 5It is the tracking error of the underwater manipulator in the x, y, and z directions in the embodiment of the present invention. By comparing with the RBF neural network (NN) and PD control, it can be seen that the control algorithm proposed in the present invention has a smaller tracking error in the x direction than the other two control methods, which verifies that the control algorithm proposed in this patent has a more stable tracking in the x direction.

Claims

1. A method for tracking and controlling underwater manipulator trajectory based on RBF neural network and sliding surface, characterized in that: The following steps are involved: Step 1: Establish an underwater dynamics model and an electric drive mathematical model to provide a theoretical basis for the construction of the cascade dynamics equations in step 2; Step 2: Construct the cascade dynamics equations to provide a more detailed and reliable mathematical model for the design of the control method; Step 3: Set the expected input signal and substitute it into the cascade dynamic equations, thereby introducing the electric drive auxiliary controller and the dynamic auxiliary controller, and defining the related errors; Step 4: Design the sliding function of the fast terminal sliding surface, define the Lyapunov equation expression and derive it; Step 5: According to the singular point problem of the sliding mode function, a function to eliminate the singular point is designed, and the derivative function of the Lyapunov equation is updated; Step 6: Design RBF neural network and weights to perform neural network approximation on the nonlinear terms of the derivative functions of the Lyapunov equation in steps 4 and 5; Step 7: Design the electric drive auxiliary controller and dynamic auxiliary controller to realize the trajectory tracking control of the underwater manipulator.

2. The underwater manipulator trajectory tracking control method based on RBF neural network and sliding surface according to claim 1 is characterized in that: In step 1, the mathematical model of the underwater manipulator and electric drive is established as follows: In the formula, q, They represent the joint angle, the first-order derivative of the joint angle, and the second-order derivative of the joint angle respectively. M(q) is the inertia matrix. is the centripetal force and Coriolis force coefficient matrix, is the water resistance coefficient matrix, G(q) is the equivalent gravity vector matrix, τ ms is the dynamic control input, Δ represents the uncertain disturbance, including the influence of the underwater robot body on the underwater manipulator, I is the current, K me is the conversion matrix between torques, τ me Indicates the motor driving force.

3. The underwater manipulator trajectory tracking control method based on RBF neural network and sliding surface according to claim 2 is characterized in that: The cascade kinetic equations are: Where L e Represents inductance, R e Represents resistance, K e represents capacitance, τ e represents a voltage source, Represents the first derivative of the current.

4. The underwater manipulator trajectory tracking control method based on RBF neural network and sliding surface according to claim 3 is characterized in that: The step 3 is specifically as follows: Set the expected input signal I d , and introduce the dynamic auxiliary controller τ1: Utilize I d The cascade dynamics equations are updated and the electric drive auxiliary controller τ2 is introduced: Define the current error η and the tracking error e of the joint: η=I d -I e=q d -q Among them, M, C, D, and G are M(q), Simplification of G(q), q d is the expected current, is the second-order derivative of the desired current.

5. The underwater manipulator trajectory tracking control method based on RBF neural network and sliding surface according to claim 4 is characterized in that: The function of the fast terminal sliding surface is: Among them, γ1 and γ2 represent positive numbers, and γ1≥1, 0≤γ2≤1, α1 and α2 are positive gain matrices, is the first-order derivative of the joint tracking error; The first derivative of the function of the fast terminal sliding surface is: Introducing auxiliary variables and μ: The specific expression of the Lyapunov equation is: Where L represents the inductance matrix, and the derivative of the Lyapunov equation is: in, is the first-order derivative of the desired input signal.

6. The underwater manipulator trajectory tracking control method based on RBF neural network and sliding surface according to claim 5 is characterized in that: The step 5 is specifically as follows: The phenomenon of singular points in the derivative function of the Lyapunov equation in step 4 Perform saturation processing and design the saturation function as follows: in, is a positive number, use sat(v z ) instead The first-order derivative of the improved sliding surface is defined as First-order derivative based on improved sliding surface Inversely infer the new sliding surface s2 and update the Lyapunov function to: And update the derivative function of the Lyapunov equation:

7. The underwater manipulator trajectory tracking control method based on RBF neural network and sliding surface according to claim 6 is characterized in that: Specifically, step 6 is to define f1 and f2 as nonlinear terms of the derivative function of the Lyapunov equation in step 4, and perform RBF neural network approximation on the nonlinear terms f1 and f2. The specific expression is: Among them, W1 and W2 represent the ideal weights of the neural network, h1(x) and h2(x) represent the output vectors of the Gaussian function, ε1 and ε2 represent the approximation errors of the network unknown to the nonlinear function, Replace f1 with f3, and define f3 as the nonlinear term of the derivative function of the Lyapunov equation in step 5. Perform RBF neural network approximation on the nonlinear term f3. The specific expression is: Among them, W 1N Represents the ideal weights of the improved neural network.

8. The underwater manipulator trajectory tracking control method based on RBF neural network and sliding surface according to claim 7 is characterized in that: The design of the electric drive auxiliary controller and the dynamic auxiliary controller in step 7 is specifically as follows: Among them, τ1 represents the dynamic auxiliary controller and τ2 represents the electric drive auxiliary controller.

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