Robotic joint adaptive control method and system with input saturation constraints

Abstract

The present application relates to the field of automation, in particular to a kind of input saturation constraint containing robot joint adaptive control method and system.This method is based on Newton-Euler method, consider friction, gap and time-varying stiffness and other nonlinear factors and input saturation constraint, establish the dynamics equation of two-mass of micro drive system.Based on the dynamics equation, disturbance observer is designed to estimate the non-matching disturbance existing in the system, and a state observer considering input saturation is designed according to the state space equation and disturbance estimate value to observe all state variables of the system.A neural network adaptive backstepping control algorithm considering input saturation is designed according to the state observation value and disturbance estimate value.Meanwhile, according to Lyapunov stability theory, it is determined whether the system is semi-global uniformly stable, and the control performance of IT2-FCMAS-DSCABM control algorithm is verified by Matlab software.

Description

Technical Field

[0001] This invention relates to the field of automation technology, and specifically to a robot joint adaptive control method and system with input saturation constraints. Background Technology

[0002] With the advent of the intelligent era, micro-drive systems have been widely used in many fields such as smart homes, service robots, and intelligent healthcare. Previously, proportional-integral-derivative control (PID control) was widely used in micro-drive systems due to its advantages of fewer control parameters, simple structure, and ease of engineering. When the requirements for tracking accuracy and response speed in micro-drive systems were not high, PID control could meet the performance requirements of micro-drive systems by improving the manufacturing process and assembly precision. However, with the increasing demands for control performance such as accuracy and response speed, and the significantly higher difficulty and cost of further improving the manufacturing and assembly precision of micro-drive systems, PID control can no longer meet the high-precision, high-reliability, and high-response speed control requirements of micro-drive systems.

[0003] Gear transmission devices exhibit nonlinear characteristics such as friction, dead zone, and time-varying stiffness during operation. These characteristics significantly impact the control accuracy, stability, and dynamic characteristics of micro-drive systems. The flexibility of gear transmissions causes gear deformation during rotation and load changes, leading to torque fluctuations at the load end and affecting the normal operation of the micro-drive system. Gear transmissions often incorporate backlash for lubrication to prevent gear jamming, but this can cause meshing impacts, affecting system stability. At low speeds, nonlinear friction affects the system's dynamic characteristics and stability, potentially causing limit cycle oscillations. Micro-drive systems frequently employ current protection mechanisms, which are related to the system's input torque and inevitably lead to input saturation constraints. Input saturation prevents the control signal from reaching the desired value, resulting in increased overshoot, slower response speed, and degraded dynamic characteristics.

[0004] Previous studies have primarily addressed constraints such as friction, dead zone, and variable stiffness. However, for micro-transmission systems that simultaneously involve multiple constraints including friction, dead zone, and variable stiffness, and also experience input saturation, achieving high-precision control requires further improvements to the control algorithm, and may even necessitate hybrid control by incorporating input saturation compensation methods.

[0005] Therefore, it is essential to provide a novel adaptive control method and system for robot joints with input saturation constraints. Summary of the Invention

[0006] The purpose of this invention is to provide a robot joint adaptive control method and system with input saturation constraints to solve the above-mentioned technical problems.

[0007] This invention provides a robot joint adaptive control method with input saturation constraints, comprising the following steps: S1, Establish the dynamic equations of the small drive system based on nonlinear factors: S11, Establish the dynamic equation of the micro-drive system, expressed as formula (1): ;in, It is the input angle. It is the input torque. It is the equivalent moment of inertia of the input shaft. It is the nonlinear frictional torque of the input shaft. It is the transmission torque. It is the equivalent moment of inertia of the output shaft. It outputs the corner. Nonlinear frictional torque of the output shaft The torque is the system load torque, and r is the transmission ratio; express The second derivative, express The second derivative; S12, establish the state-space equation in formula (1), expressed as formula (2): ,in, , , , ; for The first derivative of represents the output rotational speed; for The first derivative of represents the input rotational speed; S13, Establishment based on tooth flank clearance α and friction force The nonlinear constraint condition of meshing stiffness k; S2, Establish the observer, including: S21, establish a recursive IT2-FCMAC neural network, wherein the input space vector of the recursive IT2-FCMAC neural network is... for The output is expressed as formula (14): ,in, Let i represent the input variable of the i-th dimension; Represents an n-dimensional space; Y is the output of the neural network. The weight matrix, This is the column vector of the actual mapping of the recursive IT2-FCMAC neural network; S22, a recursive IT2-FCMAC neural network is used to approximate a pre-defined unknown smooth function. and The optimal approximation result is and define and );in, Represents a function; Represented as ; Represented as ; Represented as ; Represented as ; This represents the neural network estimation error caused by the state estimation error. Indicates the approximation error of the neural network It is the optimal estimate. Represents weight Optimal estimate, Represents weight Optimal estimate, Represents weight Estimated value Represents weight Estimated value; and The column vector representing the actual mapping; It is a bounded constant; S231, Introducing auxiliary variables Establish a disturbance observer, which is expressed as formula (21): The estimation error of the disturbance observer , represented as ; express The estimated value, express Estimates; auxiliary variables , and Represented as formula (19): , and Indicates the design parameters of the disturbance observer; It is a state variable The estimated value; express The estimated values ​​of the state variables, express The estimated values ​​of the state variables, Represents state variables Variables; Represents state variables Variables; auxiliary variables The error estimate is , represented as ; S232, Formula (2) of the system state-space equation is reconstructed into Formula (16): ; in, , ; ; , ; express , This represents the smooth approximation error of the transmitted torque. This represents the smooth approximation error of nonlinear friction. This represents the smooth approximation error of nonlinear friction. , and Let v represent a bounded positive constant, and v represent the ideal control variable of the system. Indicates system control variables. ; S233, using observed state variables to replace actual state variables, a state observer is established to observe the state of the robot joints. The expression of the state observer is formula (17): The state observation error equation of the state observer is expressed as formula (18): ;in, Represents state variables State observations; For coefficients; ; The estimation error of the state observer, ; For weight estimation error, ; The state space output error is... ; This is an estimate of y; It is a 3-order identity matrix; S3. Based on the state observer and disturbance observer, the Lyapunov function is selected to verify the stability of the state observer error and the disturbance estimation error; based on the disturbance estimate and the state observation, the ideal control quantity v and the system control quantity are calculated. The iterative update is performed, and the values ​​of the state observation equation and the disturbance observation equation are calculated using formula (17) and formula (21). Then, the process returns to step S2 and iterative calculation is performed again.

[0008] Preferably, step S13 includes: S131, the dead zone model constraint is established based on the tooth flank clearance α, expressed as formula (3): k is the meshing stiffness of the gear; It is a dead zone discontinuous model, expressed as formula (4): ,in, ; S132, the periodic variation constraint of the stiffness coefficient k is expressed as formula (5): , It refers to the degree of overlap; It is the meshing period; z is the number of teeth; It is the gear rotation angle; and These are the meshing stiffnesses for the single-meshing and double-meshing zones, respectively. Step S133, establish LuGre friction model constraints, expressed as formula (6): ; in, This represents the maximum static friction. Coulomb friction; This represents the amount of deformation of the bristles; For switching speed; , and These are the elastic coefficient, damping coefficient, and viscosity coefficient of the sliding surface of the bristles, respectively. It is the gear angular velocity.

[0009] Preferably, step S21 further includes: Step S211, Establish concept mapping: Divide the variables of the input vector into k neurons using Gaussian membership functions, and establish a set. Each neuron is represented by formula (7): And each neuron is combined with IT2-FL, and the expression is reformulated as Equation (8): ; Represents an i-dimensional input variable. , It is the mean. It has a lower limit and upper limit The uncertain variance; S212, Establish the actual mapping: Calculate the ignition intensity of the kth fuzzy rule, expressed as formula (9): , and Let represent the lower membership function and the upper membership function respectively. The actual mapped column vector is represented by formula (10): ; S213, Establish weight mapping, using the following pre-specified interval type 2 fuzzy logic inference rules to establish the connection between each layer of AP and the weight memory W, including: rule ,exist yes , yes ,… ,and yes When, there is formula (11). in, This represents the result component of the k-th rule that follows the j-th output; and Each refers to The lower and upper boundaries. Where, index term j satisfies... ; By integrating fuzzy rules, the defuzzification process can be expressed as formula (12): ; The weight matrix is ​​expressed as formula (13): ;in, .

[0010] Preferably, in step S22, for non-differentiable terms... , and Each of these can be approximated as a differentiable term and a bounded error, respectively, as expressed in formula (15): ; Considering input saturation, make Where D is a bounded positive constant; These are known parameters; ,in, This represents the amplitude constant of the voltage limiting.

[0011] Preferably, the auxiliary variable Differential , expressed as formula (20): ; (i=1,2).

[0012] Preferably, step S3 includes: S30, Establish an error stability evaluation model , expressed as formula (22): The coordinate transformation equation of formula (16) and the model of the dynamic surface controller are expressed as formula (24): ; (i=1,2,3,4) are error variables. It is a virtual control variable. It is a time parameter; 0 indicates the filtered output; 0 indicates the output compensated for input saturation. Represents the ideal trajectory; P is a positive definite symmetric matrix; S31 employs an improved BLF function, introduces dynamic surface filtering error compensation, and establishes an error stability estimation model. , expressed as formula (25): The virtual control quantity is obtained by differentiating formula (25). and adaptive rate ;in, It is a state item We are about to enter the preset constraint space boundary. This indicates the actual position of the system at time t; These are design parameters; definitions , and The initial value is bounded and is a compact set. , It is an unknown positive number; S32, Select the preset Lyapunov function and establish the error stability estimation model. , expressed as formula (30): The virtual control quantity is obtained by differentiating formula (30). and adaptive rate ;in, , and These are design parameters, defined. ; , representing the 2-norm of the weight estimate; , representing the 2-norm of the ideal weights; S33, Select the preset Lyapunov function and establish an error stability estimation model. , expressed as formula (37): The virtual control quantity is obtained by differentiating formula (37). and adaptive rate ;in, These are design parameters; S34, to mitigate the impact of input saturation, an auxiliary function is introduced. , expressed as formula (42): Select a preset Lyapunov function to establish an error stability estimation model. , expressed as formula (43): The virtual control quantity is obtained by differentiating formula (43). and adaptive rate ; These are design parameters; S35, the constructor, is represented by formula (48). ; S36, Differentiate formula (48) and solve the inequality differential equation to determine... exist Is the interior semi-globally consistent and eventually bounded? S37, when globally consistent and eventually bounded, based on the virtual control quantity and adaptive rate The ideal control quantity v and the system control quantity are obtained from the model of the dynamic surface controller. The iterative update is applied to formula (16) to calculate the state-space equation. If the value is zero, return to step S2 and perform iterative calculation again.

[0013] Preferably, step S36 includes: S360, the derivative of formula (22) is obtained Simplify by combining equations (16), (18), (19) and (20) Formula (23) is obtained: To avoid repeatedly obtaining virtual control quantities The derivative is obtained by using a dynamic surface control method. Find the approximate differential and apply its output to the control law; Q is a positive definite symmetric matrix. S361, combined with formula (24) Differentiation yields , expressed as formula (26): ,in, , and It is a guiding factor Design parameters, ; The virtual control quantity α1 is expressed as formula (27): Adaptive rate Expressed as formula (28): , , , and These are design parameters; Substituting formulas (27) and (28) into formula (26), we obtain formula (29): ; S362, combined with formula (24) Differentiation yields , expressed as formula (31): ; The virtual control quantity α2 is expressed as formula (32): Adaptive rate Expressed as formula (33): Among them, formula (34): , formula (35): , , , , and These are design parameters; Substituting formulas (32) to (35) into formula (31), we obtain formula (36): ; S363, combined with formula (24) Differentiation yields , expressed as formula (38): ; The virtual control quantity α3 is expressed as formula (39): Adaptive rate Expressed as formula (40): ; Substituting formulas (39) and (40) into formula (38), we obtain formula (41): ;in, and These are design parameters; S364, combined with formula (24) Differentiation yields , expressed as formula (44): ; The ideal control quantity v is expressed by formula (45): ; Adaptive rate Represented as formula (46): , and These are design parameters; Substituting formulas (45) and (46) into formula (44), we obtain formula (47): .

[0014] Preferably, step S36 further includes: S365, according to formulas (23), (29), (36), (41) and (47), for By performing inequality operations on the terms in the equation, we obtain formula (49): , ; ; ; ; These are design parameters. ; By designing appropriate parameters , , , , , , , , and , making , , , , , , , , To ensure the stability of the closed-loop system; Solving equation (49) yields equation (50): ;in, It is a bounded constant; It is a Lyapunov function; based on the definition of semi-globally consistent eventually bounded and equation (50), determine exist Whether the internal semi-global consistency is eventually bounded.

[0015] Preferably, in step S365, based on the definition of semi-globally consistent final boundedness and equation (50), it is determined that... exist The innermost part is semi-globally consistent and eventually bounded, where hour, , , , and It is bounded; all closed-loop signals are bounded.

[0016] The present invention also provides a robot joint adaptive control system with input saturation constraints, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the robot joint adaptive control method with input saturation constraints as described in any of the preceding claims.

[0017] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the adaptive control method for robot joints with input saturation constraints as described in any of the preceding claims.

[0018] This invention provides a robot joint adaptive control method and system with input saturation constraints. Based on the Newton-Euler method, it considers nonlinear factors such as friction, backlash, and time-varying stiffness, as well as input saturation constraints, to establish a two-mass dynamic equation for a micro-drive system. It defines state variables for angle and angular velocity, constructing the state-space equation for the micro-drive system. A disturbance observer is designed to estimate mismatched disturbances in the system. Based on the state-space equation and the disturbance estimate, a state observer considering input saturation is designed to observe all system state variables. A neural network adaptive backstepping control algorithm considering input saturation is designed. Combining an improved barrier Lyapunov function, a controller is designed using the backstepping method, and an auxiliary function is introduced in the last step of the backstepping method to compensate for system input saturation. Simultaneously, a dynamic surface control method is used to approximate the differentiation of the virtual control quantity, and dynamic surface wave error compensation is introduced to reduce the approximate differentiation error. Based on Lyapunov stability theory, it is determined whether the system is semi-globally uniformly stable. The control performance of the control algorithm is verified using Matlab software.

[0019] Taking a micro transmission system containing nonlinear factors such as friction, backlash, time-varying stiffness, and input saturation constraints as the research object, and considering the influence of the above nonlinear factors on the system's tracking accuracy and response speed, a neural network adaptive backstepping control algorithm is designed by combining dynamic surface filtering error compensation algorithm and input saturation compensation algorithm. The above nonlinear factors will lead to a decrease in the system's tracking accuracy and response speed.

[0020] An adaptive weight algorithm was designed using the Lyapunov method and integrated into the IT2-FCMAC neural network to form a recursive IT2-FCMAC neural network. The recursive IT2-FCMAC neural network was then used to estimate the unknown functions in the system, thereby constructing the control input and the observer, which improved the system robustness.

[0021] Input saturation compensation is used to eliminate the impact of input saturation on system performance. Dynamic surface control is employed to obtain the approximate derivative of the virtual control quantity, and dynamic surface filtering error compensation is introduced to improve the tracking accuracy of the system. An improved barrier Lyapunov function is used to ensure that the trajectory at the system output remains within a predetermined range and is unaffected by the initial state of the system. Attached Figure Description

[0022] The accompanying drawings, as part of this invention, are provided to further illustrate the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation thereof. Clearly, the drawings described below are merely some embodiments, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0023] Figure 1This is a dynamic model diagram of a micro-transmission system for a robot joint in one embodiment of the present invention.

[0024] Figure 2 This is a schematic diagram of a recursive IT2-FCMAC neural network in one embodiment of the present invention.

[0025] Figure 3 This is a flowchart illustrating the controller design of a robot joint adaptive control method with input saturation constraints according to an embodiment of the present invention.

[0026] Figure 4 This is a simulation model of a robot joint adaptive control system with input saturation constraints in one embodiment of the present invention.

[0027] Figure 5 This is a schematic diagram of the hardware structure of a system implementing a robot joint adaptive control method with input saturation constraints, according to an embodiment of the present invention.

[0028] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0029] The technical problems solved by the embodiments of the present invention, the technical solutions adopted, and the technical effects achieved will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other equivalent or obvious variations of embodiments obtained by those skilled in the art without creative effort fall within the protection scope of the present invention. The embodiments of the present invention can be embodied in various different ways as defined and covered by the claims.

[0030] It should be noted that many specific details are provided in the following description for ease of understanding. However, it is obvious that the implementation of the present invention may not require these specific details. It should also be noted that, unless explicitly limited or conflicting, the various embodiments and technical features of the present invention can be combined with each other to form a technical solution.

[0031] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0032] The invention will now be described in further detail with reference to the accompanying drawings.

[0033] Please combine them together Figures 1 to 4 The present invention provides a robot joint adaptive control method with input saturation constraints, comprising steps S1-S3.

[0034] S1. Establish the dynamic equations of the micro-drive system based on nonlinear factors. Specifically, the micro-drive system mainly includes a motor, gear transmission system, controller, and sensors. Due to constraints such as tooth backlash, friction, and meshing stiffness in the gear transmission system, the drive system exhibits strong nonlinear characteristics. Considering these constraints, the dynamic equations of the micro-drive system are established.

[0035] S11, Establish the dynamic equation of the micro-drive system, expressed as formula (1): ;in, It is the input angle. It is the input torque. It is the equivalent moment of inertia of the input shaft. It is the nonlinear frictional torque of the input shaft. It is the transmission torque. It is the equivalent moment of inertia of the output shaft. It outputs the corner. Nonlinear frictional torque of the output shaft The torque is the system load torque, and r is the transmission ratio; express The second derivative, express The second derivative; S12, establish the state-space equation in formula (1), expressed as formula (2): ,in, , , , ; for The first derivative of represents the output rotational speed; for The first derivative of represents the input rotational speed; S13, Establishment based on tooth flank clearance α and friction force The nonlinear constraint condition of meshing stiffness k.

[0036] Specifically, the nonlinear factor constraint conditions in step S13 include the following constraints.

[0037] S131, the design of a gear transmission system must reserve a certain tooth flank clearance. This is to prevent the gear teeth from jamming after thermal expansion, and also to ensure that lubricating oil can enter the meshing tooth surface. In addition, since the gear contact position will change, the gear teeth will undergo nonlinear elastic deformation. The clearance and elastic deformation work together to cause transmission errors in both forward and reverse motion. Nonlinear factors such as clearance and elastic deformation can be described by a dead zone model. The dead zone model constraint is established based on the tooth flank clearance α, expressed as formula (3). k is the meshing stiffness of the gear; It is a dead zone discontinuous model, expressed as formula (4): ,in, .

[0038] S132, in gear transmission, there will be alternating meshing of single teeth and double teeth, causing the stiffness coefficient k to change periodically. The constraint on the periodic change of the stiffness coefficient k is expressed as formula (5): , It refers to the degree of overlap; It is the meshing period; z is the number of teeth; It is the gear rotation angle; and These are the meshing stiffnesses for the single-meshing and double-meshing zones, respectively. In step S133, friction is a significant disturbance in the gear transmission system. Considering the abrupt change from static friction to kinetic friction, a LuGre friction model constraint is established, expressed as formula (6): ; in, This represents the maximum static friction. Coulomb friction; This represents the amount of deformation of the bristles; For switching speed; , and These are the elastic coefficient, damping coefficient, and viscosity coefficient of the sliding surface of the bristles, respectively. It is the gear angular velocity.

[0039] Interval Type-2 Fuzzy Cerebellar Model Articulation Controller (IT2-FCMAC) has significant advantages in handling uncertain dynamic system control. As a feedforward network architecture, IT2-FCMAC exhibits good generalization ability, but its performance depends on pre-trained datasets. To address this issue, a weight adaptive algorithm based on the Lyapunov method is designed and integrated into the IT2-FCMAC neural network to construct a recursive IT2-FCMAC neural network. Then, an adaptive backstepping control algorithm integrating the IT2-FCMAC neural network and dynamic surface filtering error compensation (IT2-FCMAC-DSCABM) is proposed. Based on state observations and disturbance estimates, a neural network adaptive backstepping control algorithm considering input saturation is established.

[0040] S2, Establish the observer.

[0041] S21, establish a recursive IT2-FCMAC neural network, wherein the input space vector of the recursive IT2-FCMAC neural network is... for The output is expressed as formula (14): ,in, Let i represent the input variable of the i-th dimension; Represents an n-dimensional space; Y is the output of the neural network. The weight matrix, This is the column vector of the actual mapping of the recursive IT2-FCMAC neural network.

[0042] Specifically, The IT2-FCMAC neural network integrates Interval Type 2 Fuzzy Logic (IT2-FL) and Cerebellar Joint Controller (CMAC). Traditional IT2-FCMAC neural network architectures are feedforward networks, possessing good generalization capabilities, but requiring pre-training with a dataset. To address the training problem, a weight adaptive algorithm using the Lyapunov method is designed and integrated into the IT2-FCMAC neural network, forming a recursive IT2-FCMAC neural network. The principle is described in [link to documentation]. Figure 2 .

[0043] The meanings of each layer in the recursive IT2-FCMAC network are described below: (1) Input space x: The input vector is x= .

[0044] (2) Concept mapping ): Using Gaussian membership functions, each variable in the input space is subdivided into There are 10 neurons, which belong to the set And through associated memory These neurons are received. Each neuron has the following characteristics: Formula (7): In the formula, Represents an i-dimensional input variable. , It is the mean. It has a lower limit and upper limit The uncertainty variance; each neuron is combined with IT2-FL, and is re-expressed in the following form, Equation (8): ; (3) Actual mapping ( This mapping is used to calculate the ignition intensity of the kth fuzzy rule, formula (9): In the formula, and Let represent the lower membership function and the upper membership function respectively. The actual mapped column vector is given by formula (10): ; (4) Weight mapping ): Use the following pre-specified interval type 2 fuzzy logic inference rules to establish the connection between each layer of AP and the weight memory W; rules :if yes , yes ,… ,and yes Then we have formula (11): In the formula: This represents the result component of the k-th rule that follows the j-th output; and Each refers to The lower and upper boundaries. Where, index term j satisfies... Through the integration of fuzzy rules, its defuzzification process can be expressed as formula (12): ; The weight matrix is ​​given by formula (13): ;in, ; (5) Output calculation: The output of the recursive IT2-FCMAC neural network is given by formula (14): .

[0045] S22, a recursive IT2-FCMAC neural network is used to approximate a pre-defined unknown smooth function. and The optimal approximation result is and define and );in, Represents a function; Represented as ; Represented as ; Represented as ; Represented as ; This represents the neural network estimation error caused by the state estimation error. Indicates the approximation error of the neural network It is the optimal estimate. Represents weight Optimal estimate, Represents weight Optimal estimate, Represents weight Estimated value Represents weight Estimated value; and The column vector representing the actual mapping; It is a bounded constant; S231, Introducing auxiliary variables Establish a disturbance observer, which is expressed as formula (21): The estimation error of the disturbance observer , represented as ; express The estimated value, express Estimates; auxiliary variables , and Represented as formula (19): , and Indicates the design parameters of the disturbance observer; It is a state variable The estimated value; express The estimated values ​​of the state variables, express The estimated values ​​of the state variables, Represents state variables Variables; Represents state variables Variables; auxiliary variables The error estimate is , represented as ; S232, Formula (2) of the system state-space equation is reconstructed into Formula (16): ; in, , ; ; , ; express , This represents the smooth approximation error of the transmitted torque. This represents the smooth approximation error of nonlinear friction. This represents the smooth approximation error of nonlinear friction. , and Let v represent a bounded positive constant, and v represent the ideal control variable of the system. Indicates system control variables. ; S223, Using observed state variables to replace actual state variables, a state observer is established to observe the state of the robot joints. The expression of the state observer is formula (17): The state observation error equation of the state observer is expressed as formula (18): ;in, Represents state variables State observations; For coefficients; ; The estimation error of the state observer, ; For weight estimation error, ; The state space output error is... ; This is an estimate of y; It is a 3-order identity matrix.

[0046] Specifically, the control objective of this invention is to design a full-state feedback ideal control quantity v using the backstepping method and step-by-step recursion. The design process is as follows: Figure 3 As shown. Specifically, firstly, it must be ensured that all closed-loop signals are bounded; secondly, for any given sufficiently smooth reference trajectory... To make the system output asymptotic convergence to The neighborhood of . For non-differentiable terms , and It can be approximated as a differentiable term and a bounded error, respectively, as shown in the following formula (15): ; Using an IT2-FCMAC neural network to approximate an unknown smooth function and Optimal approximation result ,in It is the optimal estimate. It is the corresponding estimation error. Definition and Combined with the recursive IT2-FCMAC neural network estimation, the system state-space expression can be written in the following form, formula (16): .in, Represented as ; Represented as ; Represented as ; Represented as ; This represents the neural network estimation error caused by the state estimation error. This represents the approximation error of the neural network. This is the corresponding estimation error; It is the optimal estimate. Represents weight Optimal estimate, Represents weight Optimal estimate, Represents weight Estimated value Represents weight Estimated value; and The column vector representing the actual mapping; It is a bounded constant.

[0047] Considering the problem of input saturation, make Among them, D, , and All are bounded positive numbers; These are known parameters, representing the amplitude constant of the voltage limiting. In the backstepping design process, all state variables of the system are required, but some state variables in the system (16) are unmeasurable. Therefore, it is necessary to design a state observer to observe the unknown state variables, and then use the observed state variables to replace the actual state variables in the backstepping design.

[0048] The state observer expression is formula (17): The state observation error equation of the state observer is expressed as formula (18): ;in, Represents state variables State observations; For coefficients; ; The estimation error of the state observer, ; For weight estimation error, ; The state space output error is... ; This is an estimate of y; It is a 3-order identity matrix.

[0049] By choosing the appropriate To ensure that matrix A is a Herwitz matrix, there must exist a positive definite symmetric matrix. and , making For unmeasurable disturbances By introducing auxiliary variables Establish a disturbance observer.

[0050] Auxiliary variables , and Represented as formula (19): ; The auxiliary variable Differential , expressed as formula (20): ; ,(i=1,2); The disturbance observer is expressed as formula (21): The estimation error of the disturbance observer , represented as ; express The estimated value, express The estimated value; and Indicates the design parameters of the disturbance observer; It is a state variable The estimated value; express The estimated values ​​of the state variables, express The estimated values ​​of the state variables, Represents state variables Variables; Represents state variables Variables; auxiliary variables The error estimate is , represented as .

[0051] S3. Based on the state observer and disturbance observer, the Lyapunov function is selected to verify the stability of the state observer error and the disturbance estimation error; based on the disturbance estimate and the state observation, the ideal control quantity v and the system control quantity are calculated. The iterative update is performed, and the values ​​of the state observation equation and the disturbance observation equation are calculated using formula (17) and formula (21). Then, the process returns to step S2 and iterative calculation is performed again.

[0052] Specifically, the stability of the state observer error and perturbation estimation error is verified by selecting a preset Lyapunov function, including: S30, Establish an error stability evaluation model , expressed as formula (22): The coordinate transformation equation of formula (16) and the model of the dynamic surface controller are expressed as formula (24): ; (i=1,2,3,4) are error variables. It is a virtual control variable. It is a time parameter; 0 indicates the filtered output; 0 indicates the output compensated for input saturation. Represents the ideal trajectory; P is a positive definite symmetric matrix; S31 employs an improved BLF function, introduces dynamic surface filtering error compensation, and establishes an error stability estimation model. , expressed as formula (25): The virtual control quantity is obtained by differentiating formula (25). and adaptive rate ;in, It is a state item We are about to enter the preset constraint space boundary. This indicates the actual position of the system at time t; These are design parameters; definitions , and The initial value is bounded and is a compact set. , It is an unknown positive number; S32, Select the preset Lyapunov function and establish the error stability estimation model. , expressed as formula (30): The virtual control quantity is obtained by differentiating formula (30). and adaptive rate ;in, , and These are design parameters, defined. ; , representing the 2-norm of the weight estimate; , representing the 2-norm of the ideal weights; S33, Select the preset Lyapunov function and establish an error stability estimation model. , expressed as formula (37): The virtual control quantity is obtained by differentiating formula (37). and adaptive rate ;in, These are design parameters; S34, to mitigate the impact of input saturation, an auxiliary function is introduced. , expressed as formula (42): Select a preset Lyapunov function to establish an error stability estimation model. , expressed as formula (43): The virtual control quantity is obtained by differentiating formula (43). and adaptive rate ; These are design parameters; S35, the constructor, is represented by formula (48). ; S36, Differentiate formula (48) and solve the inequality differential equation to determine... exist Is the interior semi-globally consistent and eventually bounded? S37, when globally consistent and eventually bounded, based on the virtual control quantity and adaptive rate The ideal control quantity v and the system control quantity are obtained from the model of the dynamic surface controller. The iterative update is applied to formula (16) to calculate the state-space equation. If the value is zero, return to step S2 and perform iterative calculation again.

[0053] Preferably, step S36 includes: S360, the derivative of formula (22) is obtained Simplify by combining equations (16), (18), (19) and (20) Formula (23) is obtained: To avoid repeatedly obtaining virtual control quantities The derivative is obtained by using a dynamic surface control method. Find the approximate differential and apply its output to the control law; Q is a positive definite symmetric matrix. S361, combined with formula (24) Differentiation yields , expressed as formula (26): ,in, , and It is a guiding factor Design parameters, ; The virtual control quantity α1 is expressed as formula (27): Adaptive rate Expressed as formula (28): , , , and These are design parameters; Substituting formulas (27) and (28) into formula (26), we obtain formula (29): ; S362, combined with formula (24) Differentiation yields , expressed as formula (31): ; The virtual control quantity α2 is expressed as formula (32): Adaptive rate Expressed as formula (33): Among them, formula (34): , formula (35): , , , , and These are design parameters; Substituting formulas (32) to (35) into formula (31), we obtain formula (36): ; S363, combined with formula (24) Differentiation yields , expressed as formula (38): ; The virtual control quantity α3 is expressed as formula (39): Adaptive rate Expressed as formula (40): ; Substituting formulas (39) and (40) into formula (38), we obtain formula (41): ;in, and These are design parameters; S364, combined with formula (24) Differentiation yields , expressed as formula (44): ; The ideal control quantity v is expressed by formula (45): ; Adaptive rate Represented as formula (46): , and These are design parameters; Substituting formulas (45) and (46) into formula (44), we obtain formula (47): .

[0054] Step S36 further includes: S365, according to formulas (23), (29), (36), (41) and (47), for By performing inequality operations on the terms in the equation, we obtain formula (49): , ; ; ; ; These are design parameters. ; By designing appropriate parameters , , , , , , , , and , making , , , , , , , , To ensure the stability of the closed-loop system; Solving equation (49) yields equation (50): ;in, It is a bounded constant; It is a Lyapunov function; based on the definition of semi-globally consistent eventually bounded and equation (50), determine exist Whether the internal semi-global consistency is eventually bounded.

[0055] In a specific instance, define We select a suitable Lyapunov function to verify the stability of the observer error and the perturbation estimation error. The formula is shown in equation (22): ; Differentiate equation (22) and simplify by combining equations (16), (18), (19) and (20). The following expression formula (23) is obtained: .

[0056] To avoid repeatedly obtaining virtual control quantities The derivative is obtained by using a dynamic surface control method. The approximate differential is obtained and its output is applied to the control law. The coordinate transformation equation of equation (16) and the dynamic surface controller are as follows: (24) ; In the formula, It is an error variable. It is a virtual control variable. It is a time parameter.

[0057] Step 1: Since the micro-transmission system has requirements for output accuracy, it is necessary to constrain the system output state. To address this constraint, the following improved BLF function is adopted, which weakens its requirement for the initial state and expands its applicable range. In addition, to further improve the tracking accuracy, dynamic surface filtering error compensation is introduced. Specifically, it is shown in equation (25): ; In the formula, It is a state It is about to enter the preset constraint space boundary; These are design parameters. (Definition) To ensure system stability and adjustable tracking error, the following should be made: and , The initial value of is bounded and is compact.

[0058] therefore, , It is an unknown normal number. To obtain the virtual control and adaptive rate, equation (24) can be combined with... Taking the derivative, we get formula (26): ; In the formula, , and It is a guiding factor Design parameters, Therefore, the virtual control quantity α1 and the adaptive rate This can be expressed as formula (27): ; and formula (28): In the formula, , , and These are design parameters. Substituting equations (27) and (28) into equation (26), we obtain equation (29): .

[0059] Step 2: Select the following Lyapunov function, formula (30): In the formula, , and These are design parameters. (Definition) ; ; Combining equation (24), for The derivative is given by formula (31): ; The virtual control quantity and its corresponding adaptive rate in the second step can be designed as follows: Formula (32): ; and formula (33): Among them, formula (34) is included: , formula (35): ; In the formula, , , , and These are design parameters. Substituting equations (32) to (35) into equation (31), we obtain equation (36): .

[0060] Step 3: Select the following Lyapunov function, formula (38): In the formula, These are design parameters. Combined with equation (24), for... Differentiating yields formula (38): ; Its virtual control quantity and its corresponding adaptive rate are designed as follows: Formula (39): And formula (40): ; In the formula, and These are design parameters. Substituting equations (39) and (40) into equation (38), we obtain equation (41): .

[0061] Step 4: To mitigate the impact of input saturation, the following auxiliary function is introduced, formula (42): ; The selected Lyapunov function is as follows, formula (43): In equation (43), These are design parameters. Combined with equation (24) for... Differentiating, we get formula (44): ; The ideal control variable and its corresponding adaptive rate can be designed as follows: Formula (45): and formula (46): In the formula, and These are design parameters. Substituting equations (45) and (46) into equation (44), we obtain equation (47): .

[0062] The stability of the system is proven as follows: Construct the following Lyapunov function, formula (48): ; Based on the above adaptive rate, virtual control quantity, and ideal control quantity, for By performing inequality operations on some terms, we can obtain equation (49): ; In equation (49), ; ; ; ; These are design parameters. ; By designing appropriate parameters , , , , , , , , and , making , , , , , , , , To ensure the stability of the closed-loop system.

[0063] Solving the above inequality differential equation yields formula (50): .

[0064] Please combine the diagram with the definition of semi-globally consistent final boundedness and equation (50) to derive the following: exist The internal semi-global consistent eventually bounded, where .So , , , and It is bounded. Therefore, all closed-loop signals are bounded.

[0065] Please combine them together Figure 5The present invention also provides a robot joint adaptive control system with input saturation constraints. The robot joint adaptive control system with input saturation constraints is based on a computer system and operates thereon. Specifically, it includes a memory 61, a processor 62, and a computer program 63 stored in the memory 61 and executable on the processor 62. When the processor 62 executes the computer program 63, it implements the steps of the robot joint adaptive control method with input saturation constraints as described in any of the above claims.

[0066] This embodiment also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the robot joint adaptive control method with input saturation constraints as described in any of the preceding embodiments.

[0067] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0068] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0069] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0070] In the embodiments provided by this invention, it should be understood that the disclosed apparatus / terminal devices and methods can be implemented in other ways. For example, the apparatus / terminal device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0071] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0072] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0073] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0074] Therefore, the embodiments should be considered as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the application are intended to be included within the invention.

[0075] In the description of this specification, references to terms such as "one embodiment," "another embodiment," "other embodiments," or "first embodiment to Xth embodiment," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, method steps, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0076] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0077] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A robot joint adaptive control method with input saturation constraints, characterized in that, Including the following steps: S1, Establish the dynamic equations of the small drive system based on nonlinear factors: S11, Establish the dynamic equation of the micro-drive system, expressed as formula (1): ;in, It is the input angle. It is the input torque. It is the equivalent moment of inertia of the input shaft. It is the nonlinear frictional torque of the input shaft. It is the transmission torque. It is the equivalent moment of inertia of the output shaft. It outputs the corner. Nonlinear frictional torque of the output shaft It is the system load torque, and r is the transmission ratio; express The second derivative, express The second derivative; S12, establish the state-space equation in formula (1), expressed as formula (2): ,in, , , , ; for The first derivative of represents the output rotational speed; for The first derivative of represents the input rotational speed; S13, establish nonlinear constraint conditions based on tooth flank clearance, friction force and meshing stiffness; S2, Establish the observer, including: S21, establish a recursive IT2-FCMAC neural network, wherein the input space vector of the recursive IT2-FCMAC neural network is... for The output is expressed as formula (14): ,in, Let i represent the input variable of the i-th dimension; Represents an n-dimensional space; Y is the output of the neural network. The weight matrix, This is the column vector of the actual mapping of the recursive IT2-FCMAC neural network; S22, a recursive IT2-FCMAC neural network is used to approximate a pre-defined unknown smooth function. and The optimal approximation result is and define and ;in, Represents a function; Represented as ; Represented as ; Represented as ; Represented as ; This represents the neural network estimation error caused by the state estimation error. This represents the approximation error of the neural network; It is the optimal estimate. Represents weight Optimal estimate, Represents weight Optimal estimate, Represents weight Estimated value Represents weight Estimated value; and The column vector representing the actual mapping; It is a bounded constant; S231, Introducing auxiliary variables Establish a disturbance observer, which is expressed as formula (21): The estimation error of the disturbance observer , represented as ; express The estimated value, express Estimates; auxiliary variables , and Represented as formula (19): , and Indicates the design parameters of the disturbance observer; It is a state variable The estimated value; express The estimated values ​​of the state variables, express The estimated values ​​of the state variables, Represents state variables Variables; Represents state variables Variables; auxiliary variables The error estimate is , represented as ; S232, Formula (2) of the system state-space equation is reconstructed into Formula (16): ； in, , ; ; , ; express , This represents the smooth approximation error of the transmitted torque. This represents the smoothing approximation error of nonlinear friction. This represents the smooth approximation error of nonlinear friction. , and Both represent bounded positive constants, and v represents the ideal control variable of the system. Indicates system control variables. ; S233, using observed state variables to replace actual state variables, a state observer is established to observe the state of the robot joints. The expression of the state observer is formula (17): The state observation error equation of the state observer is expressed as formula (18): ;in, Represents state variables State observations; For coefficients; ; The estimation error of the state observer, ; For weight estimation error, ; The state space output error is... ; This is an estimate of y; It is a 3-order identity matrix; S3. Based on the state observer and disturbance observer, the Lyapunov function is selected to verify the stability of the state observer error and the disturbance estimation error; based on the disturbance estimate and the state observation, the ideal control quantity v and the system control quantity are calculated. The iterative update is performed, and the values ​​of the state observation equation and the disturbance observation equation are calculated using formula (17) and formula (21). Then, the process returns to step S2 and iterative calculation is performed again.

2. The adaptive control method for robot joints with input saturation constraints according to claim 1, characterized in that, Step S13 includes: S131, the dead zone model constraint is established based on the tooth flank clearance α, expressed as formula (3): k is the meshing stiffness of the gear; It is a dead zone discontinuous model, expressed as formula (4): ,in, ; S132, the periodic variation constraint of the stiffness coefficient k, is expressed as formula (5): , It refers to the degree of overlap; It is the meshing period; z is the number of teeth; It is the gear rotation angle; and These are the meshing stiffnesses for the single-meshing and double-meshing zones, respectively. Step S133, establish LuGre friction model constraints, expressed as formula (6): ; in, This represents the maximum static friction. Coulomb friction; This represents the amount of deformation of the bristles; For switching speed; , and These are the elastic coefficient, damping coefficient, and viscosity coefficient of the sliding surface of the bristles, respectively. It is the gear angular velocity.

3. The adaptive control method for robot joints with input saturation constraints according to claim 1, characterized in that, Step S21 further includes: Step S211, Establish concept mapping: Divide the variables of the input vector into k neurons using Gaussian membership functions, and establish a set. Each neuron is represented by formula (7): And each neuron is combined with IT2-FL, and the expression is reformulated as Equation (8): ; Represents an i-dimensional input variable. , It is the mean. It has a lower limit and upper limit The uncertain variance; S212, Establish the actual mapping: Calculate the ignition intensity of the kth fuzzy rule, expressed as formula (9): , and Let represent the lower membership function and the upper membership function respectively. The actual mapped column vector is represented by formula (10): ; S213, Establish weight mapping, using the following pre-specified interval type 2 fuzzy logic inference rules to establish the connection between each layer of AP and the weight memory W, including: rule ,exist yes , yes ,… ,and yes When, there is formula (11). in, This represents the result component of the k-th rule that follows the j-th output; and Each refers to The lower and upper boundaries; where index term j satisfies ; By integrating fuzzy rules, the defuzzification process can be expressed as formula (12): ; The weight matrix is ​​expressed as formula (13): ;in, .

4. The adaptive control method for robot joints with input saturation constraints according to claim 1, characterized in that, In step S22, for non-differentiable terms , and Each of these can be approximated as a differentiable term and a bounded error, respectively, as expressed in formula (15): ; Considering input saturation, make Where D is a bounded positive constant; These are known parameters; ,in, This represents the amplitude constant of the voltage limiting.

5. The robot joint adaptive control method with input saturation constraints according to claim 1, characterized in that, The auxiliary variable Differential , expressed as formula (20): ; (i=1,2).

6. The adaptive control method for robot joints with input saturation constraints according to claim 5, characterized in that, Step S3 includes: S30, Establish an error stability evaluation model , expressed as formula (22): The coordinate transformation equation of formula (16) and the model of the dynamic surface controller are expressed as formula (24): ; (i=1,2,3,4) are error variables. It is a virtual control variable. It is a time parameter; 0 indicates the filtered output; 0 indicates the output compensated for input saturation. Represents the ideal trajectory; P is a positive definite symmetric matrix; S31, using an improved BLF function, introduces dynamic surface filtering error compensation to establish an error stability estimation model. , expressed as formula (25): The virtual control quantity is obtained by differentiating formula (25). and adaptive rate ;in, It is a state item We are about to enter the preset constraint space boundary. Indicates the actual position of the system at time t; These are design parameters; definitions , and The initial value is bounded and is a compact set. , It is an unknown positive number; S32, Select the preset Lyapunov function and establish the error stability estimation model. , expressed as formula (30): The virtual control quantity is obtained by differentiating formula (30). and adaptive rate ;in, , and These are design parameters, defined. ; , representing the 2-norm of the weight estimate; , representing the 2-norm of the ideal weights; S33, Select the preset Lyapunov function and establish an error stability estimation model. , expressed as formula (37): The virtual control quantity is obtained by differentiating formula (37). and adaptive rate ;in, These are design parameters; S34, to mitigate the impact of input saturation, an auxiliary function is introduced. , expressed as formula (42): Select a preset Lyapunov function to establish an error stability estimation model. , expressed as formula (43): The virtual control quantity is obtained by differentiating formula (43). and adaptive rate ; These are design parameters; S35, the constructor, is represented by formula (48). ; S36, Differentiate formula (48) and solve the inequality differential equation to determine... exist Is the interior semi-globally consistent and eventually bounded? S37, when globally consistent and eventually bounded, based on the virtual control quantity and adaptive rate The ideal control quantity v and the system control quantity are obtained from the model of the dynamic surface controller. The iterative update is applied to formula (16) to calculate the state-space equation. If the value is zero, return to step S2 and perform iterative calculation again.

7. The adaptive control method for robot joints with input saturation constraints according to claim 6, characterized in that, Step S36 includes: S360, the derivative of formula (22) is obtained Simplify by combining equations (16), (18), (19) and (20) Formula (23) is obtained: To avoid repeatedly obtaining virtual control quantities The derivative is obtained by using a dynamic surface control method. Find the approximate differential and apply its output to the control law; Q is a positive definite symmetric matrix. S361, combined with formula (24) Differentiation yields , expressed as formula (26): ,in, , and It is a guiding factor Design parameters, ; The virtual control quantity α1 is expressed as formula (27): Adaptive rate Expressed as formula (28): , , , and These are design parameters; Substituting formulas (27) and (28) into formula (26), we obtain formula (29): ; S362, combined with formula (24) Differentiation yields , expressed as formula (31): ; The virtual control quantity α2 is expressed as formula (32): Adaptive rate Expressed as formula (33): Among them, formula (34): , formula (35): , , , , and These are design parameters; Substituting formulas (32) to (35) into formula (31), we obtain formula (36): ; S363, combined with formula (24) Differentiation yields , expressed as formula (38): ; The virtual control quantity α3 is expressed by formula (39): Adaptive rate Expressed as formula (40): ; Substituting formulas (39) and (40) into formula (38), we obtain formula (41): ;in, and These are design parameters; S364, combined with formula (24) Differentiation yields , expressed as formula (44): ; The ideal control quantity v is expressed by formula (45): ; Adaptive rate Represented as formula (46): , and These are design parameters; Substituting formulas (45) and (46) into formula (44), we obtain formula (47): .

8. The robot joint adaptive control method with input saturation constraints according to claim 7, characterized in that, Step S36 further includes: S365, according to formulas (23), (29), (36), (41) and (47), for By performing inequality operations on the terms in the equation, we obtain formula (49): , ; ; ; ; These are design parameters. ； By designing appropriate parameters , , , , , , , , and , making , , , , , , , , To ensure the stability of the closed-loop system; Solving equation (49) yields equation (50): ;in, It is a bounded constant; It is a Lyapunov function; based on the definition of semi-globally consistent eventually bounded and equation (50), determine exist Whether the internal semi-global consistency is eventually bounded.

9. The robot joint adaptive control method with input saturation constraints according to claim 8, characterized in that, In step S365, based on the definition of semi-globally consistent final boundedness and equation (50), it is determined that... exist The innermost part is semi-globally consistent and eventually bounded, where hour, , , , and It is bounded; all closed-loop signals are bounded.

10. A robot joint adaptive control system with input saturation constraints, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the robot joint adaptive control method with input saturation constraints as described in any one of claims 1-9.

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