A dual-domain torque constraint control method for flexible-arm space robots based on improved FWN

Abstract

The present invention discloses a dual-domain torque constraint control method for a flexible arm space robot based on an improved FWN, comprising: constructing a dynamic model of the flexible arm space robot system, combining the control torque of the body and the joint joint with the amplitude and amplitude change rate constraints to construct a mathematical model of the torque dual-domain constraint control system; constructing a torque dual-domain constraint controller based on an improved fuzzy wavelet network, which satisfies the mathematical model of the torque dual-domain constraint control system, and the corresponding control law includes an improved fuzzy wavelet network control law and an improved fuzzy wavelet network parameter self-adjustment control law; using the dual-domain constrained control torque generated by the torque dual-domain constraint controller to adjust the robot's body posture angle, joint angle, and the deformation coordinates and vibration amplitude of the flexible arm until the control target is achieved. The present invention solves the problems of actuator saturation effect and dynamic performance degradation caused by insufficient consideration of the dual-domain constraints of the torque amplitude and change rate of the joint drive mechanism.

Description

Technical Field

[0001] The present invention relates to the field of robotic arm control, and in particular to an improved FWN dual-domain constraint control method for a flexible arm space robot. Background Art

[0002] In long-term on-orbit servicing scenarios for flexible-arm space robots, the physical characteristics of the actuators impose strict dual constraints on the output torque of the joint actuators: a saturation limit on the torque amplitude, and a dynamic threshold for the rate of change of the torque amplitude. Torque amplitude saturation can significantly degrade system control performance, leading to trajectory tracking deviations and even instability risks. A sudden increase in the rate of change of the torque amplitude can induce high-frequency vibration, exacerbating mechanical wear and threatening mission reliability. Coordinating the dual-domain dynamic constraints of torque amplitude and rate of change is a core challenge in high-precision anti-saturation control of space robots.

[0003] In current engineering practice, the following technical bottlenecks still exist for the above problems:

[0004] (1) Insufficient dynamic decoupling of dual-domain constraints: Existing anti-saturation control research focuses on scenarios where a single torque amplitude is limited. Saturation compensation or amplitude limiting design is used to suppress amplitude overlimit problems, but the dynamic modeling capability of the time-varying boundary of the torque amplitude change rate is lacking. Control strategies under amplitude-rate coupling constraints are prone to high-frequency oscillations or response lags, making it difficult to achieve adaptive coordinated regulation of the dual-domain boundary.

[0005] (2) The real-time performance of intelligent methods is limited: Although the nonlinear approximation method based on RBF neural network can partially compensate for system uncertainty, its multi-layer feedforward structure and gradient backpropagation mechanism lead to high computational complexity, which makes it difficult to meet the real-time solution requirements of on-board computers, limiting its engineering feasibility for on-orbit application.

[0006] (3) Poor time-frequency adaptability of fuzzy systems: Traditional fuzzy control systems rely on fixed membership functions and linear consequent structures and cannot effectively capture the transient time-frequency characteristics of torque constraints. The lack of static characteristics of its rule base and wavelet multi-scale analysis capabilities further weakens the system's dynamic response accuracy and control robustness to non-stationary mutation signals.

[0007] The above problems seriously restrict the control performance of space robots under complex dynamic conditions. There is an urgent need for a new intelligent control architecture that combines high real-time performance, strong nonlinear approximation capabilities and multi-scale analysis characteristics to break through the dual technical barriers of dual-domain constrained collaborative optimization and limited onboard computing resources. Summary of the Invention

[0008] The purpose of this application is to propose a dual-domain constraint control method for torque of a flexible arm space robot based on an improved FWN to address the above-mentioned technical problems.

[0009] In a first aspect, the present invention provides a method for controlling a flexible-arm space robot's torque in dual domains based on an improved FWN, comprising the following steps:

[0010] A dynamic model of a flexible-arm space robot system is constructed under the conditions where the translational degrees of freedom are not actively controlled and the posture motion is subject to servo constraints. A mathematical model of the torque dual-domain constraint control system is constructed based on the dynamic model of the flexible-arm space robot system under the conditions where the posture of the body and the control torque of the joints in the flexible-arm space robot system are subject to amplitude and amplitude change rate constraints.

[0011] A torque dual-domain constraint controller based on an improved fuzzy wavelet network is constructed. The torque dual-domain constraint controller satisfies the mathematical model of the torque dual-domain constraint control system, and its corresponding control law includes the improved fuzzy wavelet network control law and the improved fuzzy wavelet network parameter self-regulation control law.

[0012] The rotation angle vector composed of the body posture angle and the two joint angles at the current moment and the vibration mode coordinates of the flexible manipulator calculated based on the coordinates and amplitude of the flexible manipulator are obtained and an input vector is constructed; the input vector is input into the torque dual-domain constraint controller, and the parameters of the improved fuzzy wavelet network are first updated using the parameter self-regulating control law of the improved fuzzy wavelet network. Then, the improved fuzzy wavelet network control law with the updated parameters of the improved fuzzy wavelet network is used to predict the control torque after dual-domain constraint at the next moment, and the control torque after dual-domain constraint at the next moment is applied to the flexible arm space robot system to adjust the body posture angle, the two joint angles and the coordinates and amplitude of the flexible manipulator at the next moment.

[0013] Preferably, a dynamic model of a flexible-arm space robot system is constructed under the conditions that the translational degree of freedom is not actively controlled and the posture motion has servo constraints, specifically including:

[0014] The flexible arm space robot system includes a free-floating body, a rigid manipulator arm and a flexible manipulator arm, wherein joints are provided between the body and the rigid manipulator arm and between the rigid manipulator arm and the flexible manipulator arm, and each joint is articulated by a joint hinge;

[0015] The flexible manipulator is reduced in order using the hypothetical modal method. The first two dominant modes are intercepted to characterize the elastic deformation characteristics of the flexible manipulator. Based on the law of conservation of momentum and the second-kind Lagrangian equation, a dynamic model of the flexible arm space robot system is established under the conditions where the translational degree of freedom is not actively controlled and the posture motion has servo constraints, as shown in the following formula:

[0016] ;

[0017] in, represents the symmetric positive definite inertia matrix, represents the angle variable, 、 and They represent the body posture angle, the joint angle between the body and the rigid manipulator, and the joint angle between the rigid manipulator and the flexible manipulator, respectively. and Represents the angle vector The first and second derivatives with respect to time, represents the vibration mode coordinates of the flexible manipulator, and They represent the vibration mode coordinates of the first-order mode and the second-order mode, T represents the transposition, and Represent the vibration mode coordinates of the flexible manipulator The first and second derivatives with respect to time, represents the column vector containing centrifugal force and Coriolis force, is the flexible stiffness matrix, represents the unconstrained body posture and the control torque of the joint; represents the set of real numbers.

[0018] Preferably, under the condition that the posture of the body and the control torque of the joint joint in the flexible arm space robot system are constrained by the amplitude and the amplitude change rate, a mathematical model of the torque dual-domain constraint control system is constructed in combination with the dynamic model of the flexible arm space robot system, specifically including:

[0019] Assume that Unconstrained control torque at time It is constrained by the amplitude and the rate of change of the amplitude, that is:

[0020] , ;

[0021] in, Represent the known lower amplitude saturation limit value and upper amplitude saturation limit value respectively, Respectively represent the known lower amplitude change rate saturation limit value and upper amplitude change rate saturation limit value;

[0022] To handle the constraints of amplitude and amplitude change rate, the following functions are defined:

[0023] ;

[0024] in, It represents the control torque output by the torque dual-domain constraint controller after dual-domain constraint. represents the upper limit of the joint constraint, and its expression is: , express The control torque at each moment, represents the sampling time interval, It means taking the minimum value. Represents the lower limit of the joint constraint, and its expression is: , Indicates taking the maximum value among them;

[0025] Combined with the dynamic model of the flexible arm space robot system, the mathematical model of the torque dual-domain constraint control system is designed, as shown in the following formula:

[0026] .

[0027] Preferably, in the improved fuzzy wavelet network, the improved fuzzy wavelet network includes an input layer, a reconstructed fuzzification layer, a reconstructed rule layer and a reconstructed wavelet function layer;

[0028] In the reconstructed fuzzification layer, the antecedent membership function in the fuzzification layer of the traditional fuzzy wavelet network is replaced by the wavelet basis function from the Gaussian function, as shown in the following formula:

[0029] ;

[0030] in, As the mother wavelet function, multi-scale wavelet basis functions are generated through scaling and translation operations , represents the membership function; is the scaling parameter, is the translation parameter, represents the set of real numbers; Indicates the input variables, , is the input dimension, represents the index of the fuzzy subset, , is the number of fuzzy subsets for each input variable, represents the index of the translation parameter of the wavelet basis function, , is the total number of indexes of translation parameters;

[0031] In the reconstructed rule layer, define Fuzzy rules for:

[0032] like yes and yes ...and yes ,but ;

[0033] in, is the regular excitation intensity, Indicates the Rule No. The input variables are The weights of the output variables; , is the total number of rules, Indicates the output variables, , is the output dimension, represents the index of the wavelet decomposition scale, , is the total number of wavelet decomposition scales;

[0034] Combine the regular excitation intensity with the wavelet basis function to define the fuzzy wavelet basis function , as shown below:

[0035] ;

[0036] in, Represents the input vector of the improved fuzzy wavelet network, including input variables;

[0037] In the reconstructed wavelet function layer, the weight matrix and the fuzzy wavelet basis function vector The matrix multiplication of is used to perform weighted combination of the output variables of all rules, and the output vector of the improved fuzzy wavelet network is expressed in vector form, as shown in the following formula:

[0038] ;

[0039] in, represents the weight matrix, Indicates the Rule 1 The weights of the output variables, Represents the output vector of the improved fuzzy wavelet network, including output variables.

[0040] As a preferred method, a torque dual-domain constraint controller based on an improved fuzzy wavelet network is constructed, specifically including:

[0041] The ideal control law is established using the output variables of the improved fuzzy wavelet network:

[0042] ;

[0043] in, represents the ideal control torque after dual-domain constraints, which is a nonlinear uncertainty term; , is the unknown ideal weight matrix, express The fuzzy wavelet basis function vector corresponding to the input vector at time t, Represents a small error vector with boundedness, respectively Estimated , and further use the torque dual-domain constraint controller to output the control torque after dual-domain constraint As The estimated value of , the ideal control law is modified to the improved fuzzy wavelet network control law, as shown in the following formula:

[0044] ;

[0045] Therefore, the control torque after dual-domain constraint output by the torque dual-domain constraint controller can be predicted by improving the fuzzy wavelet network.

[0046] As a preferred method, the parameter self-regulating control law of the improved fuzzy wavelet network is as follows:

[0047] when ,or and ,or and When , based on the Lyapunov stability criterion, the real-time dynamic adjustment control law of the weight matrix of the reconstructed wavelet function layer of the improved fuzzy wavelet network can be expressed as:

[0048] ;

[0049] in, express The subvector of express The subvector of express The subvector of express The subvector of express The subvector of , corresponding to the body posture and two joint hinges, express The first derivative with respect to time, represents the adaptive gain coefficient, ; Indicates the adjustment gain, ;

[0050] when and or and When , based on the Lyapunov stability criterion, the real-time dynamic adjustment control law of the weight matrix of the reconstructed wavelet function layer of the improved fuzzy wavelet network can be expressed as:

[0051] ;

[0052] in, represents the robustness compensation coefficient, .

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) The dual-domain torque constraint control method of the flexible arm space robot based on the improved FWN proposed in this paper constructs a mathematical model of the dual-domain torque constraint control system based on the dynamic model of the flexible arm space robot system and the constraints of amplitude and amplitude change rate. The dual-domain torque constraint is modeled as a time-varying boundary condition, and the constraint weight distribution is optimized in real time through the fuzzy rule base. The coordinated balance between trajectory tracking and elastic deformation is achieved while ensuring the physical limit of the actuator.

[0055] (2) The core innovation of the dual-domain constraint control method for torque of flexible arm space robot based on improved FWN proposed in this paper lies in the realization of the three-level collaborative reconstruction through the improvement of fuzzy wavelet network: first, the traditional Gaussian function is replaced by wavelet basis function as the membership function, and the adaptive mechanism of scaling parameter and translation parameter is introduced, which breaks through the limitation of traditional method in time-frequency resolution, so that the transient components in the non-stationary signal of the system can be accurately captured; secondly, a real coefficient product type post-part architecture is created, and the output of the rule layer is reconstructed by nonlinear weighted combination of input vectors, which significantly enhances the modeling ability of the complex dynamics of the joint torque-posture of flexible arm space robot; finally, a fuzzy wavelet basis function fusion mechanism is constructed to fuse the rule excitation intensity with multi-scale time-frequency features, and the weight vector is used to realize the cross-level interaction between global fuzzy reasoning and local time-frequency features, finally forming an intelligent control kernel with time-frequency resolution capability. The whole reconstruction process establishes a collaborative optimization mechanism of dynamic scale factor and parameter space through dual-modal fusion, which provides a universal solution for high-precision control under complex working conditions while maintaining good interpretability of fuzzy system.

[0056] (3) The torque dual-domain constraint control method of the flexible arm space robot based on the improved FWN proposed in this invention designs a torque dual-domain constraint controller based on the improved fuzzy wavelet network through the mathematical model of the torque dual-domain constraint control system, and uses the corresponding improved fuzzy wavelet network control law and the improved fuzzy wavelet network parameter self-adjustment control law to generate the control torque after dual-domain constraint. By extracting the frequency domain features of the wavelet network and coordinating the fuzzy reasoning dynamic constraints, the system's anti-saturation ability and dynamic response robustness are significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0058] Figure 1 Schematic diagram of the flow of a dual-domain constraint control method for torque of a flexible-arm space robot based on an improved FWN according to an embodiment of the present application;

[0059] Figure 2 Schematic diagram of the structure of a flexible-arm space robot system based on an improved FWN-based flexible-arm space robot torque dual-domain constraint control method according to an embodiment of the present application;

[0060] Figure 3 Schematic diagram of the structure of the fuzzy wavelet network of the flexible arm space robot torque dual-domain constraint control method based on the improved FWN in an embodiment of the present application;

[0061] Figure 4 This is a structural schematic diagram of a torque dual-domain constraint controller for a flexible arm space robot torque dual-domain constraint control method based on an improved FWN according to an embodiment of the present application;

[0062] Figure 5 The body posture angle of the simulation 1 of the embodiment of the present application is Trajectory tracking diagram;

[0063] Figure 6 The joint angle of the simulation 1 of the embodiment of the present application is Trajectory tracking diagram;

[0064] Figure 7 A time-varying characteristic curve diagram of the vibration modal coordinates of the flexible manipulator in simulation 1 of an embodiment of the present application;

[0065] Figure 8 The body posture angle of the simulation 1 of the embodiment of the present application is Result diagram of the control torque;

[0066] Figure 9 The joint angle of the simulation 1 of the embodiment of the present application is Result diagram of the control torque;

[0067] Figure 10 The body posture angle of the simulation 1 of the embodiment of the present application is Result diagram of the rate of change of the amplitude of the control torque;

[0068] Figure 11 The joint angle of the simulation 1 of the embodiment of the present application is Result diagram of the rate of change of the amplitude of the control torque;

[0069] Figure 12 A topological map of the motion trajectory of the flexible-arm space robot in simulation 1 of an embodiment of the present application;

[0070] Figure 13 The body posture angle of the simulation 2 of the embodiment of this application is Trajectory tracking diagram;

[0071] Figure 14 The joint angle of the simulation 2 of the embodiment of this application is Trajectory tracking diagram;

[0072] Figure 15 A time-varying characteristic curve diagram of the vibration modal coordinates of the flexible manipulator in simulation 2 of an embodiment of the present application;

[0073] Figure 16 The body posture angle of the simulation 2 of the embodiment of this application is Result diagram of the control torque;

[0074] Figure 17 The joint angle of the simulation 2 of the embodiment of this application is Result diagram of the control torque;

[0075] Figure 18 The body posture angle of the simulation 2 of the embodiment of this application is Result diagram of the rate of change of the amplitude of the control torque;

[0076] Figure 19 The joint angle of the simulation 2 of the embodiment of this application is Result diagram of the amplitude change rate of the control torque. DETAILED DESCRIPTION

[0077] To make the objectives, technical solutions, and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings. It is apparent that the embodiments described are only some, not all, of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0078] Figure 1 The embodiment of the present application provides a method for controlling a flexible-arm space robot torque in dual domains based on an improved FWN, comprising the following steps:

[0079] S1. Construct a dynamic model of a flexible-arm space robot system under the conditions that the translational degree of freedom is not actively controlled and the posture motion has servo constraints. Under the conditions that the posture of the body and the control torque of the joint joint in the flexible-arm space robot system are constrained by the amplitude and the amplitude change rate, combine the dynamic model of the flexible-arm space robot system to construct a mathematical model of the torque dual-domain constraint control system.

[0080] In a specific embodiment, constructing a dynamic model of a flexible-arm space robot system under conditions where the translational degree of freedom is not actively controlled and the posture motion is subject to servo constraints specifically includes:

[0081] The flexible arm space robot system includes a free-floating body, a rigid manipulator arm and a flexible manipulator arm, wherein joints are provided between the body and the rigid manipulator arm and between the rigid manipulator arm and the flexible manipulator arm, and each joint is articulated by a joint hinge;

[0082] The flexible manipulator is reduced in order using the hypothetical modal method. The first two dominant modes are intercepted to characterize the elastic deformation characteristics of the flexible manipulator. Based on the law of conservation of momentum and the second-kind Lagrangian equation, a dynamic model of the flexible arm space robot system is established under the conditions where the translational degree of freedom is not actively controlled and the posture motion has servo constraints, as shown in the following formula:

[0083] ;

[0084] in, represents the symmetric positive definite inertia matrix, represents the angle variable, 、 and They represent the body posture angle, the joint angle between the body and the rigid manipulator, and the joint angle between the rigid manipulator and the flexible manipulator, respectively. and Represents the angle vector The first and second derivatives with respect to time, represents the vibration mode coordinates of the flexible manipulator, and They represent the vibration mode coordinates of the first-order mode and the second-order mode, T represents the transposition, and Represent the vibration mode coordinates of the flexible manipulator The first and second derivatives with respect to time, represents the column vector containing centrifugal force and Coriolis force, is the flexible stiffness matrix, represents the unconstrained body posture and the control torque of the joint; represents the set of real numbers.

[0085] In a specific embodiment, under the condition that the posture of the body and the control torque of the joint joint in the flexible arm space robot system are constrained by the amplitude and the amplitude change rate, a mathematical model of the torque dual-domain constraint control system is constructed in combination with the dynamic model of the flexible arm space robot system, specifically including:

[0086] Assume that Unconstrained control torque at time It is constrained by the amplitude and the rate of change of the amplitude, that is:

[0087] , ;

[0088] in, Represent the known lower amplitude saturation limit value and upper amplitude saturation limit value respectively, Respectively represent the known lower amplitude change rate saturation limit value and upper amplitude change rate saturation limit value;

[0089] To handle the constraints of amplitude and amplitude change rate, the following functions are defined:

[0090] ;

[0091] in, represents the control torque after dual-domain constraints, represents the upper limit of the joint constraint, and its expression is: , express The control torque at each moment, represents the sampling time interval, It means taking the minimum value. Represents the lower limit of the joint constraint, and its expression is: , Indicates taking the maximum value among them;

[0092] Combined with the dynamic model of the flexible arm space robot system, the mathematical model of the torque dual-domain constraint control system is designed, as shown in the following formula:

[0093] .

[0094] Specifically, refer to Figure 2 The flexible arm space robot system in the embodiment of the present application is composed of a free-floating body , rigid robotic arm and flexible robotic arms Components: Flexible robotic arm Can be considered as being mounted on a rigid robotic arm Cantilever beam on the connected joint hinge. As a flexible manipulator, deformation will inevitably occur during the movement, but since it is a slender rod, the influence of its axial deformation and shear deformation can be ignored and it can be treated as a Euler-Bernoulli beam. The main axis of the rectangular coordinate system ,in and The center of mass coincide, and Connection and as well as and The center of the joint hinge, For rigid robotic arms The axis of symmetry, Pass And with The symmetry axes are consistent when not deformed. and The distance is , The center of mass and The distance is , and The lengths are and , for exist Time coordinates Transverse elastic deformation at point. The mass and central inertia tensor of and ; The mass and central inertia tensor of and ; The mass per unit length is , the uniform bending stiffness is . is the total center of mass of the system, is the total mass of the system.

[0095] The flexible manipulator is reduced in order using the hypothetical modal method, and its first two dominant modes are selected to characterize the elastic deformation characteristics. The complete motion state of the flexible arm space robot system is described by a set of generalized coordinates, which contains three types of independent variables: the body posture angle, the two joint angles, and And the vibration coordinates of the flexible manipulator ; Among them, the body attitude angle Used to define the basic posture of the system, two joint angles and The modal coordinates of the flexible manipulator, which characterizes the relative rotation between its two joints, describe its dynamic behavior under elastic vibration by reflecting its natural vibration patterns of various orders. A dynamic model of the flexible-arm space robot system was established based on the law of conservation of momentum and the second-kind Lagrangian equations. This dynamic model takes into account the lack of active control of the translational degrees of freedom and the presence of servo constraints on posture motion, fully embodying the strong coupling effect brought about by the flexible manipulator.

[0096] Through the frequency domain constraint equivalent mapping, the amplitude change rate constraint is converted into the amplitude constraint, as shown in the following formula:

[0097] ;

[0098] For smaller sampling intervals , .

[0099] From the constraint functions of amplitude and amplitude change rate, we can see that if the condition is met , then the amplitude and rate of change of the control torque of the joint actuator can be strictly limited to the preset saturation range. Assuming that the control torque set of the ideal joint actuator is The dynamic range is limited to the amplitude-rate joint feasible region Based on this, the compatibility criterion can be derived .

[0100] Combined with the dynamic model of the flexible arm space robot system mentioned above, the mathematical model of the torque dual-domain constraint control system is designed. Therefore, the torque dual-domain constraint controller corresponding to the mathematical model of the torque dual-domain constraint control system can be designed. This is the dual-domain constrained control torque output by the dual-domain torque constraint controller corresponding to the mathematical model of the dual-domain torque constraint control system. This dual-domain torque constraint controller captures flexible vibration characteristics through wavelet network time-frequency analysis, embeds fuzzy logic into the dual-domain constraint rules, and combines adaptive learning to compensate for model uncertainty. Ultimately, it achieves constrained, robust, and stable control in a strongly coupled, underactuated flexible-arm space robot system. Its core innovation lies in the deep integration of frequency-domain constraint equivalence with an intelligent control architecture, breaking through the conservatism of traditional saturation control.

[0101] S2, construct a torque dual-domain constraint controller based on the improved fuzzy wavelet network. The torque dual-domain constraint controller satisfies the mathematical model of the torque dual-domain constraint control system, and its corresponding control law includes the improved fuzzy wavelet network control law and the improved fuzzy wavelet network parameter self-regulation control law.

[0102] In a specific embodiment, in the improved fuzzy wavelet network, the improved fuzzy wavelet network includes an input layer, a reconstructed fuzzification layer, a reconstructed rule layer and a reconstructed wavelet function layer;

[0103] In the reconstructed fuzzification layer, the antecedent membership function in the fuzzification layer of the traditional fuzzy wavelet network is replaced by the wavelet basis function from the Gaussian function, as shown in the following formula:

[0104] ;

[0105] in, As the mother wavelet function, multi-scale wavelet basis functions are generated through scaling and translation operations , represents the membership function; is the scaling parameter, is the translation parameter, represents the set of real numbers; Indicates the input variables, , is the input dimension, represents the index of the fuzzy subset, , is the number of fuzzy subsets for each input variable, represents the index of the translation parameter of the wavelet basis function, , is the total number of indexes of translation parameters;

[0106] In the reconstructed rule layer, define Fuzzy rules for:

[0107] like yes and yes ...and yes ,but ;

[0108] in, is the regular excitation intensity, Indicates the Rule No. The input variables are The weights of the output variables; , is the total number of rules, Indicates the output variables, , is the output dimension, represents the index of the wavelet decomposition scale, , is the total number of wavelet decomposition scales;

[0109] Combine the regular excitation intensity with the wavelet basis function to define the fuzzy wavelet basis function , as shown below:

[0110] ;

[0111] in, Represents the input vector of the improved fuzzy wavelet network, including input variables;

[0112] In the reconstructed wavelet function layer, the weight matrix and the fuzzy wavelet basis function vector The matrix multiplication of is used to perform weighted combination of the output variables of all rules, and the output vector of the improved fuzzy wavelet network is expressed in vector form, as shown in the following formula:

[0113] ;

[0114] in, represents the weight matrix, Indicates the Rule 1 The weights of the output variables, Represents the output vector of the improved fuzzy wavelet network, including output variables.

[0115] In a specific embodiment, a torque dual-domain constraint controller based on an improved fuzzy wavelet network is constructed, specifically including:

[0116] The ideal control law is established using the output variables of the improved fuzzy wavelet network:

[0117] ;

[0118] in, represents the ideal control torque after dual-domain constraints, which is a nonlinear uncertainty term; , is the unknown ideal weight matrix, express The fuzzy wavelet basis function vector corresponding to the input vector at time t, Represents a small error vector with boundedness, respectively Estimated , and further use the torque dual-domain constraint controller to output the control torque after dual-domain constraint As The estimated value of , the ideal control law is modified to the improved fuzzy wavelet network control law, as shown in the following formula:

[0119] ;

[0120] Therefore, the control torque after dual-domain constraints can be predicted by improving the fuzzy wavelet network.

[0121] In a specific embodiment, the parameter self-regulating control law of the improved fuzzy wavelet network is as follows:

[0122] when ,or and ,or and When , based on the Lyapunov stability criterion, the real-time dynamic adjustment control law of the weight matrix of the reconstructed wavelet function layer of the improved fuzzy wavelet network can be expressed as:

[0123] ;

[0124] in, express The subvector of express The subvector of express The subvector of express The subvector of express The subvector of , corresponding to the body posture and two joint hinges, express The first derivative with respect to time, represents the adaptive gain coefficient, ; Indicates the adjustment gain, ;

[0125] when and or and When , based on the Lyapunov stability criterion, the real-time dynamic adjustment control law of the weight matrix of the reconstructed wavelet function layer of the improved fuzzy wavelet network can be expressed as:

[0126] ;

[0127] in, represents the robustness compensation coefficient, .

[0128] The improved fuzzy wavelet network (improved FWN) in the embodiment of the present application achieves a breakthrough innovation by reconstructing the coupling mechanism between the three layers (fuzzification layer, rule layer, wavelet function layer) while retaining the basic four-layer architecture (input layer → fuzzification layer → rule layer → wavelet function layer):

[0129] (1) Fuzzy layer innovation: Wavelet basis function is used to replace the traditional Gaussian function as the membership function, and through dynamic adaptive adjustment of parameters, the time-frequency resolution limitation of the Gaussian function is effectively broken through, thereby accurately extracting the transient characteristics of the system's non-stationary signals;

[0130] (2) Rule layer reconstruction to establish a real coefficient product nonlinear consequence structure. This design significantly enhances the ability to accurately model strongly coupled complex dynamics such as flexible manipulators.

[0131] (3) Collaborative innovation of wavelet function layer: Constructing fuzzy wavelet basis function (FWBF). This mechanism effectively integrates the excitation intensity information of the rule layer and the multi-scale time-frequency characteristics of the wavelet function layer. With the help of the weight matrix, it realizes the deep coupling of global fuzzy reasoning and local time-frequency characteristics in the multiple-input multiple-output (MIMO) system, and ultimately comprehensively improves the control accuracy and dynamic response performance of the entire control system.

[0132] The specific instructions are as follows:

[0133] First, the embodiment of the present application reconstructs the fuzzification layer, establishes a reconstructed fuzzification layer, and replaces the antecedent membership function from the Gaussian function to the wavelet basis function with excellent time-frequency localization characteristics, so as to overcome the Gaussian function usually used as the membership function in the traditional fuzzy system. The energy dispersion characteristics of the Gaussian function in the time-frequency domain make it difficult to accurately capture the rapidly changing local features in the non-stationary signal, resulting in insufficient feature extraction capabilities. The embodiment of the present application utilizes the time-frequency localization characteristics of the wavelet basis function to accurately capture the transient features in the signal. And by adaptively adjusting the scaling parameters and translation parameters , so that the membership function has the ability to dynamically respond to changes in the input signal.

[0134] Secondly, by introducing a nonlinear product-type consequent structure in the reconstructed rule layer, the embodiments of this application significantly enhance the modeling and expression capabilities of complex nonlinear mapping relationships (such as the strong coupling between torque and position in the dynamics of a flexible-arm space robot system). In contrast, the output of the rule layer of a traditional Mandani fuzzy system is calculated using central average defuzzification (or similar linear weighting methods), which limits its ability to express complex nonlinear mapping relationships.

[0135] Finally, in the embodiment of the present application, the excitation intensity output by the regular layer is converted into Combined with the wavelet basis function, the fuzzy wavelet basis function (FWBF) is defined. Finally, we have input and The output FWN structure is as follows Figure 3 To facilitate the design of the torque dual-domain constraint controller, the final output of the improved FWN is expressed in vector form: the wavelet function layer is represented by the weight matrix and the fuzzy wavelet basis function vector The outputs of all rules are weightedly combined by performing matrix multiplication. Compared with neural networks, wavelet networks can achieve the same approximation quality with a smaller network size. Therefore, the improved FWN is used as the approximator in the design of the torque dual-domain constrained controller.

[0136] Specifically, the basic idea of ​​designing a torque dual-domain constraint controller based on an improved fuzzy wavelet network is as follows: first, the dynamic model of the flexible-arm space robot system and the physical constraints of the actuator are used, combined with the frequency domain constraint equivalent mapping principle and the joint constraint function, to establish a mathematical model of the torque dual-domain constraint control system; then, based on this mathematical model of the torque dual-domain constraint control system, a torque dual-domain constraint controller based on an improved fuzzy wavelet network is designed. Its principle structure is as follows: Figure 3 As shown in the figure, the ultimate goal is to achieve safe and feasible tracking control of the desired trajectory of the flexible arm space robot under strict physical constraints and effectively suppress the vibration of the flexible arm.

[0137] For the mathematical model of the torque dual-domain constraint control system, first define the expected angle variables of the body and joints and its tracking error , the derivatives of the expected rotation angle variables are continuous and satisfy and Existence and continuity, speed error , then the error dynamic equation is: Under the constraints of the known dynamic model of the flexible arm space robot system, a positive definite diagonal sliding surface is constructed. , For a positive-definite diagonal gain matrix, a quantized benchmark for the motion state deviation is established, and time derivatives are then applied to reveal the system's dynamic characteristics. When the mechanical system model is accurate and satisfies mathematical requirements, a globally stable linear state feedback controller can be designed based on stability theory. This method has been recognized as a standard approach in internationally recognized journals.

[0138] Will Taking the first derivative with respect to time yields:

[0139] ;

[0140] By combining the mathematical model of the torque dual-domain constraint control system with the above formula, we can obtain:

[0141] ;

[0142] The following formula is obtained by transformation:

[0143] ;

[0144] Therefore, we can get: ;

[0145] When the mechanical system model is accurate and satisfies the mathematical conditions, a linear state feedback controller is designed based on stability theory, and its corresponding control law is:

[0146] ;

[0147] in, is a symmetric positive definite gain matrix, represents a diagonal matrix, express The sub-matrix of , ;

[0148] From this we can get:

[0149] Define the Lyapunov function :

[0150] ;

[0151] calculate The total derivative of , and by and ,have to: .

[0152] Therefore, according to the Lyapunov stability theory, under the premise that the system model is accurately known, through the linear state feedback controller, if the symmetric positive definite gain matrix is ​​reasonably designed and , which can ensure that the tracking error of the closed-loop control system achieves asymptotically stable convergence. Among them, the feedforward term of the linear state feedback controller Can accurately compensate for system dynamics, while the feedback term This can ensure the stability of the error.

[0153] However, in practical space robot applications, the high complexity of their system architecture often makes accurate identification of dynamic parameters difficult, and unknown or uncertain parameters are the norm. In this context, directly designing a control law corresponding to a linear state feedback controller to simultaneously satisfy the dual-domain force-torque constraints and control a flexible-arm space robot system with unknown parameters often fails to achieve the desired control effect.

[0154] refer to Figure 4 The embodiment of the present application uses the improved FWN to efficiently approximate the nonlinear uncertainty term Compared with traditional neural networks, the improved FWN can significantly improve the approximation efficiency while simplifying the network structure by integrating the semantic interpretability of fuzzy logic and the time-frequency localization characteristics of wavelet transform: its fuzzy rule antecedent uses adaptively adjustable wavelet basis functions to capture the multi-scale dynamic characteristics of uncertain terms, and the consequent structure achieves accurate modeling of nonlinear coupling relationships through parameter optimization, and finally achieves the control of complex uncertainties with a low-dimensional rule base. Efficient online estimation of .

[0155] Furthermore, in order to solve the actuator saturation effect and control accuracy degradation problems caused by the dual-domain constraints of the control torque amplitude and its rate of change in the flexible arm space robot system, a parameter adaptive compensation mechanism is constructed based on the Lyapunov stability theory, that is, the parameter self-regulating control law of the improved fuzzy wavelet network is proposed. This is to improve the robustness of the controller and ensure Bounded.

[0156] The Lyapunov stability proof process is as follows:

[0157] Theorem 1: Based on the synergistic effect of the improved fuzzy wavelet network control law and the improved fuzzy wavelet network parameter self-regulation control law, the stability theory proves that the state of the flexible arm space robot system has global convergence. While ensuring that the tracking error converges to the preset accuracy range, the dynamic constraints of the control torque amplitude and its rate of change are strictly satisfied: ;

[0158] prove: Add or subtract on the right side , we can get:

[0159] ;

[0160] Will 、 and Substituting into the above formula, we can get:

[0161] ;

[0162] Construct the Lyapunov function as shown below:

[0163] ;

[0164] in, represents the Lyapunov function, for The estimated value of is defined as .

[0165] Taking the first-order derivative of the above formula with respect to time, we can get:

[0166] ;

[0167] in, express The first derivative with respect to time, express First derivative with respect to time.

[0168] 1) When the control torque is within the dynamic amplitude range, , that is, no saturation constraint occurs, there is .Will Substitution , it can be deduced that:

[0169] ;

[0170] 2) When and ,or and When Substitution , it can be deduced that:

[0171] ;

[0172] 3) When and ,or and When Substitution , it can be deduced that:

[0173] ;

[0174] Because of the assumption ,have , so the above formula is:

[0175] ;

[0176] It is observed that the formulas derived in 1), 2) and 3) above have a consistent parameter coupling structure. To improve writing efficiency, the subsequent analysis will take the formula derived in 1) as a representative case and systematically explain its dynamic characteristics and convergence conditions.

[0177] By inequality and , the formula derived in 1) can be rewritten as:

[0178] ;

[0179] in, To adjust the gain, To adjust the gain, is the weight coefficient, , so we can get:

[0180] ;

[0181] in, , the Lyapunov function satisfies the following conditions:

[0182] ;

[0183] From the above formula we can see that and is uniformly bounded, Converges to the interval .

[0184] S3, obtain the rotation angle vector composed of the body posture angle and the two joint angles at the current moment and the vibration mode coordinates of the flexible manipulator calculated based on the coordinates and amplitude of the flexible manipulator and construct an input vector; input the input vector into the torque dual-domain constraint controller, first use the parameter self-regulating control law of the improved fuzzy wavelet network to update the parameters of the improved fuzzy wavelet network, and then use the improved fuzzy wavelet network control law with the updated parameters of the improved fuzzy wavelet network to predict the control torque after dual-domain constraint at the next moment, and apply the control torque after dual-domain constraint at the next moment to the flexible arm space robot system to adjust the body posture angle, two joint angles and the coordinates and amplitude of the flexible manipulator at the next moment.

[0185] Specifically, the control method takes the current system state as input: the rotation angle vector composed of the body posture angle and the two joint angles at the current moment is collected, and the vibration mode coordinates of the flexible manipulator are calculated based on the coordinates and amplitude of the flexible manipulator. The two together construct the input vector ; After the input vector is input into the torque dual-domain constraint controller, the torque dual-domain constraint controller first uses the parameter self-regulating control law of the improved fuzzy wavelet network to update the parameters of the improved fuzzy wavelet network online, and then uses the improved fuzzy wavelet network control law with adjusted parameters to predict the control torque after dual-domain constraint at the next moment; finally, this predicted control torque after dual-domain constraint is applied to the flexible arm space robot system to adjust the body posture angle, two joint angles and the coordinates and amplitude of the flexible robotic arm at the next moment.

[0186] The embodiments of the present application are described below through specific simulation cases.

[0187] by Figure 2 As an example, the flexible arm space robot system is simulated. The structural parameters of the flexible arm space robot system are taken as , , ;Ontology and rigid robotic arm Quality Flexible robotic arm The uniform bending stiffness is , its mass per unit length is ;Ontology and rigid robotic arms The moment of inertia about the center of mass is .

[0188] During simulation, the expected motion laws of the flexible-arm space robot's body posture angle and two joint angles are set as follows:

[0189] , , , unit is rad.

[0190] The initial values ​​of the motion are taken as: ; Tracking time from start to finish .

[0191] The constraint range of the joint actuator output torque amplitude is set as: , , the unit is .

[0192] The constraint range of the joint actuator output torque amplitude change rate is set as:

[0193] , , the unit is .

[0194] Simulation scheme design: In order to verify the adaptability of the control method proposed in the embodiment of this application to the dual-domain constraint of joint output control torque, two sets of comparative experiments are set up:

[0195] Simulation 1: Method Verification Experiment

[0196] Example simulation content and result analysis: Using the improved fuzzy wavelet network control law and the improved fuzzy wavelet network parameter self-adjustment control law designed in the embodiment of this application, a control experiment is carried out on a flexible arm space robot system with unknown parameters and subject to dual-domain torque constraints. The simulation results are as follows Figure 5-Figure 12 As shown. Simulation verification shows that the method proposed in the embodiment of this application realizes high-precision motion control of the flexible-arm space robot system: the tracking errors of the body posture angle and the two joint angles converge to zero quickly, and the time-varying characteristics of the flexible arm vibration mode confirm that the elastic vibration is actively suppressed; the amplitude of the control torque output by the actuator and its rate of change are strictly limited to the preset threshold value, meeting the dual-domain constraint requirements, and the topological map of the motion trajectory of the multi-body system further reveals the global dynamic coordination law of the body motion, joint rotation and flexible vibration. This scheme has been verified by multi-dimensional experiments, providing a solution path for the control of strongly constrained flexible-arm space robots with both theoretical depth and engineering feasibility.

[0197] Simulation 2: Comparative verification experiment

[0198] In order to further verify the comprehensive performance of the method proposed in the embodiment of the present application under the dual-domain constraints of torque amplitude and change rate, under the same system parameters and torque dual-domain constraints, a comparative simulation study on control accuracy and robustness was carried out using the "Neural Network L2 Gain Robust Control of Flexible Arm Space Robot Based on Virtual Force" published in the Journal of Mechanical Engineering, Volume 48, Issue 23, Pages 23-29, 2012 as the benchmark control method.

[0199] The simulation comparison results show that Figures 13-19 As shown, although the baseline control method can constrain the actuator torque amplitude and its change rate within a preset range, there is a significant steady-state deviation and insufficient convergence in the trajectory tracking of the body posture angle and the two joint angles, and the flexible arm vibration suppression efficiency is simultaneously reduced; in contrast, the method proposed in the embodiment of the present application achieves a significant improvement in trajectory tracking accuracy, rapid dissipation of vibration energy, and effective smoothing of control torque fluctuations within the same constraint range through dynamic boundary coordination and multi-scale compensation mechanism, verifying its comprehensive improvement in control performance and robustness in complex constraint scenarios.

[0200] Therefore, simulation experiments show that the method proposed in the embodiment of the present application can not only constrain the control torque output by the joint actuator and its rate of change within the preset dual-domain boundaries in real time without relying on the precise model of the system, but also significantly improve the system's trajectory tracking accuracy and elastic vibration suppression capabilities under constrained working conditions through the efficient collaboration of dynamic fuzzy rules and adaptive wavelet basis functions, while achieving effective smoothing of torque fluctuation amplitudes. Compared with traditional control strategies, the proposed method combines high computational efficiency, strong parameter adaptability, and robustness to uncertain dynamics, providing a more practical solution for the engineering control of space robot systems in complex constrained environments.

[0201] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dual-domain torque constraint control method for a flexible arm space robot based on an improved FWN, characterized in that: The following steps are involved: A dynamic model of a flexible-arm space robot system is constructed under the condition that the translational degree of freedom is not actively controlled and the posture motion is subject to servo constraints. A mathematical model of a torque dual-domain constraint control system is constructed in combination with the dynamic model of the flexible-arm space robot system under the condition that the posture of the body and the control torque of the joint in the flexible-arm space robot system are subject to amplitude and amplitude change rate constraints. Constructing a torque dual-domain constraint controller based on an improved fuzzy wavelet network, wherein the torque dual-domain constraint controller satisfies the mathematical model of the torque dual-domain constraint control system, and its corresponding control law includes an improved fuzzy wavelet network control law and an improved fuzzy wavelet network parameter self-regulation control law; The invention relates to a method for predicting the control torque after dual-domain constraint at the next moment. The method comprises the following steps: obtaining the rotation angle vector composed of the body posture angle and the two joint angles and the vibration mode coordinates of the flexible manipulator calculated based on the coordinates and amplitude of the flexible manipulator at the current moment, and constructing an input vector; inputting the input vector into the torque dual-domain constraint controller, firstly updating the parameters of the improved fuzzy wavelet network by using the parameter self-regulating control law of the improved fuzzy wavelet network, and then predicting the control torque after dual-domain constraint at the next moment by using the improved fuzzy wavelet network control law with the updated parameters of the improved fuzzy wavelet network, and applying the dual-domain constraint control torque at the next moment to the flexible arm space robot system to adjust the body posture angle, the two joint angles and the coordinates and amplitude of the flexible manipulator at the next moment.

2. The method for controlling torque of a flexible-arm space robot based on an improved FWN according to claim 1 is characterized in that: Construct a dynamic model of a flexible-arm space robot system with no active control of the translational degree of freedom and servo constraints on the posture motion, specifically including: The flexible-arm space robot system comprises a free-floating body, a rigid robotic arm and a flexible robotic arm, wherein joints are provided between the body and the rigid robotic arm and between the rigid robotic arm and the flexible robotic arm, and each joint is articulated by a joint hinge; The flexible manipulator is reduced in order using the hypothetical modal method, and the first two dominant modes are intercepted to characterize the elastic deformation characteristics of the flexible manipulator. Based on the law of conservation of momentum and the second-kind Lagrangian equation, a dynamic model of the flexible arm space robot system is established under the conditions where no active control is applied to the translational degree of freedom and servo constraints are imposed on the posture motion, as shown in the following formula: in, represents the symmetric positive definite inertia matrix, q = [q0,q1,q2] T represents the angle variable, q0, q1 and q2 represent the body posture angle, the joint angle between the body and the rigid manipulator, and the joint angle between the rigid manipulator and the flexible manipulator, respectively. and They represent the first and second derivatives of the rotation vector q with respect to time, η=[η1,η2] T represents the vibration mode coordinates of the flexible manipulator, η1 and η2 represent the vibration mode coordinates of the first-order mode and the second-order mode, respectively, T represents the transposition, and They represent the first-order and second-order derivatives of the vibration mode coordinate η of the flexible manipulator with respect to time, represents the column vector containing centrifugal force and Coriolis force, is the flexible stiffness matrix, represents the unconstrained body posture and the control torque of the joint; represents the set of real numbers.

3. The method for controlling torque of a flexible-arm space robot based on an improved FWN according to claim 2 is characterized in that: Under the condition that the posture of the body and the control torque of the joint joint in the flexible arm space robot system are constrained by the amplitude and the amplitude change rate, a mathematical model of the torque dual-domain constraint control system is constructed in combination with the dynamic model of the flexible arm space robot system, specifically including: Assume that the unconstrained control torque u(t) at time t is constrained by the amplitude and amplitude change rate, that is: Among them, u min ,u max Represent the known lower amplitude saturation limit value and upper amplitude saturation limit value respectively, Respectively represent the known lower amplitude change rate saturation limit value and upper amplitude change rate saturation limit value; To handle the constraints of amplitude and amplitude change rate, the following functions are defined: Among them, σ ars (u(t)) represents the control torque output by the torque dual-domain constraint controller after dual-domain constraint, represents the upper limit of the joint constraint, and its expression is: u(t-δ) represents the control torque at time t-δ, δ represents the sampling time interval, and min represents the minimum value. u (t) represents the lower limit of the joint constraint, and its expression is: Max means taking the maximum value; Combined with the dynamic model of the flexible arm space robot system, the mathematical model of the torque dual-domain constraint control system is designed, as shown in the following formula:

4. The method for controlling torque of a flexible-arm space robot based on an improved FWN according to claim 3 is characterized in that: In the improved fuzzy wavelet network, the improved fuzzy wavelet network includes an input layer, a reconstructed fuzzification layer, a reconstructed rule layer and a reconstructed wavelet function layer; In the reconstructed fuzzification layer, the antecedent membership function in the fuzzification layer of the traditional fuzzy wavelet network is replaced by the wavelet basis function from the Gaussian function, as shown in the following formula: Among them, ψ(·) is the mother wavelet function, and the multi-scale wavelet basis function ψ is generated by scaling and translation operations. s,p (x i ), μ Asi (·) represents the membership function; is the scaling parameter, is the translation parameter, represents the set of real numbers; x i represents the i-th input variable, i=1,2,...,m, m is the input dimension, s represents the index of the fuzzy subset, s=1,2,...,S', S' is the number of fuzzy subsets for each input variable, p represents the index of the translation parameter of the wavelet basis function, p=1,2,...,P, P is the total number of translation parameter indices; In the reconstructed rule layer, define the jth fuzzy rule R j for: If x1 is A j1 And x2 is A j2 ... and x m It's A jm ,but in, is the regular excitation intensity, represents the weight of the i-th input variable to the k-th output variable in the j-th rule; j = 1, 2, ..., N, N is the total number of rules, y k represents the k-th output variable, k = 1, 2, ..., n, n is the output dimension, l represents the index of the wavelet decomposition scale, l = 1, 2, ..., L, L is the total number of wavelet decomposition scales; The regular excitation intensity is combined with the wavelet basis function to define the fuzzy wavelet basis function Ψ j (x), as shown below: Wherein, x represents the input vector of the improved fuzzy wavelet network, which includes m input variables; In the reconstructed wavelet function layer, the output variables of all rules are weighted and combined by matrix multiplication of the weight matrix W and the fuzzy wavelet basis function vector Ψ(x), and the output vector of the improved FWN is expressed in vector form, as shown in the following formula: in, represents the weight matrix, v jk represents the weight of the j-th rule on the k-th output variable, and y represents the output vector of the improved FWN, which includes n output variables.

5. The method for controlling torque of a flexible-arm space robot based on an improved FWN according to claim 4 is characterized in that: A torque dual-domain constraint controller based on the improved FWN is constructed, which includes: The ideal control law is established using the output variables of the improved FWN: s ars (u * )=W *T Ψ(x(t))+ε f (x(t)); Among them, σ ars (u * ) represents the ideal control torque after dual-domain constraints, which is a nonlinear uncertainty term; W * is the unknown ideal weight matrix, Ψ(x(t)) represents the fuzzy wavelet basis function vector corresponding to the input vector at time t, ε f (x(t)) represents a small error vector with boundedness, and W * It is estimated to be W, and further the control torque σ output by the torque dual-domain constraint controller after dual-domain constraint is ars (u(t)) as σ ars (u * ), the ideal control law is modified to the improved fuzzy wavelet network control law, as shown in the following formula: s ars (u(t))=W T ψ(x(t)); Therefore, the control torque output by the torque dual-domain constraint controller after dual-domain constraint can be predicted by the improved fuzzy wavelet network.

6. The method for controlling torque of a flexible-arm space robot based on an improved FWN according to claim 5 is characterized in that: The parameter self-regulating control law of the improved fuzzy wavelet network is as follows: when or And S<0, or u h (t)< u h (t) and S>0, based on the Lyapunov stability criterion, the real-time dynamic adjustment control law of the weight matrix of the reconstructed wavelet function layer of the improved fuzzy wavelet network can be expressed as: Among them, u h (t) represents the subvector of u(t), express The subvector of u h (t) indicates u (t), W h represents the subvector of W, S h Represents the subvector of S, h = 0, 1, 2, corresponding to the posture of the body and the two joints, respectively, W h The first derivative with respect to time, represents the adaptive gain coefficient, ξ h represents the adjustment gain, ξ h >0; when And S>0 or u h < u h When S<0, based on the Lyapunov stability criterion, the real-time dynamic adjustment control law of the weight matrix of the reconstructed wavelet function layer of the improved fuzzy wavelet network can be expressed as: Among them, ρ h Represents the robustness compensation coefficient, 0≤ρ h <1.

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