A motion control method for underwater robot based on RBF neural network

Abstract

The present invention discloses a motion control method for an underwater robot based on an RBF neural network, comprising the following steps: constructing an earth coordinate system, and constructing a dynamic model of the underwater robot in the coordinate system; designing a theoretical control law of the underwater robot based on the dynamic model; obtaining the actual control law of the underwater robot, and obtaining an inaccurate part model in the dynamic model based on the equivalent relationship between the actual control law and the theoretical control law; adaptively approximating the inaccurate part model based on an RBF neural network; correcting the theoretical control law based on the inaccurate part model after adaptive approximation to obtain a corrected control law; and controlling the motion of the underwater robot based on the corrected control law. The control method of the present invention can effectively improve the accuracy, robustness and adaptability of the control, and realize the posture stability and precise control during the operation of the underwater robot.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater robot motion control, and in particular relates to an underwater robot motion control method based on RBF neural network. Background Art

[0002] 71% of the earth's surface area is ocean, which contains valuable resources and is the second space for human survival. The rational use and development of marine resources will play an important role in the sustainable development of human society. However, the danger and complexity of the marine environment make it very difficult to develop and investigate the ocean solely by artificial means. With the need for in-depth development and exploration of the ocean by countries around the world, underwater operation equipment has emerged, and underwater robots (AUVs) are the most typical embodiment of this. Due to the special working environment of AUVs, the motion conditions are significantly different from those of land robots, and the control characteristics are also significantly different. Therefore, ensuring the stability and robustness of the AUV motion level is only the minimum requirement. Not only does the control accuracy have high requirements, but it also needs to meet the operating efficiency of the AUV, and the AUV's underwater working environment is changing at any time, so the motion control of the AUV is particularly important.

[0003] Currently, the common control algorithms in the industry include sliding mode control, PID control, S-surface control, etc.

[0004] Sliding mode control is insensitive to external disturbance factors and controlled system parameters and has good robustness. Therefore, it is suitable for control systems with large external disturbances and difficult-to-determine models. Therefore, sliding mode control has been successfully applied in underwater robot motion control. However, due to its switching characteristics, it is difficult to avoid jitter during the control process.

[0005] PID control is widely used in modern industrial control systems due to its simple structure and high control accuracy. However, since the control parameters of traditional PID control are fixed, it is difficult to achieve high-precision control of underwater robots in complex and changeable waters.

[0006] The S-surface control algorithm has a simple structure and small input, and its various characteristics are used in underwater robot motion control. However, its parameter control requires real-time manual modulation, which still has many inconveniences in practical applications.

[0007] In view of the above technical problems, it is urgent to propose an underwater robot motion control method based on RBF neural network. Summary of the invention

[0008] In order to solve the above technical problems, the present invention proposes an underwater robot motion control method based on RBF neural network to solve the problems existing in the above prior art.

[0009] To achieve the above object, the present invention provides an underwater robot motion control method based on RBF neural network, comprising the following steps:

[0010] Construct the earth coordinate system and build the dynamic model of the underwater robot under the coordinate system;

[0011] Based on the dynamic model, design the theoretical control law of the underwater robot;

[0012] Obtaining an actual control law of the underwater robot, and based on the equivalent relationship between the actual control law and the theoretical control law, obtaining an inaccurate partial model in the dynamic model, and performing adaptive approximation on the inaccurate partial model;

[0013] The theoretical control law is corrected based on the inaccurate partial model after adaptive approximation to obtain a corrected control law;

[0014] The motion of the underwater robot is controlled based on the modified control law.

[0015] Optionally, the process of constructing a dynamic model of the underwater robot includes: obtaining the fixed position and direction vector of the underwater robot in the earth coordinate system, the linear velocity and angular velocity in the body coordinate system, and all the forces and torques it is subjected to in the body coordinate system, and constructing a dynamic model based on the functional relationship between the acquired underwater robot data.

[0016] Optionally, the formula of the kinetic model is as follows:

[0017]

[0018] Among them, M RB and C RB is the inertia matrix and Coriolis effect matrix associated with the rigid body, M A is the additional mass matrix, C A is the Coriolis effect matrix caused by the additional mass, D(v) is the damping matrix including all drag and lift, g(η) is the combined effect of gravity and buoyancy, v is the velocity vector of the system, is the acceleration of the system.

[0019] Optionally, the formula of the inaccurate part model is as follows:

[0020]

[0021] Where M = M RB +M A , C=C RB +C A, ΔM=M0-M, ΔC=C0-C, ΔD=D0-D, Δg=g0-g, M0, C0, D0, g0 are the parameters of M, C, D, g under ideal conditions; ΔM, ΔC, ΔD, Δg are the parameter differences between the ideal model and the actual model, respectively, M RB and C RB are the inertia matrix and Coriolis effect matrix associated with the rigid body, M A is the additional mass matrix, C A is the Coriolis effect matrix caused by the additional mass, D is the damping matrix including all drag and lift, g is the combined effect of gravity and buoyancy, q is the actual position, and is the corresponding derivative.

[0022] Optionally, the process of adaptively approximating the inaccurate partial model includes: constructing an RBF neural network, and adaptively approximating the inaccurate partial model based on the RBF neural network.

[0023] Optionally, the formula of the RBF neural network is as follows:

[0024]

[0025] f(x)=θ T h(x)+ε

[0026] in, is the input of the RBF neural network, j is the jth node of the hidden layer of the network, c ij is the center vector of the Gaussian function, b j is the width of the basis vector, h = [h j ] T is the Gaussian basis function output of the network, θ is the weight of the network, and ε is the approximation error of the network.

[0027] Optionally, the formula of the modified control law is expressed as follows:

[0028]

[0029] Where e = qq d , q is the actual position, q d For an ideal location, is the corresponding derivative, k v is the static position error coefficient, k p is the static speed error coefficient.

[0030] Compared with the prior art, the present invention has the following advantages and technical effects:

[0031] The present invention adopts an adaptive RBF neural network control method, which can greatly accelerate the learning speed and avoid the local minimum problem compared with the traditional BP neural network. It is suitable for the requirements of real-time control, can effectively improve the accuracy, robustness and adaptability of the control system, and realize the posture stability and precise control of the underwater robot during operation. The control algorithm can ensure the boundedness of the neural network weights and solve the problem of the consistent and ultimately bounded weights of the neural network. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0033] Figure 1 A control flow chart of an underwater robot based on a dynamic model according to an embodiment of the present invention;

[0034] Figure 2 A schematic diagram of an RBF approximation neural network according to an embodiment of the present invention;

[0035] Figure 3 This is a schematic diagram of a coordinate system constructed for an underwater robot according to an embodiment of the present invention. DETAILED DESCRIPTION

[0036] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0037] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0038] Embodiment 1

[0039] This embodiment provides an underwater robot motion control method based on adaptive RBF neural network control, including the following steps:

[0040] (1) Construct the rigid body coordinate system and inertial coordinate system of the underwater robot, and construct the earth position coordinate system.

[0041] (2) Establish a mathematical model of the underwater robot, which includes the underwater dynamics model and control function of the underwater robot.

[0042] like Figure 3 As shown, is the fixed position and direction vector of the underwater robot in the earth coordinate system, where [xyz] TFor fixed position, is the direction vector.

[0043] v=[V B ω B ] T =[uvwpqr] T is the linear velocity and angular velocity of the underwater robot in the body coordinate system, where V B =[uvw] T is the linear velocity, ω B =[pqr] T is the angular velocity.

[0044] F propulsion =[XYZKMN] T It is the total force and torque acting on the underwater robot in the body coordinate system.

[0045] The Earth coordinate system is fixed on the Earth and follows the right-hand rule. Its origin coincides with the Earth's center of mass, the Z axis points to the Earth's North Pole, the X axis points to the intersection of the Earth's equatorial plane and the Greenwich meridian, and the Y axis is in the agreed equatorial plane.

[0046] The body coordinate system is fixed on the underwater robot body and follows the right-hand rule. Its origin coincides with the center of gravity of the underwater robot. The X-axis points to the positive direction of the body and is perpendicular to the Y-axis. The Z-axis points directly below the underwater robot and is perpendicular to the plane formed by the X-axis and the Y-axis.

[0047] The dynamic model of the underwater robot is:

[0048]

[0049] Among them, M RB and C RB is the inertia matrix and Coriolis effect matrix associated with the rigid body, M A is the additional mass matrix, C A is the Coriolis effect matrix caused by the additional mass, D(v) is the damping matrix including all drag and lift, g(η) is the combined effect of gravity and buoyancy. v is the velocity vector of the system, is the acceleration of the system.

[0050] Let the coordinates of the center of gravity of the underwater robot be x G =y G =z G = 0, then the inertia matrix M (M = M RB +M A )for:

[0051]

[0052] Where m is the mass of the underwater robot, I ij is the product of inertia. is the hydrodynamic parameter.

[0053] g(η) is the combined effect of gravity and buoyancy, expressed as:

[0054]

[0055] Where G and B are gravity and buoyancy respectively, x B ,y B ,z B is the buoyancy center coordinate of the underwater robot.

[0056] (3) The design theory control law is:

[0057]

[0058] Where e = qq d , q is the actual position, q d For an ideal location, is the corresponding derivative, k v is the static position error coefficient, k p is the static speed error coefficient.

[0059] A stable closed-loop system is obtained:

[0060] where q d is the ideal position, e = qq d ,

[0061] In actual engineering, it is difficult to obtain an accurate model. Let the actual model be expressed as M0(q), g0(q).

[0062] Then the control law of the actual model can be obtained as:

[0063]

[0064] Substituting it into the theoretical control law, we can get:

[0065]

[0066] Let ΔM=M0-M, ΔC=C0-C, ΔD=D0-D, Δg=g0-g, M0, C0, D0, g0 are the parameters of M, C, D, g under ideal conditions, ΔM, ΔC, ΔD, Δg are the parameter differences between the ideal model and the actual model respectively, then:

[0067]

[0068] Assumptions Construct the inaccurate part model as

[0069] The error state equation is:

[0070] in

[0071] The modified control law is:

[0072]

[0073] like Figure 2 As shown in the figure, RBF neural network control is used to ensure the global convergence of the underwater robot controller.

[0074] The RBF neural network is used to adaptively approximate the inaccurate part by modifying the weights of the RBF neural network. RBF is a 3-layer neural network with a structure like Figure 1 As shown, it includes input layer, hidden layer and output layer. The input layer to the hidden layer is a nonlinear mapping, and the activation function uses the radial basis function:

[0075] h(x,c)=h(||xc||);

[0076] Where x is an arbitrary point and c is a central point.

[0077] The input of the RBF neural network is the error between the ideal position and the actual position and the error of its derivative e=qq d ,

[0078] Then the algorithm of RBF neural network is:

[0079]

[0080] f(x)=θ T h(x)+ε

[0081] in, is the input of the RBF neural network, j is the jth node of the hidden layer of the network, c ij is the center vector of the Gaussian function, b j is the width of the basis vector, h = [h j ] T is the Gaussian basis function output of the network, θ is the weight of the network, and ε is the approximation error of the network.

[0082]

[0083] The approximation error is bounded, and its bound is ε0, that is,

[0084]

[0085] θ=[θ1,θ2,…,θ j ]There are optimal parameters:

[0086]

[0087] Where β is the domain of θ.

[0088] Define the Lyapunov function as:

[0089]

[0090] Where γ>0 is the learning rate of the neural network, is θ * The estimated value of

[0091] At this time, the state error equation can be written as:

[0092]

[0093] The matrix P is a symmetric positive definite matrix and satisfies the following Lyapunov equation:

[0094] PA+A T P = -Q;

[0095] Where Q≥0.

[0096] but:

[0097]

[0098] in:

[0099]

[0100] but:

[0101]

[0102] The adaptive law of the RBF neural network weights is:

[0103]

[0104] have to:

[0105]

[0106] Knowing the properties of the F norm, we have but:

[0107]

[0108]

[0109] Pick but Therefore, the designed control rate meets the Lyapunov stability requirements. And the boundedness of the weights can be guaranteed, which can solve the problem of consistent and ultimately bounded weights of neural networks.

[0110] At this point the actual output of the neural network is:

[0111]

[0112] (4) Construct an underwater robot controller based on the underwater dynamics model.

[0113] The controller is designed as follows:

[0114] τ=τ1+τ2

[0115] in

[0116] τ2=-M0(q)f.

[0117] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A motion control method for an underwater robot based on RBF neural network, characterized in that: The following steps are involved: Construct the earth coordinate system and build the dynamic model of the underwater robot under the coordinate system; Based on the dynamic model, design the theoretical control law of the underwater robot; Obtaining an actual control law of the underwater robot, and based on the equivalent relationship between the actual control law and the theoretical control law, obtaining an inaccurate partial model in the dynamic model, and performing adaptive approximation on the inaccurate partial model; The theoretical control law is corrected based on the inaccurate partial model after adaptive approximation to obtain a corrected control law; Control the motion of the underwater robot based on the modified control law; The design theory control law is: Where e = qq d , q is the actual position, q d For an ideal location, is the corresponding derivative, k v is the static position error coefficient, k p is the static speed error coefficient; A stable closed-loop system is obtained: In actual engineering, let the actual model be expressed as M0(q), g0(q), Then the actual control law is: Substituting the actual control law into the theoretical control law, we get: Let ΔM=M0-M, ΔC=C0-C, ΔD=D0-D, Δg=g0-g, M0, C0, D0, g0 are the parameters of M, C, D, g under ideal conditions, ΔM, ΔC, ΔD, Δg are the parameter differences between the ideal model and the actual model respectively, then: Assumptions The inaccurate part of the model is constructed as: Where M = M RB +M A , C=C RB +C A , M RB and C RB are the inertia matrix and Coriolis effect matrix associated with the rigid body, M A is the additional mass matrix, C A is the Coriolis effect matrix caused by the additional mass, D is the damping matrix including all drag and lift, g is the combined effect of gravity and buoyancy, q is the actual position, and is the corresponding derivative; The error state equation is: in The corrected control law is: Among them, f is the inaccurate part model; The process of adaptively approximating the inaccurate partial model includes: constructing an RBF neural network, and adaptively approximating the inaccurate partial model based on the RBF neural network; The formula of RBF neural network is as follows: f(x)=θ T h(x)+e in, is the input of the RBF neural network, j is the jth node of the hidden layer of the network, c ij is the center vector of the Gaussian function, b j is the width of the basis vector, h = [h j ] T is the Gaussian basis function output of the network, θ is the weight of the network, and ε is the approximation error of the network.

2. The underwater robot motion control method based on RBF neural network according to claim 1 is characterized in that: The process of constructing the dynamic model of the underwater robot includes: obtaining the fixed position and direction vector of the underwater robot in the earth coordinate system, the linear velocity and angular velocity in the body coordinate system, and all the forces and torques it is subjected to in the body coordinate system, and constructing the dynamic model based on the functional relationship between the acquired underwater robot data.

3. The underwater robot motion control method based on RBF neural network according to claim 2 is characterized in that: The formula of the kinetic model is as follows: Among them, M RB and C RB is the mass matrix and Coriolis effect matrix associated with the rigid body, M A is the additional mass matrix, C A is the Coriolis effect matrix caused by the additional mass, D(v) is the damping matrix including all drag and lift, g(η) is the combined effect of gravity and buoyancy, v is the velocity vector of the system, is the acceleration of the system.

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