Flexible space manipulator control method, device and medium based on evaluation network

Abstract

In the disclosed embodiment, a flexible space manipulator control method, device and medium based on an evaluation network are provided, which belongs to the field of control technology, and specifically includes: combining the assumed modal method and the Lagrange equation to derive the dynamic model of the flexible space manipulator system; combining the singular perturbation theory to deconstruct the dynamic model, and obtain the dynamic differential equations of the slow time-varying subsystem and the fast time-varying subsystem; designing an adaptive trajectory tracking optimal controller for the slow time-varying subsystem based on the evaluation network; designing a vibration suppression controller for the fast time-varying subsystem based on fuzzy logic; constructing a hybrid control scheme based on the adaptive trajectory tracking optimal controller of the slow time-varying subsystem based on the evaluation network and the fuzzy controller of the fast time-varying subsystem, and obtaining the total control input of the flexible space manipulator system. Through the scheme disclosed in the present invention, the controller result is simplified, and the control efficiency, control accuracy and adaptability are improved.

Description

Technical Field

[0001] The embodiments of the present disclosure relate to the field of control technology, and in particular to a flexible space robot arm control method, device and medium based on an evaluation network. Background Art

[0002] At present, space robots are special spacecraft composed of a free-floating base and a robotic arm. They are mostly used in the assembly, construction, operation and maintenance of space stations, and undertake space tasks such as cabin segment transfer and docking, extravehicular equipment installation and maintenance, spacecraft fuel filling, hovering vehicle capture, failed satellite repair, platform payload care, etc. In recent years, as space missions have developed in the direction of diversification, refinement and intelligence, the structure and material of space robots have been greatly optimized and upgraded. Due to design and manufacturing reasons, the slender and lightweight space robot arm has inherent flexibility and exhibits characteristics such as low stiffness and low damping, which can easily produce large vibrations under the impact of external loads. And because the air in the space environment is extremely thin, the vibration of the flexible arm is extremely difficult to attenuate by itself, which has a great impact on the control accuracy and stability of the space robot arm.

[0003] The flexible space robot system is a high-dimensional, strongly coupled, and highly time-varying nonlinear system. There is mutual interference between the carrier posture motion and the robot joint motion, which brings great difficulties to the dynamic modeling and control method design of the space robot. Traditional control methods based on precise dynamic models do not consider the time-varying characteristics of system parameters, making it difficult to achieve satisfactory control effects; in addition, these control methods usually adopt centralized control strategies, and the controller structure is relatively complex, which consumes more onboard computing resources.

[0004] It can be seen that there is an urgent need for a simple, efficient and adaptable evaluation network-based flexible space robot control method. Summary of the invention

[0005] In view of this, the embodiments of the present disclosure provide a flexible space robot arm control method, device and medium based on an evaluation network, which at least partially solve the problems of poor control efficiency, convenience and adaptability in the prior art.

[0006] In a first aspect, an embodiment of the present disclosure provides a flexible space manipulator control method based on an evaluation network, comprising:

[0007] Step 1, combining the assumed modal method and the Lagrange equation, derive the dynamic model of the flexible space manipulator system;

[0008] Step 2, deconstruct the dynamic model by combining singular perturbation theory to obtain the dynamic differential equations of the slow time-varying subsystem and the fast time-varying subsystem;

[0009] Step 3, the slow time-varying subsystem designs an adaptive trajectory tracking optimal controller based on the evaluation network;

[0010] Step 4, design a vibration suppression controller for the fast time-varying subsystem based on fuzzy logic;

[0011] Step 5, a hybrid control scheme is constructed according to the adaptive trajectory tracking optimal controller of the slow time-varying subsystem based on the evaluation network and the fuzzy controller of the fast time-varying subsystem to obtain the total control input of the flexible space manipulator system.

[0012] According to a specific implementation of the embodiment of the present disclosure, the expression of the kinetic model is:

[0013]

[0014] in, is the positive definite inertia matrix of the system; is the vector of the system including the Coriolis force and the centrifugal force, q s =[θ0,θ1,θ2] T is the rigid coordinate variable of the system; q f =[δ 11 ,δ 12 ,δ 21 ,δ 22 ] T is the flexible coordinate variable of the system, K f =diag(k 11 ,k 12 ,k 21 ,k 22 ) is the stiffness matrix of the flexible arm, u=[u0,u1,u2] T is the control torque of the system.

[0015] According to a specific implementation of the embodiment of the present disclosure, step 2 specifically includes:

[0016] Combined with the singular perturbation theory, the stiffness matrix K of the flexible arm is defined as f The smaller element is k min , the singular perturbation factor is ε=(1 / k min ) 1 / 2 , and introduce the state variable ξ f and K ε (ε 2 ξ f =q f ,K ε =ε 2 K f ), from which the dynamic differential equation of the slow time-varying subsystem is derived as

[0017]

[0018] in, is the quantity corresponding to {··} when ε=0, is the control torque of the slow time-varying subsystem;

[0019] Define the fast-changing time scale t f (εt f = t-t0) and boundary layer correction and The dynamic differential equation of the fast time-varying subsystem is derived as follows:

[0020]

[0021] in, u f is the control torque of the fast time-varying subsystem.

[0022] According to a specific implementation of the embodiment of the present disclosure, step 3 specifically includes:

[0023] According to the decentralized principle, the slow time-varying subsystem can be decomposed into three cross-linked subsystems and the decentralized RBF neural network is used to reconstruct the model and identify the state, and the decentralized neural network state observer is obtained.

[0024] According to the decentralized neural network state observer, the second-order subsystem is identified and its actual local nominal control input and actual local feedback control input are designed, and robust control items are added;

[0025] An adaptive trajectory tracking optimal controller is constructed based on the actual local nominal control input, the actual local feedback control input and the robust control term.

[0026] According to a specific implementation of the embodiment of the present disclosure, the expression of the decentralized neural network state observer is:

[0027]

[0028] in, and They are the unknown nonlinear terms F i (x i ,x jd ) and g i (x i ), k i1 With k i2 is the observer gain;

[0029] The expression of the adaptive trajectory tracking optimal controller is:

[0030] in, is the actual local nominal control input, is the actual local feedback control input, is a robust control term.

[0031] According to a specific implementation of the embodiment of the present disclosure, step 4 specifically includes:

[0032] Determine the input variable of the second-order subsystem vibration suppression controller of the fast time-varying subsystem as δ ij and The output variable is u fij , the input variables are fuzzified and fuzzy inferenced respectively, and the output variables are defuzzified and gain operated, and the expression of the fuzzy vibration suppression controller of the fast time-varying subsystem is obtained as follows:

[0033] u f =-K f2 [u f11 ,u f12 ,u f21 ,u f22 ] T

[0034] Among them, K f2 ∈R 3×4 is the control gain matrix.

[0035] In a second aspect, an embodiment of the present disclosure further provides an electronic device, the electronic device comprising:

[0036] at least one processor; and,

[0037] a memory communicatively connected to the at least one processor; wherein,

[0038] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the flexible space robot arm control method based on the evaluation network in the aforementioned first aspect or any implementation of the first aspect.

[0039] In the third aspect, the embodiments of the present disclosure also provide a non-transitory computer-readable storage medium, which stores computer instructions, and the computer instructions are used to enable the computer to execute the flexible space robot arm control method based on the evaluation network in the aforementioned first aspect or any implementation of the first aspect.

[0040] In a fourth aspect, an embodiment of the present disclosure further provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium, and the computer program includes program instructions, which, when executed by a computer, enable the computer to execute the flexible space robot arm control method based on the evaluation network in the aforementioned first aspect or any implementation of the first aspect.

[0041] The flexible space manipulator control scheme based on the evaluation network in the disclosed embodiment includes: step 1, combining the assumed modal method and the Lagrange equation to derive the dynamic model of the flexible space manipulator system; step 2, combining the singular perturbation theory to deconstruct the dynamic model to obtain the dynamic differential equations of the slow time-varying subsystem and the dynamic differential equations of the fast time-varying subsystem; step 3, designing an adaptive trajectory tracking optimal controller for the slow time-varying subsystem based on the evaluation network; step 4, designing a vibration suppression controller for the fast time-varying subsystem based on fuzzy logic; step 5, constructing a hybrid control scheme based on the adaptive trajectory tracking optimal controller of the slow time-varying subsystem based on the evaluation network and the fuzzy controller of the fast time-varying subsystem to obtain the total control input of the flexible space manipulator system.

[0042] The beneficial effects of the embodiments of the present disclosure are as follows: through the scheme of the present disclosure, the flexible space manipulator system is dynamically modeled by the Lagrangian method, and then the system is decomposed into a slow time-varying subsystem that characterizes rigid motion and a fast time-varying subsystem that characterizes flexible vibration based on the singular perturbation method. For the slow time-varying subsystem, a decentralized neural network is used to reconstruct its dynamic model and identify its state variables, and an adaptive trajectory tracking optimal controller is designed in combination with the evaluation network and the performance index function; for the fast time-varying subsystem, an active vibration suppression controller is designed based on the fuzzy logic concept. The present invention can effectively simplify the controller structure and improve the model training speed, and can achieve high-precision, high-stability and rapid control of the flexible space manipulator without obtaining the precise dynamic parameters of the model, and has high engineering application potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0044] Figure 1 A schematic flow chart of a flexible space manipulator control method based on an evaluation network provided in an embodiment of the present disclosure;

[0045] Figure 2 A schematic diagram of the planar structure of a flexible space robot arm provided in an embodiment of the present disclosure;

[0046] Figure 3 A schematic diagram of a control structure of a second-order subsystem of a slowly time-varying subsystem provided in an embodiment of the present disclosure;

[0047] Figure 4 A membership function curve diagram of an input variable and an output variable provided in an embodiment of the present disclosure;

[0048] Figure 5 A schematic diagram of the structure of a fast time-varying subsystem fuzzy controller provided in an embodiment of the present disclosure;

[0049] Figure 6 A schematic diagram of the control system structure of a flexible space manipulator control method based on an evaluation network provided in an embodiment of the present disclosure;

[0050] Figure 7 A flow chart of a flexible space manipulator control method based on an evaluation network provided in an embodiment of the present disclosure;

[0051] Figure 8 A schematic diagram of an electronic device provided in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0052] The embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.

[0053] The following describes the embodiments of the present disclosure through specific examples, and those skilled in the art can easily understand other advantages and effects of the present disclosure from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all of the embodiments. The present disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present disclosure.

[0054] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0055] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present disclosure. The drawings only show components related to the present disclosure rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0056] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects described may be practiced without these specific details.

[0057] The disclosed embodiment provides a flexible space robot arm control method based on an evaluation network, and the method can be applied to the flexible space robot arm control process in scenarios such as space robots.

[0058] See also Figure 1 , is a flow chart of a flexible space manipulator control method based on an evaluation network provided by an embodiment of the present disclosure. Figure 1 As shown, the method mainly comprises the following steps:

[0059] Step 1, combining the assumed modal method and the Lagrange equation, derive the dynamic model of the flexible space manipulator system;

[0060] Furthermore, the expression of the kinetic model is:

[0061]

[0062] in, is the positive definite inertia matrix of the system; is the vector of the system including the Coriolis force and the centrifugal force, q s =[θ0,θ1,θ2] T is the rigid coordinate variable of the system; q f =[δ 11 ,δ 12 ,δ21 ,δ 22 ] T is the flexible coordinate variable of the system, K f =diag(k 11 ,k 12 ,k 21 ,k 22 ) is the stiffness matrix of the flexible arm, u=[u0,u1,u2] T is the control torque of the system.

[0063] When implementing it, Figure 2 As shown, the control object of the present invention is a flexible space manipulator system, which consists of a free-floating carrier base B0, a flexible arm (simply supported beam) B1, a flexible arm (cantilever beam) B2, and two joint motors. The carrier adjusts its posture through an air jet device, and the flexible arm controls the rotation of its arm joint through a joint motor. The carrier attitude angle is θ0, the center moment of inertia is J0, and the distance between the carrier center of mass and the rotation center of the flexible arm B1 is d0; the flexible arm B i The linear density, axial length and cross-sectional bending stiffness of (i=1,2) are ρ i , l i and EI i ; OXY is the world coordinate system, o i x i y i (i=0,1,2) is split B i There is a dynamic coupling between the base motion and the robot arm motion in this system, and solving this problem is the prerequisite for the subsequent controller design.

[0064] The key processing methods and steps in the implementation process of the flexible space manipulator control method and device based on the evaluation network of the present invention are as follows:

[0065] Dynamics model of flexible space manipulator

[0066] Combining the assumed modal method with the Lagrange equation, the dynamic differential equation of the flexible space manipulator system can be derived as follows:

[0067]

[0068] in, is the positive definite inertia matrix of the system; is the vector of the system including the Coriolis force and the centrifugal force; q s =[θ0,θ1,θ2] T is the rigid coordinate variable of the system; q f =[δ 11 ,δ 12 ,δ21 ,δ 22 ] T is the generalized coordinate variable of the system; K f =diag(k 11 ,k 12 ,k 21 ,k 22 ) is the stiffness matrix of the flexible arm, u=[u0,u1,u2] T is the control torque of the system.

[0069] Step 2, deconstruct the dynamic model by combining singular perturbation theory to obtain the dynamic differential equations of the slow time-varying subsystem and the fast time-varying subsystem;

[0070] Based on the above embodiment, step 2 specifically includes:

[0071] Combined with the singular perturbation theory, the stiffness matrix K of the flexible arm is defined as f The smaller element is k min , the singular perturbation factor is ε=(1 / k min ) 1 / 2 , and introduce the state variable ξ f and K ε (ε 2 ξ f =q f ,K ε =ε 2 K f ), from which the dynamic differential equation of the slow time-varying subsystem is derived as

[0072]

[0073] in, is the quantity corresponding to {··} when ε=0, is the control torque of the slow time-varying subsystem;

[0074] Define the fast-changing time scale t f (εt f = t-t0) and boundary layer correction and The dynamic differential equation of the fast time-varying subsystem is derived as follows:

[0075]

[0076] in, u f is the control torque of the fast time-varying subsystem.

[0077] When implementing it, Figure 3As shown, the present invention uses singular perturbation technology to deconstruct a high-dimensional and complex flexible space manipulator system into two subsystems that represent different motion modes, and separate the rigid motion and flexible vibration of the system. For the slow time-varying subsystem, a decentralized strategy is used to obtain a second-order subsystem model, and the RBF neural network is used to reconstruct the model and identify the state variables; then, an adaptive trajectory tracking optimal control method based on an evaluation network is designed for the reconstructed second-order subsystem. This method has a simple control structure and strong robustness. Without the need to establish an execution network and obtain accurate dynamic parameters and state variables, high-precision and fast tracking control of the flexible space manipulator can be achieved by relying on a single evaluation network. The key issue in the design of an adaptive trajectory tracking optimal control method based on an evaluation network is how to deal with the influence of the cross-linking terms of each second-order subsystem on the stability of the control system.

[0078] Combined with the singular perturbation theory, the stiffness matrix K of the flexible arm can be defined as f The smaller element is k min , the singular perturbation factor is ε=(1 / k min ) 1 / 2 , and introduce the state variable ξ f and K ε (ε 2 ξ f =q f ,K ε =ε 2 K f ), from which the dynamic differential equation of the slow time-varying subsystem can be derived as

[0079]

[0080] in, is the quantity corresponding to {··} when ε=0, is the control torque of the slow time-varying subsystem.

[0081] Define the fast-changing time scale t f (εt f = t-t0) and boundary layer correction and From this, we can deduce that the dynamic differential equation of the fast time-varying subsystem is

[0082]

[0083] in,

[0084] u f is the control torque of the fast time-varying subsystem.

[0085] In summary, the slow time-varying subsystem model (2) and the fast time-varying subsystem model (3) constitute the singular perturbation model of the flexible space manipulator system.

[0086] Step 3, the slow time-varying subsystem designs an adaptive trajectory tracking optimal controller based on the evaluation network;

[0087] Based on the above embodiment, step 3 specifically includes:

[0088] According to the decentralized principle, the slow time-varying subsystem can be decomposed into three cross-linked subsystems and the decentralized RBF neural network is used to reconstruct the model and identify the state, and the decentralized neural network state observer is obtained.

[0089] According to the decentralized neural network state observer, the second-order subsystem is identified and its actual local nominal control input and actual local feedback control input are designed, and robust control items are added;

[0090] An adaptive trajectory tracking optimal controller is constructed based on the actual local nominal control input, the actual local feedback control input and the robust control term.

[0091] Furthermore, the expression of the decentralized neural network state observer is:

[0092]

[0093] in, and They are the unknown nonlinear terms F i (x i ,x jd ) and g i (x i ), k i1 With k i2 is the observer gain;

[0094] The expression of the adaptive trajectory tracking optimal controller is:

[0095] in, is the actual local nominal control input, is the actual local feedback control input, is a robust control term.

[0096] In recent years, the adaptive dynamic programming method has been gradually applied to the control of complex nonlinear systems. The control structure of this method mainly includes a dynamic model, an evaluation function and an execution function. Neural networks can be used to approximate these parts, and then the dynamic system, the optimal performance index function and the optimal controller are obtained respectively. The evaluation network and the execution network are combined to form an intelligent agent. After the execution function acts on the dynamic model, it will react to the evaluation function according to the rewards or penalties generated by the external environment (or the controlled object) at different stages. The main control goal of the intelligent agent is to obtain a suitable control strategy through continuous iterative learning so that the total value of the reward (or penalty) obtained is optimal. In order to further simplify the controller structure, the present invention proposes an adaptive trajectory tracking optimal control method based on the evaluation network on the basis of model reconstruction and state identification of the slow time-varying subsystem of the flexible space manipulator using a decentralized neural network. Under the condition of not having to establish an execution network and obtain accurate dynamic parameters and state variables, high-precision, high-precision and fast tracking control of the flexible space manipulator can be achieved by relying on a single evaluation network, which is easy to implement in engineering.

[0097] In specific implementation, the design process of the optimal controller for adaptive trajectory tracking of the slow time-varying subsystem based on the evaluation network can be as follows:

[0098] 3.1 Model reconstruction and state recognition of the slow time-varying subsystem based on decentralized RBF neural network

[0099] To achieve the split B i (i=0,1,2) can be controlled individually. According to the dispersion principle, the slow time-varying subsystem (2) can be decomposed into the following three cross-linked subsystems:

[0100]

[0101]

[0102] Among them, q si , and The vector q s , and The i-th (i=1,2,3) element of and The matrices are and The ijth element of .

[0103] In order to facilitate the subsequent controller design, define the state variables Formula (4) can be rewritten as the following state equation:

[0104]

[0105] in,

[0106] The difficulty of decentralized control lies mainly in dealing with the cross-linking terms of the second-order subsystem. Since the flexible space manipulator is a high-dimensional, strongly coupled, and strongly time-varying nonlinear system, its second-order subsystem S i The coupling cross-linking term h i (x) contains the information of the other second-order subsystems. To solve this problem, the information of the other second-order subsystems is replaced by the corresponding expected values. i (x) can be described as

[0107] h i (x) = h i (x i ,x jd )+Δh i (x,x jd ) (7)

[0108] Among them, x jd (j=1,2,3) is the expected information of other second-order subsystems, Δh i (x,x jd )=h i (x)-h i (x i ,x jd ) is the substitution error, so the second-order subsystem S i (6) can be expressed as

[0109]

[0110] Among them, F i (x i ,x jd ) = f i (x i )+h i (x i ,x jd ) is a continuous Lipschitz function.

[0111] According to the substitution principle, the substitution error Δh i (x,x jd ) satisfies the Lipschitz bounded condition, that is,

[0112]

[0113] Among them, d ij ≥0 is the Lipschitz constant, E j =x j -x jd .

[0114] By replacing the cross-link term h i (x i ,x jd ) is still difficult to express explicitly, and the nonlinear term F i (x i ,x jd ) and nonlinear term g i (x i ) is also time-varying and unknown. Since RBF neural network has strong approximation accuracy and fast approximation speed for continuous nonlinear functions, the decentralized RBF neural network is used to approximate the second-order subsystem containing h i (x i ,x jd ) i (x i ,x jd ) and nonlinear term g i (x i ) are approximated respectively, thus solving the interference problem of the cross-link term and achieving optimal control without the need for precise parameters of the slowly varying subsystem.

[0115] Based on the above analysis, a decentralized RBF neural network is used to reconstruct the model and identify the state of the second-order subsystem (8), and the following decentralized neural network state observer is designed:

[0116]

[0117] in, F i (x i ,x jd ), g i (x i ), k i1 , k i2 is the observer gain.

[0118] Defining Observation Error Combining equations (8) and (10), we can obtain

[0119]

[0120] Define the unknown nonlinear term F i (x i ,x jd ) and g i (x i ) are approximated by the ideal neural network respectively.

[0121]

[0122]

[0123] Among them, Wif and W ig is the ideal weight, Φ(·) is the neural network basis function, ε if and ε ig is the estimation error.

[0124] Define the unknown nonlinear term F i (x i ,x jd ) and g i (x i ) are estimated by the neural network

[0125]

[0126]

[0127] Among them, the definition and are the ideal weights W if and W ig The estimated value of .

[0128] Combining equations (12)-(15), we get

[0129]

[0130]

[0131] in, and is the neural network weight approximation error, and is the approximation error of the neural network basis function, which is specifically expressed as follows

[0132]

[0133]

[0134] Define the minimum estimation error of the neural network as

[0135]

[0136] Weight and The update laws are designed as

[0137]

[0138]

[0139] Among them, η if and η ig All are normal numbers.

[0140] Assumption 1 The minimum estimation error ω of the neural network i Satisfies the following bounded conditions

[0141] ||ω i ||≤z i1 (twenty three)

[0142] Among them, κ1 is an unknown positive constant.

[0143] Theorem 1 For the second-order subsystem (8), if the weight update law is designed as in (21) and (22), the decentralized neural network state observer (10) can ensure that the estimation error e io Eventually uniformly bounded convergence.

[0144] Proof: Choose the following Lyapunov function

[0145]

[0146] V i1 Taking the derivative with respect to time t, we get

[0147]

[0148] According to Assumption 1, and combined with Equations (21) and (22), Equation (25) can be rewritten as

[0149]

[0150] From formula (26), we can see that when e i2o In Collection In addition, k i1 ≥1 / 2 and k i2 ≥1 / 2, Therefore, according to the Lyapunov stability theorem, the estimated error e can be guaranteed to be io It will maintain eventually uniformly bounded convergence. So far, Theorem 1 has been proved.

[0151] 3.2 Design of adaptive trajectory tracking optimal controller for the slow time-varying subsystem based on evaluation network

[0152] Assumption 2 Expected trajectory q id It is second-order differentiable and satisfies the following boundedness conditions.

[0153]

[0154] Among them, q iA Unknown positive constant.

[0155] The trajectory tracking error and its derivative are defined as

[0156] e i =xi -x id (28)

[0157]

[0158] Among them, x id is the expected trajectory.

[0159] In order to achieve decentralized optimal control of the second-order subsystem, the performance index function is defined as

[0160]

[0161] in, is the effect function, Z i (0,0)=0, and for all e i and u ie All satisfied Q i ∈R 2×2 With R i ∈R 3×3 is a positive definite matrix. is the local feedback control torque, is the local nominal control torque.

[0162] Since the optimal tracking control problem requires the information of all second-order subsystems, the local nominal control input can be obtained according to equation (8): for

[0163]

[0164] Among them, x d =[x 1d ,x 2d ,x 3d ] T , The generalized inverse of (I∈R 3×3 is the identity matrix).

[0165] Definition 1 Considering the second-order subsystem (8), for If there is a permissible control input And the control input is in Ω i Continuous on, while satisfying but It can ensure that the second-order subsystem (8) is in the compact set Ω i ∈R 3 converges on, and the performance indicator function is finite.

[0166] For any admissible control of the second-order subsystem (4) If the performance indicator function

[0167]

[0168] If the continuous differentiability condition is satisfied, the infinitesimal form of equation (32) can be expressed as

[0169]

[0170] Among them, V i (0) = 0, ▽ V i (e i ) is V i (e i ) relative to e i The partial derivative of

[0171] Based on the above conditions, the following Hamiltonian function can be defined:

[0172]

[0173] Then we can get the following optimal performance index function:

[0174]

[0175] and satisfy

[0176]

[0177] in, If V i * (e i ) exists and is continuously differentiable, then the ideal local feedback control input is

[0178]

[0179] Therefore, the ideal decentralized control input of the second-order subsystem (8) is

[0180]

[0181] Combining the decentralized state observer (10) and Theorem 1, the identified second-order subsystem is

[0182]

[0183] in, is the control input of the decentralized state observer.

[0184] According to equation (31), the actual local nominal control input of the second-order subsystem (8) is

[0185]

[0186] Define the ideal output of the evaluation network as

[0187]

[0188] in, To evaluate the ideal weight of the network, l i is the number of neurons in the hidden layer, σ ic (e i ) is the neural network activation function, ε ic To evaluate the approximation error of the network.

[0189] Then V i (e i ) can be expressed as

[0190]

[0191] in, and Represent the gradients of the activation function and the approximation error of the evaluation network function respectively.

[0192] Combining equation (33) and equation (43), we get

[0193]

[0194] Therefore, the local Hamiltonian function of the second-order subsystem (8) can be expressed as

[0195]

[0196] Among them, e icH is the approximation error of the neural network to the evaluation network.

[0197] definition is the weight W ic The actual output of the second-order subsystem evaluation network is

[0198]

[0199] but The gradient of

[0200]

[0201] Therefore, the approximate value of formula (44) can be expressed as

[0202]

[0203] definition Considering that the following minimum performance criteria need to be met during training

[0204]

[0205] According to the gradient descent method, the weight update law is designed as follows:

[0206]

[0207] Among them, α ic >0 is the learning rate of the second-order subsystem evaluation network.

[0208] The weight estimation error is defined as

[0209]

[0210] Combining equations (44), (47) and (50), we get

[0211]

[0212] Based on this, the update law of the weight estimation error is designed as follows:

[0213]

[0214] Therefore, combining equations (37) and (42), the ideal local feedback control input of the second-order subsystem (8) is obtained as

[0215]

[0216] According to the nonlinear term (15) after the second-order subsystem is identified and the actual output of the evaluation network (45), the actual local feedback control input is

[0217]

[0218] Theorem 2 For the second-order subsystem (8), if the weight update law of the evaluation network is designed as formula (49), then the weight error Eventually uniformly bounded convergence.

[0219] Proof: Define the following Lyapunov function

[0220]

[0221] V i2 (t) Take the time derivative of t and consider equation (52), we get

[0222]

[0223] Here we assume that ||θ i ||≤θ iM , it is not difficult to find In the collection outside, It can be concluded that the weight approximation error satisfies the ultimate uniformly bounded convergence. Therefore, Theorem 4.2 is proved.

[0224] Figure 5 Schematic diagram of the control structure of the second-order subsystem (8).

[0225] Based on the above analysis, it can be seen that there is a neural network approximation error between the second-order subsystem control inputs (31) and (40) and the control inputs (37) and (54), which will have an adverse effect on the tracking performance of the second-order subsystem. Therefore, the following robust control term is used to compensate for the approximation error:

[0226]

[0227] Among them, sgn(e i )=[sgn(e i1 ),sgn(e i2 ),sgn(e i3 )] T , is the upper bound of the overall approximation error The estimated value of , and its adaptive update law is designed as follows

[0228]

[0229] in, Is a normal number.

[0230] It can be seen from this that the decentralized controller of the second-order subsystem (8) It mainly consists of the local nominal control input (40), the local feedback control input (54) and the robust control term (57), namely

[0231]

[0232] Theorem 3 For the second-order subsystem (8) and the local performance index function (41), if a decentralized controller of the form (59) is designed, the tracking error of the second-order subsystem can converge to zero asymptotically.

[0233] Proof: Define the following Lyapunov function

[0234]

[0235] V i3 Taking the derivative with respect to time t and combining it with equation (33), we can get

[0236]

[0237] Considering F i (·) is a Lipschitz function, then there exists L if> 0, so that ||F i (x i ,x jd )-F i (x d )||≤L if ||e i ||. According to hypothesis 2, we know And define and Then formula (61) can be rewritten as

[0238]

[0239] make is the overall approximation error and satisfies Then equation (62) becomes

[0240]

[0241]

[0242] Substituting equation (57) and equation (58) into equation (63), we get

[0243]

[0244] Therefore, if the positive definite matrix Q i With R i Meet the following conditions

[0245]

[0246] Then we can get According to the Lyapunov stability theorem, the trajectory tracking error of the second-order subsystem can converge to zero asymptotically. So far, Theorem 3 has been proved.

[0247] The control structure of the second-order subsystem of the slow time-varying subsystem is as follows Figure 3 shown.

[0248] Step 4, design a vibration suppression controller for the fast time-varying subsystem based on fuzzy logic;

[0249] Based on the above embodiment, step 4 specifically includes:

[0250] Determine the input variable of the second-order subsystem vibration suppression controller of the fast time-varying subsystem as δ ij and The output variable is u fij , the input variables are fuzzified and fuzzy inferenced respectively, and the output variables are defuzzified and gain operated, and the expression of the fuzzy vibration suppression controller of the fast time-varying subsystem is obtained as follows:

[0251] u f=-K f2 [u f11 ,u f12 ,u f21 ,u f22 ] T

[0252] Among them, K f2 ∈R 3×4 is the control gain matrix.

[0253] When implementing it, Figure 4 and Figure 5 As shown, the present invention designs a vibration suppression controller for the fast-changing subsystem based on fuzzy logic theory, so that the active suppression of the vibration of the flexible arm can be achieved without obtaining the model parameters, thereby improving the control stability of the system. The specific composition of the fuzzy control module is derived from the industrial process control strategy. The fuzzy controller consists of a fuzzification interface, an inference engine, and a defuzzification (inverse) interface; wherein the inference engine consists of a knowledge base and a rule base. The function of the fuzzification interface is to convert the actual determined value into a fuzzy vector described by fuzzy language; the knowledge base in the inference engine is the membership vector value of all input variables and output variables, and the rule base is the language rules derived by industry experts based on empirical reasoning; the function of the defuzzification interface is to convert the fuzzy vector into an interface with a clear form of output quantity.

[0254] First, determine the input variable of the second-order subsystem vibration suppression controller of the fast time-varying subsystem as δ ij and The output variable is u fij ; At each input variable δ ij and and the output variable u fij A set of seven fuzzy linguistic variables is set up: {negative large (LN), negative medium (MN), negative small (SN), zero (ZE), positive small (SP), positive medium (MP), positive large (LP)},

[0255] The membership function of each language word set adopts an isosceles triangle function, such as Figure 4 shown.

[0256] The fuzzy control rules are shown in Table 1, which are 49 in total.

[0257]

[0258] Table 1

[0259] Based on Mamdani's max-min synthesis method, fuzzy reasoning is performed on the above variables, and then the fuzzy quantity is converted into a clear quantity that can drive the fast time-varying subsystem by combining the area centroid method.

[0260] The output of the second-order subsystem of the fast time-varying subsystem is processed by gain, and the expression of the fuzzy vibration suppression controller of the fast time-varying subsystem is obtained as follows:

[0261] u f =-K f2 [u f11 ,u f12 ,u f21 ,u f22 ] T (66)

[0262] Among them, K f2 ∈R 3×4 is the control gain matrix.

[0263] The structure of the fuzzy controller for the fast time-varying subsystem is as follows: Figure 5 shown.

[0264] The present invention uses RBF neural network and fuzzy logic theory to model and control the slow time-varying subsystem and the fast time-varying subsystem of the flexible space robot arm respectively, which is independent of specific model parameters, enhances the robustness of the control method, and can effectively reduce the influence of external interference and time-varying parameters on the control accuracy, while improving the system control stability.

[0265] Step 5, a hybrid control scheme is constructed according to the adaptive trajectory tracking optimal controller of the slow time-varying subsystem based on the evaluation network and the fuzzy controller of the fast time-varying subsystem to obtain the total control input of the flexible space manipulator system.

[0266] In the specific implementation, the slow time-varying subsystem is based on the adaptive trajectory tracking optimal controller u of the evaluation network and the fast time-varying subsystem is based on the fuzzy controller u f The hybrid control scheme is constructed, and finally the total control input u of the system is obtained. The flexible space manipulator adopts the hybrid control scheme to realize the carrier attitude stabilization, joint trajectory tracking control and active suppression of flexible arm vibration.

[0267] At the same time, the embodiment of the present disclosure also discloses the software design process of the flexible space manipulator control method based on the evaluation network. The physical parameters of the flexible space manipulator system controlled by the present invention are shown in Table 2.

[0268] <![CDATA[m0]]> <![CDATA[ρ1]]> <![CDATA[ρ2]]> <![CDATA[d1]]> <![CDATA[l1]]> <![CDATA[l2]]> <![CDATA[J0]]> <![CDATA[EI1]]> <![CDATA[EI2]]> 40kg 1.8kg / m 1.2kg / m 1m 3m 3m <![CDATA[34kg·m 2 ]]> <![CDATA[50N·m 2 ]]> <![CDATA[50N·m 2 ]]>

[0269] Table 2

[0270] The software of a flexible space manipulator control method based on an evaluation network is written in Matlab language to generate a .m file. The control system structure of the flexible space manipulator control method based on an evaluation network is as follows: Figure 6As shown. First, the program is initially configured, giving the initial value of the state variable y(0), the running time T and the solution step length dt; secondly, the initial time t=0, y(t)=y(0) and the expected trajectory are specified; then, the dynamic matrix of the flexible space manipulator system is updated; then, the rigid motion subsystem model reconstruction results and the state observer estimation results are updated; according to the results of the first two steps, the output results of the adaptive evaluation network optimal controller and the active fuzzy vibration suppression controller are updated, and the rigid state variables and flexible state variables of the dynamic matrix of the system are solved accordingly; again, the fourth-order Longo-Kutta method is used for one integration to obtain y(t+dt); according to the result of the previous step, the running time is determined: if t<T, execute step (2); otherwise execute step (8); the state data y(t) and other data are stored in the specified file for output; finally, the simulation terminates. The control parameters of a flexible space manipulator control method based on an evaluation network are shown in Table 3, and the control solution process of the above method is shown in Figure 7 shown.

[0271]

[0272]

[0273] Table 3

[0274] By clicking the "Start (Run)" button, the system can be run. First, the flexible space manipulator system is decomposed into two subsystems at different time scales, and then controllers are designed for each subsystem. When the hybrid controller based on the evaluation network is started, the carrier attitude stabilization and joint trajectory tracking, as well as the active suppression of the elastic vibration of the flexible arm can be achieved. The simulation results can be saved in files such as Word, Excel and LaTeX.

[0275] The flexible space manipulator control method based on the evaluation network provided in this embodiment adopts the singular perturbation technology to deconstruct the high-dimensional and complex flexible space manipulator system into two subsystems representing different motion modes, thereby eliminating the dynamic coupling effect of the system; adopts a decentralized control strategy, and only uses the self-information of the joint module of the slow-time-varying subsystem to achieve independent control of each second-order subsystem, thereby simplifying the controller structure and saving limited onboard computing resources; uses a decentralized RBF neural network to reconstruct the model of the slow-time-varying subsystem of the flexible space manipulator and identify its state variables, so that the subsequent control method does not depend on specific model parameters and state variables, thereby enhancing the control The robustness of the method can effectively reduce the influence of external interference and time-varying parameters on control accuracy; the fuzzy logic theory is used to model and control the fast time-varying subsystem of the flexible space manipulator, so that the active suppression of the flexible arm vibration can be achieved without obtaining the model parameters of the fast time-varying subsystem, thereby improving the system control stability; for the neural network reconstruction model of the slow time-varying subsystem, the present invention proposes an adaptive trajectory tracking optimal control method based on the evaluation network on the basis of the traditional ADP method. Without the need to establish an execution network, high-precision and fast tracking control of the flexible space manipulator can be achieved by relying on a single evaluation network, thereby further simplifying the structure of the controller.

[0276] See also Figure 8 The embodiment of the present disclosure further provides an electronic device 80, which includes: at least one processor and a memory connected to the at least one processor. The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the flexible space manipulator control method based on the evaluation network in the aforementioned method embodiment.

[0277] The embodiment of the present disclosure also provides a non-transitory computer-readable storage medium, which stores computer instructions, and the computer instructions are used to enable the computer to execute the flexible space robot arm control method based on the evaluation network in the aforementioned method embodiment.

[0278] The embodiments of the present disclosure also provide a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium, and the computer program includes program instructions. When the program instructions are executed by a computer, the computer executes the flexible space robot arm control method based on the evaluation network in the aforementioned method embodiment.

[0279] Reference below Figure 8, which shows a schematic diagram of the structure of an electronic device 80 suitable for implementing the embodiment of the present disclosure. The electronic device in the embodiment of the present disclosure may include, but is not limited to, mobile terminals such as mobile phones, notebook computers, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), vehicle terminals (such as vehicle navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. Figure 8 The electronic device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present disclosure.

[0280] like Figure 8 As shown, the electronic device 80 may include a processing device (e.g., a central processing unit, a graphics processing unit, etc.) 801, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 802 or a program loaded from a storage device 808 into a random access memory (RAM) 803. In the RAM 803, various programs and data required for the operation of the electronic device 80 are also stored. The processing device 801, the ROM 802, and the RAM 803 are connected to each other via a bus 804. An input / output (I / O) interface 805 is also connected to the bus 804.

[0281] Typically, the following devices may be connected to the I / O interface 805: input devices 806 including, for example, a touch screen, a touchpad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; output devices 807 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; storage devices 808 including, for example, a magnetic tape, a hard disk, etc.; and communication devices 809. The communication device 809 may allow the electronic device 80 to communicate with other devices wirelessly or by wire to exchange data. Although the electronic device 80 with various devices is shown in the figure, it should be understood that it is not required to implement or have all the devices shown. More or fewer devices may be implemented or have alternatively.

[0282] The computer-readable medium may be included in the electronic device, or may exist independently without being incorporated into the electronic device.

[0283] The computer-readable medium carries one or more programs. When the one or more programs are executed by the electronic device, the electronic device can execute the relevant steps of the method embodiment.

[0284] Alternatively, the computer-readable medium carries one or more programs, and when the one or more programs are executed by the electronic device, the electronic device can perform the relevant steps of the method embodiment.

[0285] Computer program code for performing the operations of the present disclosure may be written in one or more programming languages, or a combination thereof, including object-oriented programming languages, such as Java, Smalltalk, C++, and conventional procedural programming languages, such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0286] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present disclosure. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some implementations as replacements, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0287] The units involved in the embodiments described in the present disclosure may be implemented by software or by hardware.

[0288] It should be understood that various parts of the present disclosure may be implemented in hardware, software, firmware or a combination thereof.

[0289] The above is only a specific implementation of the present disclosure, but the protection scope of the present disclosure 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 disclosure should be included in the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be based on the protection scope of the claims.

Claims

1. A flexible space manipulator control method based on an evaluation network, characterized in that: include: Step 1, combining the assumed modal method and the Lagrange equation, derive the dynamic model of the flexible space manipulator system; Step 2, deconstruct the dynamic model by combining singular perturbation theory to obtain the dynamic differential equations of the slow time-varying subsystem and the fast time-varying subsystem; Step 3, the slow time-varying subsystem designs an adaptive trajectory tracking optimal controller based on the evaluation network; Step 4, design a vibration suppression controller for the fast time-varying subsystem based on fuzzy logic; Step 5, a hybrid control scheme is constructed according to the adaptive trajectory tracking optimal controller of the slow time-varying subsystem based on the evaluation network and the fuzzy controller of the fast time-varying subsystem to obtain the total control input of the flexible space manipulator system.

2. An electronic device, characterized in that: The electronic device comprises: at least one processor; and, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the flexible space robot arm control method based on the evaluation network as described in claim 1.

3. A non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable the computer to execute the flexible space robot arm control method based on the evaluation network as described in claim 1.

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