A flexible space manipulator tracking control method based on credibility gating interval type-2 fuzzy neural network

Abstract

This invention discloses a tracking control method for a flexible space robot arm based on a credibility-gated interval type-II fuzzy neural network, belonging to the field of space robot control. To address the technical problem of insufficient tracking accuracy in existing space robot arm tracking control methods, this invention establishes a dynamic model of the flexible space robot arm system considering lumped uncertainties. It then uses a credibility-gated interval type-II fuzzy neural network to approximate the lumped uncertainties in the dynamic model online, obtaining an estimate of the lumped uncertainty. The lumped uncertainty estimate, network compensation term, robust saturation term, and flexible modal active suppression term are jointly introduced into the nominal control law, simultaneously achieving high-precision joint tracking, floating base coupling compensation, and residual vibration suppression of flexible links for the floating-based flexible space robot arm under complex trajectory conditions. This method is primarily used for tracking control of flexible space robots.

Description

Technical Field

[0001] This invention relates to the field of space robot control, specifically to a method for trajectory tracking and flexible vibration suppression control of a flexible space robot with uncertainties. Background Technology

[0002] The flexible space robotic arm is a serially connected multi-joint actuator used for on-orbit servicing, target acquisition, payload transfer, extravehicular assembly, and space structure maintenance. It consists of a free-floating base, several discrete rotary joints, lightweight, slender elastic links, and an end effector. To reduce launch weight and expand the operating range, the links employ a lightweight, slender structure, resulting in a flexible link effect. In microgravity or zero gravity environments, the base is floating, and joint motion, floating base motion, and flexible link vibration are coupled. Joint acceleration easily excites flexible modes in the links, while link vibration conversely degrades joint trajectory tracking and end-effector positioning accuracy. The system exhibits strong nonlinearity, multi-field coupling, and significant model uncertainty. The core control objectives are high-precision trajectory tracking and active suppression of flexible vibration.

[0003] During complex trajectory tracking, the dynamic model of a space robotic arm is susceptible to various uncertainties, including perturbations of flexible modal parameters of the links, modal truncation errors, momentum coupling errors between the floating base and the robotic arm, joint friction and unmodeled nonlinearities, load inertia variations, actuator deviations, and external disturbances. These factors are interconnected, making it difficult to guarantee tracking accuracy under complex conditions using computational torque control that relies solely on an accurate model. Traditional robust control methods typically rely on large gains to suppress model uncertainties and external disturbances; however, for flexible space robotic arms, excessive gains may cause high-frequency fluctuations in joint control torque, thereby inducing modal vibrations of the flexible links and reducing trajectory tracking accuracy.

[0004] Therefore, there is an urgent need to propose a control method that takes into account floating base coupling compensation, flexible modal vibration suppression, and online approximation of lumped uncertainty. Summary of the Invention

[0005] To overcome the technical problem of insufficient tracking accuracy in existing space robotic arm tracking control methods, this invention provides a flexible space robotic arm tracking control method based on a confidence-gated interval type II fuzzy neural network.

[0006] A tracking control method for a flexible spatial robotic arm based on a confidence-gated interval type-II fuzzy neural network includes:

[0007] S1: Establish a dynamic model of the flexible space robot manipulator system considering lumped uncertainties; lumped uncertainties include model uncertainties and external disturbances;

[0008] S2: The lumped uncertainty in the dynamic model is approximated online using a confidence-gated interval type II fuzzy neural network to obtain the estimated value of the lumped uncertainty;

[0009] S3: Design a tracking controller for a space robot manipulator system based on lumped uncertainty estimates.

[0010] Furthermore, the dynamic model of the flexible space robot's space manipulator system is as follows:

[0011] ;

[0012] In the formula, This is the joint angular acceleration vector; For nominal dynamics; Input matrix for nominal value; For joint control torque; To aggregate uncertainty, Let be the system state vector. For time variables, In the formula, This represents the uncertainty caused by inertial parameter perturbation. This represents the error in the nonlinear velocity term. This represents the flexible modal coupling error and the flexible modal truncation error. This indicates the floating base coupling error. This represents external disturbances and remaining unmodeled dynamics.

[0013] Furthermore, the confidence-gated interval type II fuzzy neural network includes: a first layer: an input layer; a second layer: a membership function layer; a third layer: a rule layer; a fourth layer: a confidence-gated layer; a fifth layer: a type reduction layer; and a sixth layer: an output layer.

[0014] Furthermore, the working process of the trust gating layer is as follows:

[0015] For each fuzzy rule, construct the rule confidence coefficient:

[0016] No. The rule credibility coefficient of a fuzzy rule ,in, For the Sigmoid function, and These are the weighting coefficients. For bias terms, For the first The compactness of the activation interval of a fuzzy rule. For the first Consistency of the consequent of a fuzzy rule. For the first Consistency of neighborhood evidence for the first fuzzy rule; the first Compactness of the activation interval of a fuzzy rule ,in, For the first The activation strength of a fuzzy rule. For the first The activation strength under a fuzzy rule, To prevent constants with a denominator of zero; the first Consistency of the consequent of a fuzzy rule ,in, and The first The left and right endpoints of the output of the fuzzy rule consequent; the first Neighborhood evidence consistency of fuzzy rules ,in, For the first The consequent center of a fuzzy rule For the first The mean of the consequent center of a fuzzy rule. For the first The set of local rules corresponding to each fuzzy rule. This is the neighborhood consistency adjustment coefficient;

[0017] The set of local rules , including with the The neighborhood fuzzy rules associated with the first fuzzy rule, and the fuzzy rules associated with the second fuzzy rule. A fuzzy rule is a fuzzy rule that activates correlation;

[0018] For each fuzzy rule, the original activation intensity is gating-corrected using the rule credibility coefficient of the fuzzy rule to obtain the corrected activation intensity, which includes the corrected upper activation intensity and the corrected lower activation intensity; The modified activation strength of the fuzzy rule , No. The modified activation strength of the fuzzy rule .

[0019] Furthermore, the first The consequent center of a fuzzy rule The first The mean of the consequent of a fuzzy rule ,in, For a set of local rules The number of fuzzy rules in the middle; This is the fuzzy rule index variable used for summation.

[0020] Furthermore, the working process of the type reduction layer is as follows: using the modified activation intensity, the left and right endpoint outputs of the confidence-gated interval type II fuzzy neural network are determined; the left endpoint output... and right endpoint output The expressions are as follows: , .

[0021] Furthermore, the working process of the output layer is as follows:

[0022] For each fuzzy rule, the activation weights of the fuzzy rule are constructed using the modified activation strength:

[0023] No. Activation weights of fuzzy rules ,in, For the fuzzy rule index variable used for summation;

[0024] Based on the activation weights and rule credibility coefficients of each fuzzy rule, a global weighted credibility is constructed. ;

[0025] Based on global weighted credibility and output range width ratio Effectiveness and reliability of constructing fuzzy rules : ,in, This is the interval width penalty coefficient;

[0026] Based on effective credibility Constructing a non-saturated dynamic fusion factor ; ,in, The fusion sensitivity coefficient, The confidence center value, For fusion bias terms;

[0027] Utilizing dynamic fusion factors Adjusting the output of the confidence-gated interval type II fuzzy neural network , ,in, This serves as the input to a confidence-gated interval type-II fuzzy neural network. and These are the left and right endpoint outputs of the confidence-gated interval type II fuzzy neural network, respectively.

[0028] Furthermore, the candidate network consequent weights of the confidence-gated interval type II fuzzy neural network are updated online using the whale optimization algorithm, including the following steps:

[0029] 1) Initialize the whale population: Generate The weight vectors of each candidate network consequent in the confidence-gated interval type II fuzzy neural network are mapped to the position vectors of each individual whale.

[0030] 2) Fitness evaluation: Calculate the fitness value for each individual whale and select the whale with the lowest fitness value as the current best individual globally. And based on the effective reliability of the optimal whale individual matching Build whale location optimization update gain , ,in, Based on search gain;

[0031] 3) Iterative update of individual whale positions: The position of individual whales in the whale population is iterated through position convergence update formula and position spiral update formula; after each round of individual position update, the weight vector of each candidate network consequent is subject to boundary constraints.

[0032] The formula for updating positions is: ,in, For the first Individual whales The position vector at time , In order to be in The position vector of the globally optimal individual whale at any given time. For the first Individual whales The position vector at time , Update the step size based on the baseline;

[0033] The formula for position spiral update is: ,in, The constant for the spiral shape. It is a random number;

[0034] 4) Convergence Determination and Parameter Output: The whale individual position iteration continues until the preset maximum number of iterations is reached, or the change in the minimum fitness value meets the preset condition, at which point the whale individual position iteration update terminates; the best individual in the whale population is selected. The candidate network consequent weights of the corresponding confidence-gated interval type-II fuzzy neural network are denoted as the optimal network consequent weights. The optimal network consequent weights are written back to the rule layer of the confidence-gated interval type II fuzzy neural network to complete the update.

[0035] Furthermore, the control law of the tracking controller is:

[0036] ,

[0037] in, For joint control torque, For the nominal inertia matrix Let be the nominal inertia matrix. For nominal flexible coupling terms; This represents the lumped uncertainty estimate output by the confidence-gated interval type-II fuzzy neural network. The robust gain matrix; It is a saturation function; These are boundary layer parameters; This is a combined error that includes joint position error and joint velocity error; For virtual control of acceleration.

[0038] Furthermore, the virtual control acceleration The expression is:

[0039] ,

[0040] in, Let be the desired joint angular acceleration vector. It is a positive definite matrix. Joint tracking error The derivative, The active suppression term for flexible modes is expressed as follows:

[0041] ,

[0042] in, and All are positive definite matrices. For flexible modal coordinate vectors, This is the velocity vector for the flexible mode.

[0043] The beneficial effects of this invention are:

[0044] This invention uses model uncertainty and external disturbance as lumped uncertainty to establish a dynamic model of a flexible space robot space manipulator system that considers lumped uncertainty; it no longer models various error components separately, but fully characterizes the multiple coupled unknown factors of the system, solves the problems of traditional torque control relying on precise models and poor tracking accuracy in complex working conditions, and improves the adaptability of the dynamic model to changing working conditions.

[0045] This invention utilizes a confidence-gated interval type II fuzzy neural network to approximate the lumped uncertainty in the dynamic model online, obtaining an estimate of the lumped uncertainty. During the online approximation process, the fusion weights of the interval endpoints are dynamically adjusted based on the real-time confidence of the reasoning results of each fuzzy rule, abandoning the fixed-ratio fusion mode, which greatly improves the online fitting and estimation accuracy of time-varying strongly coupled uncertainty, providing a precise basis for error compensation for the controller.

[0046] This invention designs a tracking controller for a space robot manipulator system based on lumped uncertainty estimates. Network compensation, robust saturation, and flexible modal active suppression terms are all incorporated into the nominal control law to simultaneously achieve high-precision joint tracking, floating base coupling compensation, and residual vibration suppression of the flexible links in the floating-based flexible space manipulator under complex trajectory conditions.

[0047] This invention also employs the whale optimization algorithm to update the consequent weights of the confidence-gated interval type II fuzzy neural network online, enabling the weight update amplitude to adaptively adjust according to the current rule confidence state, thereby improving the network approximation accuracy and parameter update stability. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0049] Figure 1 This is a schematic diagram of joint trajectory tracking in one embodiment of the method of the present invention.

[0050] Figure 2 This is a schematic diagram of joint tracking error in one embodiment of the method of the present invention.

[0051] Figure 3 This is a schematic diagram of the controller torque input in one embodiment of the method of the present invention.

[0052] Figure 4 This is a schematic diagram of the flexible modal response of a connecting rod in one embodiment of the method of the present invention.

[0053] Figure 5 This is a schematic diagram of the floating base pose in one embodiment of the method of the present invention.

[0054] Figure 6 This is a schematic diagram illustrating the rule credibility in one embodiment of the method of the present invention.

[0055] Figure 7 This is a schematic diagram of the interval width ratio in one embodiment of the method of the present invention.

[0056] Figure 8 This is a schematic diagram of the fusion factor in one embodiment of the method of the present invention.

[0057] Figure 9 This is a schematic diagram illustrating optimal adaptation of a whale in one embodiment of the method of the present invention.

[0058] Figure 10This is a schematic diagram comparing joint tracking errors in one embodiment of the method of the present invention.

[0059] Figure 11 This is a schematic diagram comparing the flexible modal responses of a joint in one embodiment of the method of the present invention.

[0060] Figure 12 This is a schematic diagram of the lumped uncertainty estimation error in one embodiment of the method of the present invention.

[0061] Figure 13 This is a schematic diagram of the execution flow of a flexible spatial robotic arm tracking control method based on a confidence-gated interval type II fuzzy neural network in one embodiment of the method of the present invention. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] This embodiment provides a tracking control method for a flexible spatial robotic arm based on a confidence-gated interval type-II fuzzy neural network, such as... Figure 13 As shown, it includes the following steps:

[0064] Step S100: Establish a dynamic model of the flexible space robot space manipulator system considering lumped uncertainties; lumped uncertainties include model uncertainties and external disturbances.

[0065] The controlled object in this embodiment is a three-joint floating base planar flexible spatial manipulator. The manipulator includes a floating base, three planar rotational joints, and three flexible links. The floating base has two translational degrees of freedom and one rotational degree of freedom in the plane. The main bending vibration of each flexible link is approximated by a first-order principal mode.

[0066] Step S101: Define the system's generalized coordinates:

[0067] (1)

[0068] in, For the system's generalized coordinate vector, The floating base plane position, The base attitude angle, , and There are three joint angles. , and These are the first-order principal mode coordinates corresponding to the three flexible links.

[0069] Step S102: Considering the coupling relationship between the floating base motion, joint motion, and flexible modal vibration, establish the dynamic formula of the joint subsystem:

[0070] (2)

[0071] in, Let the joint equivalent inertia matrix be... Joint angle vector, This is the joint angular acceleration vector; For Coriolis force and centrifugal force terms, This is the joint angular velocity vector; For flexible modal coupling, For flexible modal coordinate vectors; The velocity vector is the flexible mode velocity vector. This represents the unknowns caused by the uncertainties resulting from inertial parameter perturbations, floating base coupling, flexible mode truncation, tribolinearity, unmodeled dynamics, and external disturbances. It is a time variable; For joint control torque.

[0072] Step s103: ... As a set of uncertainties, denoted as The expression is:

[0073] (3)

[0074] in, This is the system state vector; It is a time variable; This represents the uncertainty caused by inertial parameter perturbation. This indicates the error caused by Coriolis force, centrifugal force, frictional nonlinearity, and other velocity-related unmodeled nonlinearities. This represents the flexible modal coupling error and the modal truncation error. This indicates the coupling error between the floating base and the robotic arm. This represents external disturbances and remaining unmodeled dynamics.

[0075] Step S104: Establish a framework considering lumped uncertainty Dynamic model of a flexible space robot space manipulator system:

[0076] (4)

[0077] in, For nominal dynamics, The nominal input matrix is ​​given.

[0078] Lumped uncertainty This is the objective that the present invention requires for online approximation and compensation.

[0079] Step S200: Use a confidence-gated interval type II fuzzy neural network to approximate the lumped uncertainty in the dynamic model online and obtain the estimated value of the lumped uncertainty.

[0080] The inventors of this application discovered that although traditional interval type-2 fuzzy neural networks can describe uncertainty through upper and lower membership functions, their output stage typically uses a fixed average or fixed ratio fusion of the left and right endpoints, failing to fully utilize the credibility information contained in the rule activation interval, consequent interval, and output interval width. Therefore, an improvement is made to the traditional interval type-2 fuzzy neural network: a credibility gating layer is added between the rule layer and the type reduction layer, so that each fuzzy rule undergoes credibility evaluation and gating correction before participating in output fusion.

[0081] Step S201: Construct a confidence-gated interval type II fuzzy neural network.

[0082] The constructed confidence-gated interval type-II fuzzy neural network includes: first layer: input layer; second layer: membership function layer; third layer: rule layer; fourth layer: confidence-gated layer; fifth layer: type reduction layer; sixth layer: output layer.

[0083] The working process of the confidence-gated interval type II fuzzy neural network is as follows:

[0084] First layer: Input layer;

[0085] Receive input vector , input vector Transmitted to the membership function layer.

[0086] The input data The expression is:

[0087] (5)

[0088] in, This refers to joint tracking error; This represents the overall error variable; superscript symbol. This is the transpose symbol.

[0089] Input vector Each component in the matrix corresponds to A vague rule.

[0090] Second layer: Membership function layer;

[0091] For the input vector The first in Input variables The corresponding number Upper interval type II Gaussian membership function of fuzzy rules The lower interval type II Gaussian membership function The expressions are as follows:

[0092] (6)

[0093] (7)

[0094] in, Input variables Corresponding to the The center of the Gaussian membership function of the fuzzy rule, The width parameter of the membership function. This is the width parameter of the subordinate function.

[0095] No. The original activation intensity of a fuzzy rule includes the upper activation intensity. and lower activation intensity The expressions are as follows:

[0096] (8)

[0097] (9)

[0098] in, The total number of input variables for the antecedent center of the fuzzy rule.

[0099] The consequent of each fuzzy rule is output in interval form, the first... Consequence output of a fuzzy rule for:

[0100] (10)

[0101] in, and The first The left and right endpoints of the output of the fuzzy rule consequent.

[0102] The third layer: the rules layer;

[0103] Receive from the rule layer The fuzzy rules and the original activation strength of each fuzzy rule, the original activation strength including the upper activation strength and the lower activation strength.

[0104] Fourth layer: Trustworthiness gating layer;

[0105] For each fuzzy rule, a rule credibility coefficient is constructed. The rule credibility coefficient is formed by fusing the rule activation interval compactness, consequent consistency, and neighborhood evidence consistency.

[0106] (4.1) Calculate the tightness of the rule activation interval for each fuzzy rule. The calculation formula is as follows:

[0107] (11)

[0108] in, For the first The compactness of the activation interval of a fuzzy rule. For the first The activation strength of a fuzzy rule. For the first The activation strength under a fuzzy rule, To prevent constants with a denominator of zero, .

[0109] No. Compactness of the activation interval of a fuzzy rule Used to describe the The relative consistency between the activation intensities of the upper and lower fuzzy rules, with a value range of [value range missing]. When the rule activates interval compactness Approaching 1 or greater than the preset tightness threshold When, it indicates the first The smaller the difference in activation intensity between the upper and lower parts of a fuzzy rule, the higher the activation certainty of the fuzzy rule in the current input region; when the rule's activation interval is compact... Approaching 0 or less than the preset tightness threshold When, it indicates the first The activation strength of the fuzzy rule differs significantly between the upper and lower parts, indicating that the activation of the fuzzy rule in the current input region is highly uncertain.

[0110] (4.2) Calculate the consequent consistency degree of each fuzzy rule using the following formula:

[0111] (12)

[0112] in, For the first Consistency of the consequent of a fuzzy rule.

[0113] No. Consistency of the consequent of a fuzzy rule Used to describe the The degree of relative consistency between the left and right endpoints of the consequent output of a fuzzy rule, with a value range of [value missing]. When the first Consistency of the consequent of a fuzzy rule Approaching 1 or greater than the consequent consistency threshold When the difference between the left and right endpoints of the consequent output of the rule is smaller, the consistency of the current fuzzy rule consequent inference result is higher; when the... Consistency of the consequent of a fuzzy rule Approaching 0 or less than the consequent consistency threshold When, it indicates the first The left and right endpoints of the consequent output of the fuzzy rule differ significantly, and the consequent output range is wide, indicating that the current fuzzy rule consequent inference result has strong uncertainty.

[0114] (4.3) Calculate the neighborhood evidence consistency for each fuzzy rule, including the following steps:

[0115] (4.3.1) Calculate the first The consequent center of a fuzzy rule:

[0116] (13)

[0117] in, For the first The consequent center of a fuzzy rule.

[0118] (4.3.2) Obtaining and the first A set of local rules associated with fuzzy rules Calculate the local rule set Mean of the consequent centers of all fuzzy rules:

[0119] (14)

[0120] in, For a set of local rules The mean of the consequent centers of all fuzzy rules in the equation. For a set of local rules The number of fuzzy rules in the middle This is the fuzzy rule index variable used for summation.

[0121] The set of local rules , including with the Neighborhood fuzzy rules associated with fuzzy rules, and related to A fuzzy rule is a fuzzy rule that has activation correlation.

[0122] The neighborhood fuzzy rule refers to the rule whose position in the antecedent space is related to the first... Fuzzy rules adjacent to the first fuzzy rule; that is, fuzzy rules adjacent to the first fuzzy rule. The fuzzy rule is one where the distance between the centers of the antecedent membership functions is less than a set threshold, or where a fuzzy rule uses adjacent linguistic values ​​only on one input variable. When the fuzzy rule numbers are arranged according to the antecedent adjacency relationship, the 1st... and the The fuzzy rule is the one that is related to the first... Neighborhood fuzzy rules associated with a fuzzy rule.

[0123] The activation correlation is used to characterize the degree of proximity of two fuzzy rules being simultaneously activated in the current input state. Since each interval type-2 fuzzy rule includes an upper activation intensity and a lower activation intensity, the method for determining whether two fuzzy rules have activation correlation is as follows: For each fuzzy rule, calculate the average of the upper and lower activation intensities as the comprehensive activation intensity of the fuzzy rule. Calculate the difference between the comprehensive activation intensities of the two fuzzy rules. If the difference is less than a preset threshold, the two fuzzy rules are considered to have activation correlation. The smaller the difference in the comprehensive activation intensities of the two fuzzy rules, the higher the activation correlation; the larger the difference, the lower the activation correlation.

[0124] Local rule set The middle also includes the first The neighborhood fuzzy rule of the fuzzy rule and the fuzzy rule of the fuzzy rule. A fuzzy rule is a fuzzy rule with high activation relevance, that is, it considers both the proximity relationship in the rule structure and the activation similarity relationship in the current input state.

[0125] (4.3.3) Based on the first The consequent center of a fuzzy rule and the corresponding local rule set The mean of the consequent centers of all fuzzy rules in the equation is used to determine the first... Neighborhood evidence consistency of fuzzy rules :

[0126] (15)

[0127] in, For the first The consequent center of a fuzzy rule For the first The mean of the consequent center of a fuzzy rule. For the first The set of local rules corresponding to each fuzzy rule. This is the neighborhood consistency adjustment coefficient. ;

[0128] No. Neighborhood evidence consistency of fuzzy rules , by the Fuzzy rule consequent center and local rule set The distance between the mean values ​​of the consequent centers of the fuzzy rule is calculated, and the value range is [value range missing]. ; It is negatively correlated with the distance: when the first Fuzzy rule consequent center and local rule set The smaller the distance between the mean values ​​of the consequent centers in a fuzzy rule, the greater the consistency of neighborhood evidence. The closer the value is to 1, the more it indicates that the first... Fuzzy rules and local rule sets The higher the consistency of evidence output by the fuzzy rule, the better; when the... Fuzzy rule consequent center and local rule set The greater the distance between the mean values ​​of the consequent centers of the fuzzy rule, the greater the consistency of neighborhood evidence. The closer the value is to 0, the more it indicates that the first... Fuzzy rules and local rule sets The lower the consistency of evidence output by the fuzzy rule, the less consistent the evidence.

[0129] (4.4) Based on the first Compactness of the activation interval of a fuzzy rule Consistency of successor Consistency with neighboring evidence Get the first The rule credibility coefficient of a fuzzy rule The expression is:

[0130] (16)

[0131] in, and These are the weighting coefficients; For bias terms; The Sigmoid function has the following expression:

[0132] (17)

[0133] in, Use the Sigmoid activation function; Scalar input variables for the Sigmoid activation function.

[0134] In this step, Rule credibility coefficient Reflects the first The reliability of a fuzzy rule participating in reasoning under the current input state, and its credibility coefficient. The closer it is to 1, the better it indicates that the first... The more reliable the result obtained by using fuzzy rules in the current input state, the higher the reliability.

[0135] (4.5) For each fuzzy rule, the original activation intensity is gating and corrected using the rule credibility coefficient of the fuzzy rule to obtain the corrected activation intensity, which includes the corrected upper activation intensity. and the corrected lower activation strength .

[0136] No. The modified expression for the activation strength after the fuzzy rule is:

[0137] (18)

[0138] No. The modified expression for the subactivation strength after the fuzzy rule is:

[0139] (19)

[0140] By gating the original activation intensity, the fuzzy rules with higher credibility in the current inference process can maintain a large contribution to the network output, while the rules with lower credibility are adaptively weakened, thereby improving the approximation reliability of the interval type II fuzzy neural network for the lumped uncertainty of the flexible space robot.

[0141] Fifth layer: Type reduction layer;

[0142] Using the modified activation intensity, the left and right endpoint outputs of the confidence-gated interval type II fuzzy neural network are calculated.

[0143] The left endpoint output of a confidence-gated interval type-II fuzzy neural network The expression is:

[0144] (20)

[0145] The right endpoint output of a confidence-gated interval type-II fuzzy neural network The expression is:

[0146] (twenty one)

[0147] Traditional interval type II fuzzy neural networks typically use and Fixed averaging or using preset fixed weights to obtain the final output are simple methods, but they weaken the credibility information formed during the interval type II fuzzy inference process, making it difficult for the output interval width, rule consistency, and rule activation state to truly participate in the final decision. Therefore, this invention proposes a dynamic fusion method. and The method.

[0148] Sixth layer: Output layer;

[0149] (6.1) For each fuzzy rule, construct the activation weights of the fuzzy rule using the modified activation strength:

[0150] No. Activation weights of fuzzy rules The expression is:

[0151] (twenty two)

[0152] in, This is the fuzzy rule index variable used for summation.

[0153] (6.2) Construct a global weighted credibility based on the activation weights and rule credibility coefficients of each fuzzy rule. The expression is:

[0154] (twenty three)

[0155] Unlike simple average confidence, It places greater emphasis on the contribution of currently activated rules to the overall trustworthy state, thus more accurately reflecting the network's reasoning trustworthiness within the current input region.

[0156] (6.3) Based on global weighted credibility and output range width ratio Effectiveness and reliability of constructing fuzzy rules .

[0157] In this step, the output interval width ratio The expression is:

[0158] (twenty four)

[0159] when and A large difference indicates that the network's current output has high uncertainty, and the interval width is greater than that. Increase; when the two are close, it indicates that the network output is more concentrated and the interval width is greater than that. Smaller.

[0160] The effective credibility The expression is:

[0161] (25)

[0162] in, This is the interval width penalty coefficient. .

[0163] Effective confidence is affected not only by the confidence of the fuzzy rule itself, but also by the width of the output interval. When the output interval is wide, the effective confidence automatically decreases; when the rule activation states are consistent and the outputs of the left and right endpoints are close, the effective confidence increases.

[0164] (6.4) Based on effective credibility Constructing a non-saturated dynamic fusion factor The expression is:

[0165] (26)

[0166] in, The fusion sensitivity coefficient, ; To preset the confidence center value, For fusion bias terms;

[0167] (6.5) Utilizing dynamic fusion factors Adjusting the left endpoint output of the confidence-gated interval type II fuzzy neural network and right endpoint output The weights, confidence levels, and gated intervals of the type II fuzzy neural network are used to determine the input and output data. Output results ,calculate The expression is formula (27):

[0168] (27)

[0169] (28)

[0170] Formula (28) indicates the output result The contents contained therein, The first joint channel lumped uncertainty estimate is the output of the confidence-gated interval type-II fuzzy neural network. The second joint channel lumped uncertainty estimate is the output of the confidence-gated interval type-II fuzzy neural network. The lumped uncertainty estimate of the third joint channel output by the confidence-gated interval type II fuzzy neural network is given.

[0171] Through the aforementioned dynamic fusion method, the network's final output no longer relies on a fixed average. Instead, it can adaptively adjust the fusion ratio of the left and right endpoints based on the current rule credibility, activation rule distribution, and output interval width. This structure transforms the interval information of the interval type II fuzzy neural network from a traditional intermediate computational burden into an output decision basis, which is beneficial for improving the reliability and adaptability of lumped uncertainty estimation under complex trajectory conditions.

[0172] This application embodiment also includes using the whale optimization algorithm to update the candidate network consequent weights of the confidence-gated interval type II fuzzy neural network online. The specific steps are as follows:

[0173] (a) Initialize the whale population: Generate The weight vectors of each candidate network consequent in the confidence-gated interval type II fuzzy neural network are mapped to the position vectors of each individual whale.

[0174] The expression for mapping the successor weight vectors of each candidate network in the confidence-gated interval type-II fuzzy neural network to the position vectors of each individual whale is as follows:

[0175] (29)

[0176] in, For the first The position vectors of individual whales at the initial moment; For the initial time, the first The set of candidate network consequent weight vectors corresponding to each individual whale is expressed as follows:

[0177] (30)

[0178] in, and These are the preset lower and upper bounds of the network consequent weight vector, which together determine the allowable range of the weights. ; To and Consistent dimensions, elements distributed in random vectors, This indicates element-wise multiplication.

[0179] (b) Fitness evaluation: Calculate the fitness of each individual whale and select the whale with the minimum fitness as the current best individual globally. And based on the effective reliability of the optimal whale individual matching Build whale location optimization update gain .

[0180] Specifically, the candidate network consequent weight vectors corresponding to each individual whale are loaded into the interval-gated type-II fuzzy neural network described in this invention. Under the same lumped uncertainty input, the corresponding set of lumped uncertainty estimates is calculated in batches, and the network approximation error of each whale is defined as:

[0181] (31)

[0182] in, For lumped uncertainty or its observable equivalent residual, For the first The estimated ensemble uncertainty for each individual whale. For the first The network approximation error corresponding to each individual whale.

[0183] The fitness of an individual whale is determined based on its network approximation error, expressed as follows:

[0184] (32)

[0185] in, The number of sampling points. For the first The fitness of an individual whale; the lower the fitness value, the better the fitness of the whale. The consequent weights corresponding to individual whales have a better uncertainty approximation effect.

[0186] In each iteration, the whale individual with the minimum fitness value is selected as the current best individual globally. :

[0187] (33)

[0188] Based on the optimal individual whale Effective reliability of matching Build whale location optimization update gain The expression is:

[0189] (34)

[0190] in, Based on search gain, This item is used to ensure credibility even in the current valid state. At lower levels, individual whales still retain some search capabilities; when the effective confidence level is low... When the value is higher, the update gain increases, and the network weights can move closer to the current optimal solution more quickly.

[0191] (c) Iterative update of individual whale positions: The position of individual whales in the whale population is iterated using position convergence update formula and position spiral update formula; after each round of individual position update, boundary constraints are applied to the weight vectors of each candidate network consequent. This invention adopts a simplified whale optimization structure, retaining only the two core mechanisms of position convergence update and spiral update.

[0192] The formula for updating the position convergence is:

[0193] (35)

[0194] in, For the first Individual whales The position vector at time , In order to be in The position vector of the globally optimal individual whale at any given time. For the first Individual whales The position vector at time , Update the step size based on the baseline; Formula (35) indicates that the current whale individual moves towards the current optimal individual, and the movement range is adjusted by the effective confidence level.

[0195] The formula for the position spiral update is:

[0196] (36)

[0197] in, The constant for the spiral shape. ; It is a random number. Formula (36) is used to simulate the spiral search process of a whale around the current optimal solution, so that the algorithm can maintain local convergence ability while having a certain search perturbation.

[0198] The formula for applying boundary constraints to the weight vectors of each candidate network successor is as follows:

[0199] (37)

[0200] in, This means projecting the candidate network consequent weights to the allowable weight range. This is to prevent excessively large weights in the network consequents from causing abnormal estimated outputs or to control input fluctuations.

[0201] (d) Convergence Judgment and Parameter Output: The whale individual position iteration continues until the preset maximum number of iterations is reached, or the change in the minimum fitness value meets the preset condition, at which point the whale individual position iteration update is terminated; the best individual in the whale population is selected. The candidate network consequent weights of the corresponding confidence-gated interval type-II fuzzy neural network are denoted as the optimal network consequent weights. The optimal network consequent weights are written back to the rule layer of the confidence-gated interval type II fuzzy neural network to complete the update, which is then used for the lumped uncertainty estimation at the next time step.

[0202] Specifically, the optimal consequent weights are written back to the consequent parameter positions corresponding to each fuzzy rule in the rule layer of the confidence-gated interval type-II fuzzy neural network, updating the original left-endpoint and right-endpoint consequent weights. The confidence-gated interval type-II fuzzy neural network constructed in this invention does not have a separate consequent layer; therefore, the consequent weights belong to the parameters associated with each fuzzy rule in the rule layer, rather than being a newly added confidence-gated layer. After the consequent weights are written back to the rule layer, the confidence-gated interval type-II fuzzy neural network forms the consequent output interval for each rule based on the updated consequent parameters. The type reduction layer then calculates the left and right endpoint outputs by combining the activation intensity of the rules after confidence gating. Finally, the output layer completes the fusion and obtains the lumped uncertainty estimate.

[0203] The optimal network consequent weights The expression is:

[0204] (38)

[0205] This invention proposes a weight update method for optimizing consequent weights in a confidence-gated interval type-II fuzzy neural network. Unlike conventional whale optimization algorithms that rely solely on a fitness function for global search, this invention updates the effective confidence obtained from the confidence-gated layer. By introducing the position update process of individual whales, the network weight update magnitude can be adaptively adjusted according to the current rule reasoning credibility state, thereby improving the stability and convergence efficiency of the parameter update process.

[0206] The network consequent weight update method proposed in this invention couples the network parameter optimization process with the current rule credibility state: when the rule credibility is high, the weight update tends towards local rapid convergence; when the rule credibility is low, the weight update maintains a relatively smooth search state, avoiding premature convergence to the unreliable parameter region. This method can improve the network's approximation accuracy for lumped uncertainties and enhance the stability of the control system in complex trajectory stages.

[0207] Step S300: Based on the lumped uncertainty estimate, design the tracking controller for the space robot's manipulator system. Specifically, this includes:

[0208] Step S301: Construct the comprehensive error variable , specifically:

[0209] First, set the desired joint trajectory:

[0210] (39)

[0211] in, For the desired joint trajectory vector, For the expected angular position trajectory of the first joint, For the expected angular position trajectory of the second joint, The upper right corner symbol represents the expected angular position trajectory of the third joint. This indicates transpose.

[0212] Based on the desired joint trajectory, we define the joint tracking error and the derivative of the joint tracking error:

[0213] (40)

[0214] (41)

[0215] in, For joint tracking error, This is the derivative of the joint tracking error.

[0216] A comprehensive error variable is constructed based on joint tracking error and joint tracking derivative. :

[0217] (42)

[0218] in, The design matrix is ​​positive definite. Combined error variables. It also includes joint position error and velocity error, which are used to construct control laws and neural network inputs.

[0219] Step S302: Define the active suppression term for flexible modes :

[0220] (43)

[0221] in, and All are positive definite matrices, used to suppress the first-order principal mode vibration of the three flexible links.

[0222] Step S303: Construct virtual control acceleration :

[0223] (44)

[0224] in, It is a positive definite feedback gain matrix.

[0225] Step S304: Design the control law for the tracking controller:

[0226] (45)

[0227] in, For joint control torque, For the nominal inertia matrix Let be the nominal inertia matrix. For nominal flexible coupling terms; This represents the lumped uncertainty estimate output by the confidence-gated interval type-II fuzzy neural network. The robust gain matrix; It is a saturation function; These are boundary layer parameters; This is a combined error that includes joint position error and joint velocity error; For virtual control of acceleration.

[0228] In a control law, the nominal control term Neural network compensation term used to implement basic trajectory tracking Used for online approximation and offsetting of lumped uncertainty, robust saturation term Active suppression term for flexible modes used to suppress residual approximation error. Used to reduce residual vibration of flexible connecting rods.

[0229] To verify the beneficial effects of the method of the present invention, a simulation model of a three-joint floating base plane flexible spatial manipulator was established for numerical verification.

[0230] The simulation object consists of a floating base, three planar rotation joints, and three flexible connecting rods, with the lengths of the three connecting rods set as follows: , and The equivalent mass of the floating base is set to Each flexible link retains a first-order principal mode, and its modal natural frequencies are respectively set to... and The controller consists of a nominal control term, a confidence-gated interval type II fuzzy neural network compensation term, a robust saturation term, and a flexible modal active suppression term. The network consequent weights are updated using a whale optimization algorithm based on rule confidence weighting.

[0231] Figures 1 to 9 The main simulation results of the proposed control method are presented respectively, among which Figure 1 The trajectory tracking curves are the actual angular positions and desired angular positions of the three joints. Figure 2 The curves show the variation of tracking error of the three joints over time. Figure 3 The curves showing the comparison between the control inputs for each joint channel, the network-estimated lumped uncertainty, and the actual lumped uncertainty are presented. Figure 4 The first-order principal modal response curves of the three flexible connecting rods are shown. Figure 5 The curves show the changes in the planar position and attitude angle of the floating base. Figure 6 This is the curve showing the change in the reliability of rules in an interval-type II fuzzy neural network. Figure 7 Output the curves showing the change in the width ratio of the intervals at the left and right endpoints of the network. Figure 8 This is a curve showing the change in dynamic evidence fusion factors. Figure 9 The curve shows the optimal fitness change of the whale optimization algorithm based on rule credibility weighting.

[0232] Two ablation control experiments were set up, removing the confidence gating layer and the rule confidence weighted whale optimization algorithm, respectively. Figures 10 to 12 The results comparing the joint tracking error norm, flexible modal response norm, and lumped uncertainty estimation error norm of the three methods are presented. As can be seen from the figures, the method of this invention outperforms the two control methods in terms of tracking error, uncertainty estimation error, and flexible vibration suppression.

[0233] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0234] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A tracking control method for a flexible spatial robotic arm based on a confidence-gated interval type-II fuzzy neural network, characterized in that, include: S1: Establish a dynamic model of the flexible space robot manipulator system considering lumped uncertainties; lumped uncertainties include model uncertainties and external disturbances; S2: The lumped uncertainty in the dynamic model is approximated online using a confidence-gated interval type II fuzzy neural network to obtain the estimated value of the lumped uncertainty; S3: Design a tracking controller for a space robot manipulator system based on lumped uncertainty estimates.

2. The method according to claim 1, characterized in that, The dynamic model of the flexible space robot manipulator system is as follows: ； In the formula, This is the joint angular acceleration vector; For nominal dynamics; Input matrix for nominal value; For joint control torque; To aggregate uncertainty, Let be the system state vector. For time variables, In the formula, This represents the uncertainty caused by inertial parameter perturbation. This represents the error in the nonlinear velocity term. This represents the flexible modal coupling error and the flexible modal truncation error. This indicates the floating base coupling error. This represents external disturbances and remaining unmodeled dynamics.

3. The method according to claim 2, characterized in that, The confidence-gated interval type II fuzzy neural network includes: a first layer: input layer; a second layer: membership function layer; a third layer: rule layer; a fourth layer: confidence-gated layer; a fifth layer: type reduction layer; and a sixth layer: output layer.

4. The method according to claim 3, characterized in that, The working process of the credibility gating layer is as follows: For each fuzzy rule, construct the rule confidence coefficient: No. The rule credibility coefficient of a fuzzy rule ,in, For the Sigmoid function, and These are the weighting coefficients. For bias terms, For the first The compactness of the activation interval of a fuzzy rule. For the first Consistency of the consequent of a fuzzy rule. For the first Consistency of neighborhood evidence for the first fuzzy rule; the first Compactness of the activation interval of a fuzzy rule ,in, For the first The activation strength of a fuzzy rule. For the first The activation strength under a fuzzy rule, To prevent constants with a denominator of zero; the first Consistency of the consequent of a fuzzy rule ,in, and The first The left and right endpoints of the output of the fuzzy rule consequent; the first Neighborhood evidence consistency of fuzzy rules ,in, For the first The consequent center of a fuzzy rule For the first The mean of the consequent center of a fuzzy rule. For the first The set of local rules corresponding to each fuzzy rule. This is the neighborhood consistency adjustment coefficient; The set of local rules , including with the The neighborhood fuzzy rules associated with the first fuzzy rule, and the fuzzy rules associated with the second fuzzy rule. A fuzzy rule is a fuzzy rule that activates correlation; For each fuzzy rule, the original activation intensity is gating-corrected using the rule credibility coefficient of the fuzzy rule to obtain the corrected activation intensity, which includes the corrected upper activation intensity and the corrected lower activation intensity; The modified activation strength of the fuzzy rule , No. The modified activation strength of the fuzzy rule .

5. The method according to claim 4, characterized in that, The first The consequent center of a fuzzy rule The first The mean of the consequent of a fuzzy rule ,in, For a set of local rules The number of fuzzy rules in the middle; This is the fuzzy rule index variable used for summation.

6. The method according to claim 5, characterized in that, The working process of the type reduction layer is as follows: using the corrected activation intensity, the left and right endpoint outputs of the confidence-gated interval type II fuzzy neural network are determined; the left endpoint output... and right endpoint output The expressions are as follows: , .

7. The method according to claim 6, characterized in that, The working process of the output layer is as follows: For each fuzzy rule, the activation weights of the fuzzy rule are constructed using the modified activation strength: No. Activation weights of fuzzy rules ,in, For the fuzzy rule index variable used for summation; Based on the activation weights and rule credibility coefficients of each fuzzy rule, a global weighted credibility is constructed. ; Based on global weighted credibility and output range width ratio Effectiveness and reliability of constructing fuzzy rules : ,in, This is the interval width penalty coefficient; Based on effective credibility Constructing a non-saturated dynamic fusion factor ; ,in, This is the fusion sensitivity coefficient. The confidence center value, For fusion bias term; Utilizing dynamic fusion factors Adjusting the output of the confidence-gated interval type II fuzzy neural network , ,in, This serves as the input to a confidence-gated interval type-II fuzzy neural network. and These are the left and right endpoint outputs of the confidence-gated interval type II fuzzy neural network, respectively.

8. The method according to claim 7, characterized in that, The candidate network consequent weights of the confidence-gated interval type II fuzzy neural network are updated online using the whale optimization algorithm, including the following steps: 1) Initialize the whale population: Generate The weight vectors of each candidate network consequent in the confidence-gated interval type II fuzzy neural network are mapped to the position vectors of each individual whale. 2) Fitness evaluation: Calculate the fitness value for each individual whale and select the whale with the lowest fitness value as the current best individual globally. And based on the effective reliability of the optimal whale individual matching Build whale location optimization update gain , ,in, Based on search gain; 3) Iterative update of individual whale positions: The position of individual whales in the whale population is iterated through position convergence update formula and position spiral update formula; after each round of individual position update, the weight vector of each candidate network consequent is subject to boundary constraints. The formula for updating positions is: ,in, For the first Individual whales The position vector at time , In order to be in The position vector of the globally optimal individual whale at any given time. For the first Individual whales Position vector at time, Update the step size based on the baseline; The formula for position spiral update is: ,in, The constant for the spiral shape. It is a random number; 4) Convergence Determination and Parameter Output: The whale individual position iteration continues until the preset maximum number of iterations is reached, or the change in the minimum fitness value meets the preset condition, at which point the whale individual position iteration update terminates; the best individual in the whale population is selected. The candidate network consequent weights of the corresponding confidence-gated interval type-II fuzzy neural network are denoted as the optimal network consequent weights. The optimal network consequent weights are written back to the rule layer of the confidence-gated interval type II fuzzy neural network to complete the update.

9. The method according to claim 8, characterized in that, The control law of the tracking controller is: ， in, For joint control torque, For the nominal inertia matrix Let be the nominal inertia matrix. For nominal flexible coupling terms; This represents the lumped uncertainty estimate output by the confidence-gated interval type-II fuzzy neural network. The robust gain matrix; It is a saturation function; These are boundary layer parameters; This is a combined error that includes joint position error and joint velocity error; For virtual control of acceleration.

10. The method according to claim 9, characterized in that, The virtual control acceleration The expression is: ， in, Let be the desired joint angle acceleration vector. It is a positive definite matrix. Joint tracking error The derivative of The active suppression term for flexible modes is expressed as follows: ， in, and All are positive definite matrices. For flexible modal coordinate vectors, This is the velocity vector for the flexible mode.

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