Textile machine arm adaptive impedance control method based on interaction optimization

Abstract

The application belongs to the technical field of industrial robot control, and particularly discloses a textile mechanical arm adaptive impedance control method based on interactive optimization. The method designs a textile mechanical arm adaptive impedance controller based on interactive optimization; and the specific process is as follows: for the dynamic interaction relationship between the mechanical arm and the unknown contact surface, a Stackelberg game is used to build an interactive optimization mechanism for the contact process, the force-position tracking error is optimized, and the force constraint condition is relaxed, so that the dynamic update of the impedance parameters is realized; then the force tracking problem is converted into a position tracking problem; and then an adaptive law is designed according to the command filter backstepping method. The application makes the mechanical arm system have smaller trajectory tracking error and more accurate constant force tracking effect, has good control effect, solves the force fluctuation problem of the yarn sliding on the curved surface edge, and is suitable for the scene with high requirements for force and position tracking of the textile industrial production robot.

Description

Technical Field

[0001] This invention belongs to the field of industrial robot control technology, specifically relating to an adaptive impedance control method for a textile robotic arm based on interactive optimization. Background Technology

[0002] As the world's largest textile producer, my country's textile industry plays a vital role in the national economy. With the development of intelligent manufacturing, the automation upgrade of textile equipment has become a key breakthrough for industrial transformation. The textile industry is also transforming from traditional clothing to "industrial textiles," particularly in fields such as aerospace, automotive lightweighting, and wind turbine blades, where textile composite materials, due to their lightweight and high-strength properties, have become crucial materials. For example, in manufacturing three-dimensional textile preforms, yarns or narrow-ribbed fabrics need to be wound around a mandrel (such as T-tubes or aero-engine blades) at specific angles. During the winding process, the yarn tension must be kept constant; excessive tension will break the fibers, while insufficient tension will cause the winding to loosen. However, automated mechanical winding faces challenges due to the complex surface of the mandrel and the difficulty in achieving constant force interaction between the robotic arm and the flexible textile material.

[0003] In contact tasks of robotic arms, existing technologies generally employ impedance control methods, adjusting inertia, damping, and stiffness parameters to regulate the dynamic relationship between force and position of the end effector. This method avoids the direct decomposition of position control and force control and has been widely used in industrial robotic arms, significantly improving the execution efficiency of complex contact tasks. Building upon this, adaptive variable impedance control technology, by adjusting impedance parameters online based on force tracking error, can effectively compensate for unknown environmental conditions and dynamic force requirements, achieving relatively accurate force tracking. However, existing adaptive variable impedance control still has the following shortcomings: at the moment of initial contact between the robotic arm and the contact surface, the relatively high speed can easily generate excessively large peak contact force. This impact force may cause damage to the robotic arm body or the contact surface, and existing impedance control and adaptive variable impedance control methods lack effective limiting mechanisms for this. When the stiffness, position, and other parameters of the contact surface are unknown, most existing studies only focus on force tracking accuracy, failing to systematically incorporate constraints on the contact force amplitude into the control framework, making it difficult to guarantee safe operation on complex and unknown surfaces. There is an inherent contradiction between tracking performance (such as trajectory tracking accuracy and force tracking accuracy) and the limitation of peak contact force. Existing methods typically focus on a single metric, lacking a design framework capable of dynamically optimizing between the two. Furthermore, during the contact process between a textile robotic arm and an unknown contact surface, the arm's state affects the change in contact force, which in turn influences the arm's behavior, demonstrating a clear bidirectional coupling relationship. Traditional control methods mostly treat the contact surface as a passive object, lacking a unified consideration of the dynamic interaction characteristics between the robotic arm and the contact surface, making it difficult to achieve coordinated optimization between tracking performance and safety constraints under complex contact tasks.

[0004] In summary, existing robotic arm impedance control technology still has significant shortcomings in dealing with unknown surfaces, suppressing initial impact forces, and optimization. Summary of the Invention

[0005] The purpose of this invention is to propose an adaptive impedance control method for textile robotic arms based on interactive optimization, so as to achieve precise force-position tracking control of the constrained robotic arm system.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: The adaptive impedance control method for textile robotic arms based on interactive optimization includes the following steps: Step 1. Establish the dynamic model of the robotic arm; Step 2. Based on the robotic arm dynamics model established in Step 1, design an adaptive impedance controller for the textile robotic arm based on interaction optimization. The specific process is as follows: To address the dynamic interaction between the robotic arm and the unknown contact surface, a Stackelberg game is used to construct an interactive optimization mechanism oriented towards the contact process, which optimizes the force-position tracking error and relaxes the force constraint conditions to achieve dynamic updating of impedance parameters. Then the force tracking problem is transformed into a position tracking problem; Then, an adaptive law is designed based on the instruction filtering backstepping method and the barrier Lyapunov function; Step 3. Using the interactive optimization-based adaptive impedance controller for the textile robotic arm designed in Step 2, precise force-position tracking control of the robotic arm is achieved.

[0007] Furthermore, based on the aforementioned adaptive impedance control method for textile robotic arms based on interactive optimization, this invention also proposes a corresponding adaptive impedance control system for textile robotic arms based on interactive optimization, which adopts the following technical solution: The interactive optimization-based adaptive impedance control system for textile robotic arms includes the following modules: The model building module is used to build the dynamic model of the robotic arm; The controller design module is used to design an adaptive impedance controller for a textile robotic arm based on interaction optimization. The specific process is as follows: To address the dynamic interaction between the robotic arm and the unknown contact surface, a Stackelberg game is used to construct an interactive optimization mechanism oriented towards the contact process. This mechanism optimizes the force-position tracking error and relaxes the force constraints to achieve dynamic updates of the impedance parameters. Then the force tracking problem is transformed into a position tracking problem; Then, an adaptive law is designed based on the instruction filtering backstepping method and the barrier Lyapunov function; The trajectory tracking module is used to achieve precise force-position tracking control of the robotic arm by utilizing an interactively optimized adaptive impedance controller based on the design of the module.

[0008] Furthermore, based on the aforementioned adaptive impedance control method for textile robotic arms based on interaction optimization, this invention also proposes a computer device comprising a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it implements the steps of the aforementioned adaptive impedance control method for textile robotic arms based on interaction optimization.

[0009] Furthermore, based on the aforementioned adaptive impedance control method for textile robotic arms based on interactive optimization, this invention also proposes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of the aforementioned adaptive impedance control method for textile robotic arms based on interactive optimization.

[0010] The present invention has the following advantages: As described above, this invention discloses an adaptive impedance control method for textile robotic arms based on interactive optimization. This method models the interaction process between the end effector of the robotic arm and the unknown contact surface through Stackelberg game modeling, realizing dynamic updating of impedance parameters and achieving an optimal balance between force tracking accuracy and trajectory tracking accuracy. This avoids the problem of force / position control conflict in traditional methods. This invention relaxes the force constraint conditions using a game optimization framework, enabling the active suppression of excessive contact force peaks in the initial contact stage, protecting the robotic arm body and contact surface from damage. Simultaneously, this invention transforms the force tracking problem into a position tracking problem using an impedance model. Furthermore, this invention designs an adaptive law based on the instruction filtering backstepping method and the obstacle Lyapunov function, which can strictly ensure that each state variable (such as position, velocity, etc.) does not exceed the preset safety range during trajectory tracking, making it particularly suitable for precision winding operations of textile robotic arms on complex mandrel surfaces (such as T-tubes, blades, etc.). This invention constructs an auxiliary system to compensate for saturation errors generated when the control input exceeds the actuator limit in real time, preventing control performance degradation due to torque or velocity saturation and improving the robustness of the system under high load or high-speed conditions. In summary, compared with existing methods, the robotic arm system controlled by the method of this invention has smaller trajectory tracking errors and a smoother force tracking process, which can meet the constant force control requirements for yarn tension during the winding process of three-dimensional textile preforms (avoiding yarn breakage due to excessive tension or loosening due to insufficient tension). Furthermore, through online adjustment and game optimization of adaptive impedance parameters, this invention can automatically adapt to the surface of mandrels of different shapes and materials without prior knowledge of parameters such as the stiffness and position of the contact surface, thus improving the versatility and intelligence level of the textile robotic arm. Attached Figure Description

[0011] Figure 1 This is a flowchart of the adaptive impedance control method for textile robotic arms based on interaction optimization in an embodiment of the present invention; Figure 2 This is a schematic diagram of the robotic arm system in an embodiment of the present invention; Figure 3 The constant force tracking trajectory curves are obtained by using the control method of this invention and by using the adaptive variable impedance control method. Figure 4 The input curve of the system using the control method of the present invention; Figure 5 To obtain a robotic arm using the control method of this invention Position trajectory tracking curve in the axial direction; Figure 6 To obtain a robotic arm using the control method of this invention Position trajectory tracking curve in the axial direction; Figure 7 To obtain a robotic arm using the control method of this invention shaft and Position tracking error in the axial direction; Figure 8 To obtain a robotic arm using the control method of this invention shaft and Velocity tracking error in the axial direction; Figure 9 To obtain a robotic arm using the control method of this invention shaft and Position compensation error in the axial direction; Figure 10 To obtain a robotic arm using the control method of this invention shaft and Speed ​​compensation error in the axial direction; Figure 11 To obtain constant force tracking trajectory curves using the control method of this invention and the adaptive variable impedance control method under different stiffnesses; Figure 12 The system input curves obtained by using the control method of this invention under different stiffnesses; Figure 13 To obtain a robotic arm using the control method of this invention under different stiffness conditions Position trajectory tracking curve in the axial direction;

[0012] Figure 14 To obtain a robotic arm using the control method of this invention under different stiffness conditions Position trajectory tracking curve in the axial direction; Figure 15 To obtain a robotic arm using the control method of this invention under different stiffness conditions shaft and Position tracking error in the axial direction; Figure 16 To obtain a robotic arm using the control method of this invention under different stiffness conditions shaft and Velocity tracking error in the axial direction; Figure 17 To obtain a robotic arm using the control method of this invention under different stiffness conditions shaft and Position compensation error in the axial direction; Figure 18 To obtain a robotic arm using the control method of this invention under different stiffness conditions shaft and Speed ​​compensation error in the axial direction. Detailed Implementation

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 For constrained robotic arm systems with model uncertainties, this embodiment 1 proposes an adaptive impedance control method for textile robotic arms based on interactive optimization. This method utilizes impedance control and game theory to achieve tracking control of the desired trajectory and constant force of the robotic arm system.

[0014] like Figure 1 As shown, the adaptive impedance control method for textile robotic arms based on interactive optimization includes the following steps: Step 1. Establish the dynamic model of the robotic arm, that is, establish a nonlinear system.

[0015] Figure 2 This demonstrates a rigid robotic arm with 2 degrees of freedom, where X is the horizontal axis and Z is the vertical axis. This indicates the joint angle of joint 1. This indicates the joint angle of joint 2. It is the length of link 1. It is the length of link 2; It is the distance from the center of mass of link 1 to its joint axis. It is the distance from the center of mass of link 2 to its joint axis.

[0016] The dynamic model of the m-link robotic arm is established as follows: (1) in denoted as a symmetric positive definite inertia matrix; n represents the dimension of the robotic arm's end effector in Cartesian space, with a value that is a positive integer; m=2.

[0017] For unknown nonlinear terms, denoted as the Coriolis force and centrifugal force matrices in the Cartesian coordinate system.

[0018] For an unknown nonlinear term, represents the gravity vector in Cartesian space.

[0019] , These represent the position, velocity, and acceleration of the robotic arm's end effector in Cartesian space, respectively. , and , The relationship between them is , ; in These are the joint angles, angular velocities, and angular accelerations of the m-link robotic arm, respectively. It is a Jacobian matrix.

[0020] ; in It is the base joint angle. It's the elbow joint angle. .

[0021] express The saturation function, Represents the control input vector. , for Elements in; This represents the contact force vector of the robotic arm's end effector in Cartesian space.

[0022] make , ;in for The elements in for The elements in.

[0023] The dynamic model of the robotic arm is then expressed as: (2) in , ; for The elements in for The elements in.

[0024] Saturation function The expression is as follows: (3) in and These are the upper and lower bounds of the saturation function, respectively.

[0025] Using the smooth hyperbolic tangent function to approximate the saturation function, we have: Established;

[0026] in ; This represents the smooth hyperbolic tangent function, used for approximation. , ; Indicates the approximation error. ; ; Where |·| represents taking the absolute value, This indicates taking the maximum value.

[0027] Step 2. Based on the robotic arm dynamics model established in Step 1, design an adaptive impedance controller for the textile robotic arm based on interaction optimization. The specific process is as follows: To address the dynamic interaction between the robotic arm and the unknown contact surface, a Stackelberg game is employed to construct an interactive optimization mechanism oriented towards the contact process. This mechanism optimizes the force-position tracking error and relaxes the force constraints to achieve dynamic updates of the impedance parameters. Then, based on the interaction model between the robotic arm system and the unknown contact surface, an adaptive law is designed to estimate the stiffness and position of the unknown contact surface, transforming the force tracking problem into a position tracking problem. Furthermore, an adaptive law is designed based on the command filtering backstepping method and the obstacle Lyapunov function to ensure accurate trajectory tracking while keeping the system state within safe boundaries. An auxiliary system is also constructed to overcome the input saturation effect.

[0028] The interaction between the robotic arm and the unknown contact surface exhibits a hierarchical structure: the robotic arm actively plans its motion trajectory and impedance parameters, while the surface generates corresponding reaction forces. This invention precisely describes this asymmetric structure using Stackelberg game theory.

[0029] The aforementioned interactive optimization mechanism refers to constructing a hierarchical decision-making mechanism for the information interaction and dynamic response process between the robotic arm and the unknown contact surface, and using Stackelberg game theory to optimize the solution of the interactive process.

[0030] Because the robotic arm actively adjusts its trajectory and impedance parameters, while the unknown contact surface generates corresponding force feedback based on the contact state, the two form a hierarchical interactive structure with sequential decision-making characteristics. Therefore, to address the dynamic interactive relationship between the robotic arm and the unknown contact surface, a Stackelberg game-based interactive optimization mechanism for the contact process is constructed. The specific process is as follows: In each interaction between the robotic arm's end effector and the unknown contact surface, the robotic arm first selects a set of optimal impedance parameters based on its current estimation of the unknown contact surface parameters, and the unknown contact surface makes a deterministic response. The goal of this game is to optimize the robotic arm's impedance parameters step by step by estimating the unknown contact surface parameters online, while ensuring contact stability and safety, and finally reach a game equilibrium. Under this equilibrium, the robotic arm makes the optimal impedance parameters for its estimated unknown contact surface parameters.

[0031] The impedance model is established as follows: (4) in , and These are the desired mass coefficient, damping coefficient, and stiffness coefficient, respectively. Indicates the reference trajectory. For the desired force, The contact force represents the interaction force between the end effector of the robotic arm and an unknown contact surface, and this force can be measured by a force sensor. , , , .

[0032] Since the Cartesian coordinate variables are independent of each other, this embodiment uses a one-dimensional case as an example for simplification.

[0033] An unknown contact surface can be modeled as a linear structure. If the unknown contact surface is modeled as a linear spring model, then the contact force... Represented as: (5) in , Indicates the stiffness of the contact surface. Indicates the location of the contact surface.

[0034] Substituting equation (5) into the impedance model, i.e., equation (4), and letting... Reference trajectory Under steady-state conditions, it satisfies Then we get: (6) When required force When it is a constant, .

[0035] Applying the final value theorem to the Laplace transform of formula (6) yields the steady-state force error. The calculation formula is as follows: (7) To ensure that the steady-state force error converges to 0, equation (7) satisfies: .

[0036] By incorporating trajectory tracking error, force tracking error, and maximum contact force limit into the cost function of optimizing the robotic arm's impedance parameters, the cost function becomes... Represented as: (8) in It is a given parameter used to balance tracking error and force safety limits; , To find the norm, Indicates the maximum contact force; It is a column vector composed of impedance parameters. ], , Indicates impedance parameters; A column vector consisting of estimates of the stiffness and position of the unknown contact surfaces; , express The estimated value, express The estimated value.

[0037] By minimizing the cost function It will tend towards a better value. This achieves a balance between tracking performance and security. The expression is as follows: (9) in Represents the independent variable that makes the function reach its minimum value. express The set that constitutes the composition.

[0038] According to the chain rule, the cost function has the following relationship: The gradient calculation formula is: (10) in It is the learning rate matrix. , and It is a positive definite constant. {} represents a diagonal matrix; Representing the cost function For impedance parameters The first-order partial derivative vector is the gradient; .

[0039] because This update may cause system instability, so only update... and , , , express .

[0040] This invention addresses the dynamic interaction between a robotic arm and an unknown contact surface by constructing an interaction optimization mechanism oriented towards the contact process. This mechanism can dynamically adjust the control strategy based on the contact state, thereby achieving coordinated optimization of tracking performance and safety constraints.

[0041] The specific process of transforming the force tracking problem into a position tracking problem is as follows: Define the reference trajectory estimate as: ; in for The estimated value, for The estimated value.

[0042] The estimated contact force value is: ; in for The estimated value, for The estimated value, .

[0043] At this time, the estimated contact force value Compared with actual value The error between them is: ; Choosing Lyapunov functions for: .

[0044] in , and It is a positive number.

[0045] time derivative for: .

[0046] Subsequently, the design and An adaptive law is used to ensure that the estimated value converges to the true value, and its expression is: ; .

[0047] Based on the error between the current contact force and the desired force, we obtain: ; in This indicates the position correction amount of the end effector of the robotic arm. ; This indicates the error in the contact force estimation; at this point, the desired trajectory... for: .

[0048] Position correction amount when the robotic arm moves in free space =0, that is .

[0049] The specific process of designing an adaptive law based on the instruction filtering backstepping method and the barrier Lyapunov function is as follows: Define the instruction filter as follows: ; in and All are output signals of the command filter. Indicates the input signal. , Indicates the parameters of the instruction filter.

[0050] If the input signal The following condition must be met: for any time variable t ≥ 0, , , and It is a positive integer, and initial value , initial value Then for any > 0, exists ∈(0,1] and > 0, making ,and , Both are bounded.

[0051] Error variables , , and The definition is as follows: ; in It is the expected trajectory. The control input signal is a virtual control law. The output signal of the time command filter.

[0052] , ; for The elements in for The elements in.

[0053] , ; for The elements in for The elements in.

[0054] , ; for The elements in for The elements in.

[0055] , This is an error compensation signal used to eliminate filtering errors; , ; for The elements in for The elements in.

[0056] definition As an auxiliary system, ; in for The elements in.

[0057] Define compact set , , , for: ; ; ; ; in , , , All are positive numbers, representing state variables. , , , The upper bound (absolute value limit).

[0058] For ease of representation, , , Simplified to , , .

[0059] but and The derivative is expressed as: (11) (12) in This represents the gain matrix.

[0060] The design support system is as follows: .

[0061] Fuzzy logic systems are used to approximate unknown nonlinear functions. Let... To be compact For a continuous function on a given surface, there exists a weight vector. , making .

[0062] in For the input vector, ; To approximate the error, and , Indicates the approximation error The upper realm, ; for The elements in.

[0063] Let N be the weight vector. N>1 indicates the number of network nodes.

[0064] Represents a basis function vector. , for The elements in It is a Gaussian function.

[0065] definition Unknown nonlinear term Approximated as ;in ,and Then the following inequalities hold: ; in express The ideal value, ; supremum indicates supremum; ; for The elements in for Elements in; This represents an n-dimensional column vector whose elements are all 1s. It represents the Hadamardi (or Hadama) stack.

[0066] Design virtual control law Control input vector Compensation signal and and adaptive laws as follows: ; ; ; = ; = ; in , Here is the gain matrix. , ;in , For positive integers, {} represents a diagonal matrix; for The estimated value, .

[0067] and It is an n-dimensional column vector. , ; in for The elements in for The elements in.

[0068] , ; in , It is a positive number. for The estimated value, Right now .

[0069] Lyapunov function for selection barrier for: ; right Taking the derivative and combining it with formulas (11)-(12), we get: ; in Indicates the estimation error. .

[0070] After completing the design of the adaptive impedance controller for the textile robotic arm based on interactive optimization, a stability analysis was performed on the textile robotic arm system controlled by the adaptive impedance controller based on interactive optimization. The specific process of the stability analysis is as follows: To verify system stability, Lyapunov functions are defined. for: ; The time derivative is shown below: ; because: (13) (14) (15) in This represents a positive constant in the design.

[0071] Substitute formulas (13)-(15) into have to: (16) in ; , , They represent 2 respectively , , The minimum value.

[0072] .

[0073] Formula (16) shows Bounded: All signals in a closed-loop system remain bounded.

[0074] Step 3. Using the interactive optimization-based adaptive impedance controller for the textile robotic arm designed in Step 2, precise force-position tracking control of the robotic arm is achieved.

[0075] To verify the effectiveness of the method proposed in this invention, the following experiments were conducted.

[0076] The following parameters were selected for simulation of the robotic arm control system: Select the physical parameters of the robotic arm: kg, kg, m, m, m, m, kg⋅m 2 , kg⋅m 2 ; in, This indicates the mass of link 1. This indicates the mass of link 2. This represents the moment of inertia of link 1. This represents the moment of inertia of link 2.

[0077] Select the initial state of the robotic arm and .

[0078] Initial value of error compensation signal The simulation time is 10 seconds.

[0079] Define the actual position of the unknown surface stiffness .

[0080] Select the desired quality coefficient The initial value of the damping coefficient The initial value of the stiffness coefficient .

[0081] Learning rate for contact surface parameter estimation , .

[0082] Learning rate of gradient , .

[0083] The maximum limit value of force is , , .

[0084] Command filter parameters , .

[0085] and The initial value is set to 0.

[0086] Setting: Upper bound of position compensation error Lower bound of position compensation error Upper bound of speed compensation error Lower bound of speed compensation error .

[0087] The selected design parameters are: , , , , , , ;in , , .

[0088] Figure 3 The figure shows the constant force tracking trajectory curves using the control method of this invention and the adaptive variable impedance control method. It can be seen from the figure that the control method of this invention can achieve force tracking in a shorter time, and its maximum force value is 85N, which is significantly lower than the maximum force value of 150N exhibited by the adaptive variable impedance control method.

[0089] Figure 4 The system obtained by using the control method of the present invention is in shaft and Axis control input , The curve and in shaft and Saturation control input of axis , The curve shows that even under input saturation conditions, the robotic arm can still achieve fast and accurate force tracking and position tracking.

[0090] Figure 5 To obtain a robotic arm using the control method of this invention Position trajectory tracking curve in the axial direction. Figure 6 To obtain a robotic arm using the control method of this invention Position trajectory tracking curve in the axial direction. Figure 7 To obtain a robotic arm using the control method of this invention Position tracking error in the axial direction and Position tracking error in the axial direction . Figure 8 To obtain a robotic arm using the control method of this invention Axial velocity tracking error and Axial velocity tracking error . Figure 9 To obtain a robotic arm using the control method of this invention Axial position compensation error and Axial position compensation error . Figure 10 To obtain a robotic arm using the control method of this invention Axial velocity compensation error and Axial velocity compensation error .

[0091] To further verify the advantages of the control method of the present invention when the robotic arm contacts surfaces with different stiffnesses, this embodiment sets the stiffness of the contact surface to 800, while keeping other parameters unchanged.

[0092] Figure 11 The constant force tracking trajectory curves of the control method of the present invention and the adaptive variable impedance control method under different stiffness are shown in the figure. It can be seen from the figure that the control method of the present invention achieves force tracking in a shorter time, and its maximum force value is 83N, which is significantly lower than the 240N achieved by the adaptive variable impedance control method. Figure 12 To obtain a system using the control method of this invention under different stiffnesses... shaft and Axis control input , The curve and in shaft and Saturation control input of axis , The curve. Figure 13 To obtain a robotic arm using the control method of this invention under different stiffness conditions Position trajectory tracking curve in the axial direction. Figure 14 To obtain a robotic arm using the control method of this invention under different stiffness conditions Position trajectory tracking curve in the axial direction. Figure 15 To obtain a robotic arm using the control method of this invention under different stiffness conditions Position tracking error in the axial direction and Position tracking error in the axial direction . Figure 16 To obtain a robotic arm using the control method of this invention under different stiffness conditions Axial velocity tracking error and Axial velocity tracking error . Figure 17 To obtain a robotic arm using the control method of this invention under different stiffness conditions Axial position compensation error and Axial position compensation error . Figure 18 To obtain a robotic arm using the control method of this invention under different stiffness conditions Axial velocity compensation error and Axial velocity compensation error .

[0093] For constrained robotic arms, this invention effectively tracks command trajectories and maintains constant force, with rapid convergence. Simulation results show that the method achieves the expected goals of improving control performance and reducing computational complexity under uncertain model conditions. This invention addresses the strong nonlinear dynamics, input saturation, state constraints, and force constraints inherent in robotic arm systems, as well as the force / position hybrid control problem during task execution. The designed adaptive impedance controller for textile robotic arms, based on interactive optimization, effectively solves the force-position hybrid control problem during operation and achieves compliance.

[0094] Example 2 This embodiment 2 describes an adaptive impedance control system for a textile robotic arm based on interactive optimization. This system is based on the same inventive concept as the adaptive impedance control method for a textile robotic arm based on interactive optimization in embodiment 1 above.

[0095] The interactive optimization-based adaptive impedance control system for textile robotic arms includes the following modules: The model building module is used to build the dynamic model of the robotic arm; The controller design module is used to design an adaptive impedance controller for a textile robotic arm based on interaction optimization. The specific process is as follows: To address the dynamic interaction between the robotic arm and the unknown contact surface, a Stackelberg game is used to construct an interactive optimization mechanism oriented towards the contact process. This mechanism optimizes the force-position tracking error and relaxes the force constraints to achieve dynamic updates of the impedance parameters. Then the force tracking problem is transformed into a position tracking problem; Then, an adaptive law is designed based on the instruction filtering backstepping method and the barrier Lyapunov function; The trajectory tracking module is used to achieve precise force-position tracking control of the robotic arm by utilizing an interactively optimized adaptive impedance controller.

[0096] It should be noted that any content not mentioned in the above-described functional modules of the system described in Embodiment 2 can be referred to the step description of the corresponding method in Embodiment 1 above, and will not be repeated in detail here.

[0097] Example 3 This embodiment 3 describes a computer device including a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it implements the steps of the interactive optimization-based adaptive impedance control method for textile robotic arms described in embodiment 1 above.

[0098] Example 4 This embodiment 4 describes a computer-readable storage medium storing a program that, when executed by a processor, is used to implement the steps of the interactive optimization-based adaptive impedance control method for textile robotic arms in embodiment 1 above.

[0099] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. An adaptive impedance control method for a textile robotic arm based on interactive optimization, characterized in that, Includes the following steps: Step 1. Establish the dynamic model of the robotic arm; Step 2. Based on the robotic arm dynamics model established in Step 1, design an adaptive impedance controller for the textile robotic arm based on interaction optimization. The specific process is as follows: To address the dynamic interaction between the robotic arm and the unknown contact surface, a Stackelberg game is used to construct an interactive optimization mechanism oriented towards the contact process. This mechanism optimizes the force-position tracking error and relaxes the force constraints to achieve dynamic updates of the impedance parameters. Then the force tracking problem is transformed into a position tracking problem; Then, an adaptive law is designed based on the instruction filtering backstepping method and the barrier Lyapunov function; Step 3. Using the interactive optimization-based adaptive impedance controller for the textile robotic arm designed in Step 2, precise force-position tracking control of the robotic arm is achieved.

2. The adaptive impedance control method for textile robotic arms based on interactive optimization according to claim 1, characterized in that, Step 1 specifically involves: The dynamic model of the m-link robotic arm is established as follows: (1) in Represents a symmetric positive definite inertial matrix. It is the dimension of the robotic arm's end effector in Cartesian space; For unknown nonlinear terms, denoted as the Coriolis force and centrifugal force matrices in the Cartesian coordinate system; For an unknown nonlinear term, represents the gravity vector in Cartesian space; , These represent the position, velocity, and acceleration of the robotic arm's end effector in Cartesian space. ， ； in It is a Jacobian matrix. These are the joint angles, angular velocities, and angular accelerations of the m-link robotic arm, respectively. express The saturation function, Represents the control input vector. ,in for Elements in; This represents the contact force vector of the robotic arm's end effector in Cartesian space; make , ; in for The elements in for Elements in; The dynamic model of the robotic arm is then expressed as: (2) ， ； in for The elements in for Elements in; Saturation function The expression is as follows: (3) in and These are the upper and lower bounds of the saturation function, respectively; Using the smooth hyperbolic tangent function to approximate the saturation function, we have: Established; in ; Represents the smooth hyperbolic tangent function. ; Indicates the approximation error. ; ； Where |·| represents taking the absolute value, This indicates taking the maximum value.

3. The adaptive impedance control method for textile robotic arms based on interactive optimization according to claim 2, characterized in that, In step 2, the specific process of constructing an interaction optimization mechanism oriented towards the contact process using Stackelberg game theory is as follows: The impedance model is established as follows: (4) in , and These are the desired mass coefficient, damping coefficient, and stiffness coefficient, respectively. Indicates the reference trajectory. For the desired force, The contact force represents the interaction force between the end effector of the robotic arm and an unknown contact surface. ， 、 ， ； If the unknown contact surface is modeled as a linear spring, then the contact force... Represented as: (5) in , Indicates the stiffness of the contact surface. Indicate the position of the contact surface; substitute formula (5) into the impedance model, i.e., formula (4), and let Reference trajectory Under steady-state conditions, it satisfies Then we get: (6) when When it is a constant, ; Applying the final value theorem to the Laplace transform of formula (6) yields the steady-state force error. The calculation formula is as follows: (7) To ensure that the steady-state force error converges to 0, equation (7) satisfies: ; By incorporating trajectory tracking error, force tracking error, and maximum contact force limit into the cost function of optimizing the robotic arm's impedance parameters, the cost function is obtained. Represented as: (8) in It is a given parameter used to balance tracking error and force safety limits; , To find the norm, Indicates the maximum contact force; It is a column vector composed of impedance parameters. ], , Indicates impedance parameters; A column vector consisting of estimates of the stiffness and position of the unknown contact surfaces; , express The estimated value, express The estimated value; By minimizing the cost function It will tend towards a better value. Its expression is as follows: (9) in Represents the independent variable that makes the function reach its minimum value. express The set that constitutes; According to the chain rule, the cost function has the following relationship: The gradient calculation formula is: (10) in It is the learning rate matrix. , and It is a positive definite constant. {} represents a diagonal matrix; Representing the cost function right The first-order partial derivative vector is the gradient.

4. The adaptive impedance control method for textile robotic arms based on interactive optimization according to claim 3, characterized in that, In step 2, the specific process of transforming the force tracking problem into a position tracking problem is as follows: Define the reference trajectory estimate as: ； in for The estimated value; the estimated value of the contact force is: ； in for The estimated value, At this point, the estimated contact force value Compared with actual value The error between them is: ； Choosing Lyapunov functions for: ； in , and It is a positive number; time derivative for: ； Subsequently, the design and The adaptive law is: ； ； Based on the error between the current contact force and the desired force, we obtain: ； in This indicates the position correction amount of the end effector of the robotic arm. ; This indicates the error in the contact force estimation; at this point, the desired trajectory... for: ； Position correction amount when the robotic arm moves in free space =0, that is ; At this point, the expectation force tracking problem is transformed into a trajectory tracking problem.

5. The adaptive impedance control method for textile robotic arms based on interactive optimization according to claim 4, characterized in that, In step 2, the specific process of designing the adaptive law based on the instruction filtering backstepping method and the barrier Lyapunov function is as follows: Define the instruction filter as follows: ； in and The output signal of the instruction filter. Indicates the input signal. , Indicates the parameters of the instruction filter; Error variables , , and The definition is as follows: ； in It is the expected trajectory. The control input signal is a virtual control law. The output signal of the time command filter; ， ； in for The elements in for Elements in; ， ； in for The elements in for Elements in; ， ； in for The elements in for Elements in; , For error compensation signal, , ; in for The elements in for Elements in; definition As an auxiliary system, ; in for Elements in; Define compact set , , , for: ; ; ; ; in , , , All are positive numbers, representing state variables. , , , The upper bound; For ease of representation, , , Simplified to , , ; but and The derivative is expressed as: (11) (12) in Represent the gain matrix; design the auxiliary system as follows: ； Fuzzy logic systems are used to approximate unknown nonlinear functions, and are defined as follows: To be compact For a continuous function on a given surface, there exists a weight vector. , making ; in For the input vector, ; To approximate the error, and , Indicates the approximation error The upper realm, ; for Elements in; Let N be the weight vector. N>1 indicates the number of network nodes; Represents a basis function vector. , for The elements in It is a Gaussian function; definition Unknown nonlinear term Approximated as ; ,and Then the following inequalities hold: ； in express The ideal value, ; supremum indicates supremum. ; for The elements in for Elements in; Represents an n-dimensional column vector whose elements are all 1; It represents the Hadamardi (or Hadama) stack; Design virtual control law Control input vector Compensation signal and and adaptive law as follows: ； ； ； = ； = ； in , Here is the gain matrix. , ;in , For positive integers, {} represents a diagonal matrix; for The estimated value, ; and It is an n-dimensional column vector; ， ； in for The elements in for Elements in; ， ； in , It is a positive number. for The estimated value, Right now ; Lyapunov function for selection barrier for: ； right Taking the derivative and combining it with formulas (11)-(12), we get: ； in Indicates the estimation error. .

6. The adaptive impedance control method for textile robotic arms based on interactive optimization according to claim 5, characterized in that, In step 2, after completing the design of the adaptive impedance controller for the textile robotic arm based on interactive optimization, a stability analysis is performed on the textile robotic arm system controlled by the adaptive impedance controller based on interactive optimization.

7. The adaptive impedance control method for textile robotic arms based on interactive optimization according to claim 6, characterized in that, The specific process of stability analysis is as follows: Define Lyapunov functions for: ； The time derivative is shown below: ； because: (13) (14) (15) in Represent positive constants; substitute formulas (13)-(15) into... have to: (16) in ; , , They represent 2 respectively , , The minimum value; ; Formula (16) shows Bounded: All signals in a closed-loop system remain bounded.

8. An adaptive impedance control system for a textile robotic arm based on interactive optimization, characterized in that, Includes the following modules: The model building module is used to build the dynamic model of the robotic arm; The controller design module is used to design an adaptive impedance controller for a textile robotic arm based on interaction optimization. The specific process is as follows: To address the dynamic interaction between the robotic arm and the unknown contact surface, a Stackelberg game is used to construct an interactive optimization mechanism oriented towards the contact process. This mechanism optimizes the force-position tracking error and relaxes the force constraints to achieve dynamic updates of the impedance parameters. Then the force tracking problem is transformed into a position tracking problem; Then, an adaptive law is designed based on the instruction filtering backstepping method and the barrier Lyapunov function; The trajectory tracking module is used to achieve precise force-position tracking control of the robotic arm by utilizing an interactively optimized adaptive impedance controller.

9. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements the steps of the adaptive impedance control method for textile robotic arms based on interactive optimization as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the interactive optimization-based adaptive impedance control method for textile robotic arms as described in any one of claims 1 to 7.

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