Robot-assisted sewing feeding method based on normal pressure and cloth tension control

Abstract

The present application relates to the field of robot trajectory planning, and particularly relates to a robot-assisted sewing feeding method based on normal pressure and cloth tension control, which first establishes a position-based impedance control model, analyzes the influence of different impedance parameters on the response of the control system, and determines the impedance parameter adjustment range through the Routh stability criterion; then improves the objective function and adaptive inertia factor based on the improved particle swarm algorithm, so that the control system has optimal fitness index, and the optimal impedance parameter is obtained, and the normal pressure is tracked and controlled; finally, an adaptive impedance controller is designed by dynamically adjusting the expected damping parameter, the environmental disturbance is dynamically compensated, the stability of the adaptive controller is analyzed by using the Routh stability criterion, the value range of the adaptive update rate is determined, and the cloth tension is tracked and controlled. The present application can solve the problems of cloth sliding and edge wrinkling caused by the fluctuation of normal pressure and cloth tension in the process of robot-assisted sewing.

Description

Technical Field

[0001] This invention relates to the field of robot trajectory planning, and more particularly to a robot-assisted sewing feeding method based on normal pressure and fabric tension control. Background Technology

[0002] During the sewing process, the robot presses the fabric against the sewing base plate, using the friction between the fabric and the base plate and work surface to move the fabric and feed it. However, because the sewing process is dynamic, the forces acting on the fabric by the robot's end effector, the friction between the fabric and the base plate and work surface, and the forces between the fabric and the sewing machine's feed dogs and other mechanisms create dynamic changes, causing the fabric edges to bend, resulting in wrinkles and affecting the sewing quality. Current research on tracking the normal pressure and fabric tension of sewing robots mainly faces the following problems:

[0003] (1) Existing research on tracking and control of normal pressure in sewing robots is lacking: Normal pressure is the basis for robot fabric feeding. The robot uses normal pressure to press the fabric onto the worktable. The friction between the fabric and the sewing base plate is greater than the friction between the fabric and the worktable, thus completing the feeding under the robot's drive. However, due to uneven worktable height and robot movement deviation, the robot's normal pressure fluctuates, causing the sewing base plate to fail to press the fabric tightly, resulting in relative sliding between the fabric and the sewing base plate.

[0004] (2) The tracking control of fabric tension does not take into account the uncertainty and disturbance of the fabric: constant fabric tension can avoid the bending and deformation of the fabric edge and avoid the reduction of sewing quality. However, due to the diversity of planned sewing trajectories and the uncertainty of fabric characteristics, dynamic force changes occur between the fabric and the sewing machine. The impedance control with fixed parameters is difficult to compensate for the dynamic force and is prone to tracking error of the desired fabric tension.

[0005] Therefore, there is a lack of a method to effectively control the normal pressure and fabric tension during robot-assisted sewing. Summary of the Invention

[0006] To address the aforementioned technical problems in the existing technology, this invention proposes a robot-assisted sewing feeding method based on normal pressure and fabric tension control, the specific technical solution of which is as follows:

[0007] A robot-assisted sewing feeding method based on normal pressure and fabric tension control specifically includes the following steps:

[0008] Step 1: Establish a location-based impedance control model and analyze the influence of different impedance parameters on the response of the impedance control system. Determine the adjustment range of the impedance control parameters using the Routh stability criterion.

[0009] Step 2: Based on the improved particle swarm optimization algorithm, the objective function and adaptive inertia factor are improved to optimize the fitness index of the impedance control system, obtain the optimal impedance parameters, and achieve tracking control of the normal pressure.

[0010] Step 3: Design the robot's adaptive impedance controller by dynamically adjusting the desired damping parameters to dynamically compensate for environmental disturbances. Then, use the Routh stability criterion to analyze the stability of the adaptive impedance controller, determine the range of adaptive update rate, and achieve tracking control of the fabric tension.

[0011] Step four involves performing steady-state force tracking error analysis and verification on the impedance control system after the parameter adaptive control adjustments in steps three and four.

[0012] Furthermore, the establishment of the location-based impedance control model in step one specifically involves: Let X... d , X represents the desired reference position, velocity, and acceleration, respectively. c , θ represents the end effector position, velocity, and acceleration sent to the robot after impedance control model compensation. c θ represents the joint position to be input into the robot controller, obtained from inverse kinematics. m Indicates the actual joint position executed by the controller, X e X represents the given environmental location information. m F represents the actual position reached by the robot's end effector. e F represents the actual contact force with the environment. d Let the desired contact force be represented by the position-based impedance control model, then the expression for the model is:

[0013]

[0014] Where M d B d K d Let F represent the desired inertia parameter matrix, desired damping parameter matrix, and desired stiffness parameter matrix in impedance control, respectively. Let ΔF represent the actual contact force F between the robot end effector and the environment. e and desired contact force F d deviation:

[0015] ΔF(t)=F e (t)-F d (t) (2)

[0016] Through Laplace transform, the impedance control model can be expressed in the frequency domain as follows:

[0017]

[0018] In the formula, E(s) = X m (s)-X d ΔF(s) represents the deviation between the actual and desired positions of the robot's end effector; ΔF(s) represents the deviation between the actual and desired contact forces of the robot's end effector, based on the robot's workspace dimension h and impedance parameter M. d B d K d The transfer function is set as an h×h positive definite diagonal matrix; the robot controller controls the robot's motion through discrete points, therefore the transfer function is discretized, as follows:

[0019] make Discretizing equation (3) using the Tustin transform, we get:

[0020]

[0021] In the formula, c1 = 4M d +2B d T s +K d T s 2 c2 = 2K d T s 2 -8M d c3 = K d T s 2 -2B d T s +4M d Let z be a complex variable. From equation (4), we obtain the impedance control difference equation, which is expressed as:

[0022]

[0023] In the formula T s The robot controller instruction execution cycle is represented by E(t), the robot end position deviation at time t is represented by ΔF(t), and the robot end force deviation at time t is represented by ΔF(t). At the initial time, the position deviation and force deviation are set to be zero. Equation (5) is used for iterative calculation. The robot end position deviation is adjusted to compensate for the end force deviation, so that the robot end contact force is always the expected value.

[0024] Furthermore, in step one, the influence of different impedance parameters on the response of the impedance control system is analyzed, and the adjustment range of the impedance control parameters is determined by the Routh stability criterion. Specifically:

[0025] The parameter matrix in the impedance control model is a positive definite diagonal matrix, meaning that the forces of the robot in each direction in the task space are decoupled. Therefore, the analysis is performed on the force in a single direction of the robot, and equation (1) is expressed as:

[0026]

[0027] In the formula f e f d m d b d k d x m x d F e F d M d B d K d X m X d The unidirectional element, in the robot controller, is discretized by integral form of equation (6) to obtain:

[0028]

[0029] In the formula T s This represents the robot controller instruction execution cycle, where n represents the nth control cycle;

[0030] For a continuous impedance control system, the impedance control parameters m, b, and k are greater than zero. According to the Routh stability criterion, the impedance control system is always stable. However, when the continuous system is discretized, the stability of the impedance control system changes. When the impedance control parameters m, b, and k satisfy the relevant constraints, the impedance control system reaches stability.

[0031] Specifically, based on modern control theory, the state variables and output variables are determined as follows:

[0032]

[0033] Substituting equation (8) into equation (7), we get:

[0034]

[0035] After rearranging equation (9), we get:

[0036]

[0037] From equation (10), we can see that the state-space expression of the system is:

[0038]

[0039] In the formula, u represents the system's input vector, u n-1 =Δf(n-1), and from equation (11), we know that the system matrix A, control matrix b, and output matrix c are respectively:

[0040]

[0041] For a linear time-invariant system, when all eigenvalues ​​of the system matrix A have negative real parts, the system is asymptotically stable in equilibrium. However, from an engineering application perspective, the stability of the system output is more important. From equation (12), the characteristic equation of the system is:

[0042]

[0043] β is an eigenvalue, and equation (13) is expanded as follows:

[0044]

[0045] Let β = (s + 1) -1 Substituting (s-1) into equation (14), we get:

[0046] kT s 2 s 2 +2T s (b-kT s )s+(kT s 2 -2bT s +4m)=0 (15)

[0047] According to the Routh stability criterion for linear systems, the system is stable when all coefficients in the characteristic equation have the same sign and are not zero. Considering the practical meaning of the impedance control parameters, the condition for stable system output is as follows:

[0048]

[0049] Solving equation (16) further, we get:

[0050]

[0051] When the impedance control parameters m, b, and k satisfy the conditions shown in equation (17), the system output is stable. Then, different combinations of impedance control parameters m, b, and k can be selected to make the system have the desired dynamic performance.

[0052] Furthermore, step two mainly includes the following sub-steps:

[0053] Step 1: Particle Swarm Optimization: Based on the stability conditions of the control system, set the impedance control parameter optimization range x. limit Randomly generate the initial velocity v0 and initial position x0 of the particles, and set the optimal position P for each individual particle. pos Individual optimal fitness P best Optimal position G of the group pos and the optimal fitness G of the populationbest Parameters are used to complete particle swarm initialization;

[0054] Step 2: Calculation of the fitness index of the impedance control system: The particle fitness is the basis for algorithm optimization. The system fitness value under the current particle is calculated using the objective function and used as a performance evaluation index of the impedance control system. Based on the input and output of the impedance control system, a quadratic objective function is designed to iteratively optimize the particle in the direction of minimizing the combined input error and output energy. The expression is:

[0055]

[0056] In the formula, e represents the input error of the impedance control system, u represents the system output, and the corresponding parameters are force deviation Δf and position deviation Δx in formula (6), respectively, and ρ1 is a constant between 0 and 1;

[0057] Based on the application scenario of impedance control, the objective function is improved, and equation (18) becomes:

[0058]

[0059] In the formula M p This represents the maximum overshoot of the system. ρ2 is a weighting coefficient between 0 and 1. Particle values ​​are used to assign values ​​to the impedance parameters m, b, and k in sequence. Running the Simulink control model yields the system force deviation Δf, position deviation Δx, and system overshoot M. p Substituting into equation (19), the fitness value J of the control system under the current parameter combination is calculated. i ;

[0060] Step 3, Calculation of individual particle optimal value and population optimal value: Calculate the current particle fitness value J. i With the individual's optimal fitness P best Compare, if J i <P best Then P best =J i At the same time, update the optimal position P of the corresponding individual particle. pos J i With the optimal fitness G of the group best Compare, if J i <G best Then G best =J i At the same time, update the corresponding optimal position G of the particle swarm. pos ;

[0061] Step 4, Particle Velocity and Position Update: Update particle velocity based on the optimal position of the individual particle and the optimal position of the group.

[0062] vi k+1 =ωv i k +c1rand1(P pos -x i k )+c2rand2(G pos -x i k (20)

[0063] In the formula This represents the position of the i-th particle in the k-th iteration. Let ω represent the velocity of the i-th particle in the (k+1)-th iteration, ω represent the inertia factor, c1 represent the individual learning factor, c2 represent the group learning factor, rand1 and rand2 represent random values ​​between 0 and 1, the superscript k represents the k-th iteration, and the subscript i represents the i-th particle; where the inertia factor ω determines the global optimization capability of the algorithm, an adaptive inertia factor is used to improve the fixed value, and the expression is as follows:

[0064]

[0065] In the formula ω represents the inertia factor of the i-th particle in the k-th iteration. min ω max These represent the preset minimum inertia factor and maximum inertia factor, respectively. Let represent the minimum fitness value of all particles at the k-th iteration. This represents the average fitness value of all particles at the k-th iteration; combining equations (21) and (22), the particle positions are updated:

[0066]

[0067] Step 5, Iterative Loop: Apply boundary constraints to the updated particle positions and velocities. If the algorithm termination condition is met, output the optimization result, i.e., the optimal parameters of the impedance control system; otherwise, continue iterating until the algorithm termination condition is met.

[0068] Furthermore, step three, which involves designing an adaptive impedance controller by dynamically adjusting the desired damping parameters to dynamically compensate for environmental disturbances, specifically includes:

[0069] The unidirectional impedance model of the robot in the task space is established as follows:

[0070]

[0071] In the formula, e = x m -x d, representing the deviation between the actual and desired positions of the robot's end effector in a single direction, and Δf representing the tracking error of the impedance control force in a single direction. If the environment model is equivalent to a linear spring system, then the contact force between the robot's end effector and the environment is expressed as:

[0072] f e =k e (x e -x m ) (twenty four)

[0073] In the formula k e For the equivalent spring stiffness, x e Given the environmental reference position, from equation (3), let g(s) = 1 / (m d s 2 +b d s+k d From this, we can obtain e = g(s)Δf, that is:

[0074] x m =e+x d =g(s)Δf+x d (25)

[0075] Substituting equations (24) and (25) into equation (6), the force tracking error is expressed as:

[0076] Δf=k e x e -k e (g(s)Δf+x d )-f d (26)

[0077] Let g(s) = 1 / (m d s 2 +b d s+k d Substituting into equation (26) and rearranging, we get:

[0078] Δf(m d s 2 +b d s+k d +k e )=(m d s 2 +b d s+k d (k) e (x e -x d )-f d (27)

[0079] When the system is stable, the tracking error of the force in steady state is obtained:

[0080]

[0081] According to equation (28), if the tracking deviation Δf of the desired force in the steady state of the system is... ss It is zero, that is, the expression k e (x e -x d )-f d If it is zero, then we get:

[0082]

[0083] According to equation (29), if the tracking error of the force is zero in steady state, then the desired position x of the robot end effector is... d relative to environmental reference position x e The constraints must be met, which requires accurate information on the environmental location and environmental stiffness.

[0084] When the environmental stiffness information k e When the information is unknown, to ensure the tracking error is zero when the system is stable, i.e., Δf ss =0, let the desired stiffness parameter k in equation (23) be 0. d =0, then equation (23) becomes:

[0085]

[0086] Based on equation (29) and practical applications, let the environmental reference position x e Replace x d Then the positional deviation e becomes e = x m -x e Substituting equation (24) into equation (30), we get:

[0087]

[0088] According to equation (31), when the environmental stiffness information k e When the value is unknown, the desired stiffness parameter k in the impedance control system is set. d =0, adjust the desired inertia parameter m d With the desired damping parameter b d This results in a force tracking error Δf in the steady state of the system. ss =0;

[0089] When environmental location information x e When the situation is unknown, there are various different scene environments, including: the environment is a plane, an inclined plane, or other irregular environments. Therefore, a targeted analysis is performed for each different scene. First, let e = x m -x e Substituting into equation (30), we get:

[0090]

[0091] For a two-dimensional environment, the environment reference position. Substituting into equation (32), we get:

[0092]

[0093] According to equation (33), when the system is stable, the force tracking error Δf ss Zero error means achieving zero-error force tracking in a planar environment where the environmental position information is unknown.

[0094] For environments that are slopes or other irregular scenes. or According to equation (32), after the system stabilizes, the force tracking error Δf ss If the value is not equal to 0, then the impedance control needs to be improved. Next, we will analyze the case where the environmental location information is unknown. The accurate environmental location can be expressed by an estimated value as follows:

[0095]

[0096] In the formula ξx e This represents the deviation from the estimated environmental position; the corresponding robot position deviation then becomes:

[0097]

[0098] Substituting equation (35) into equation (30) yields:

[0099]

[0100] In the formula f e f d Furthermore, since e varies with time, and even when the system is stable, there is still a force tracking error, an adaptive control method is adopted, which adjusts the damping parameter b by adding an adaptive term Δb(t). d To dynamically compensate for tracking errors, equation (36) becomes:

[0101]

[0102] In the formula, the adaptive term Δb(t) is updated as the force error changes, and is expressed as:

[0103]

[0104] In the formula, μ represents the update rate, λ represents the sampling rate, which depends on the controller sampling time, and ε is the denominator adjustment parameter, which is set to 10e-8.

[0105] Furthermore, in step three, the stability of the adaptive impedance controller is analyzed using the Routh stability criterion to determine the range of values ​​for the adaptive update rate, specifically as follows:

[0106] Applying the adaptive control law shown in equation (38) to the control system, and substituting equation (38) into equation (37), we get:

[0107]

[0108] Rearranging equation (39) and moving the position estimation term to the left side, we get:

[0109]

[0110] Based on the contact force model between the robot and the environment (equation (24), we obtain:

[0111]

[0112] From e = x m -x e Substituting into equation (41), we get:

[0113]

[0114] Substituting equation (42) into equation (40), we get:

[0115]

[0116] Add to both sides of equation (43) and If the term is given, then equation (43) becomes:

[0117]

[0118] For ease of analysis, let Λ(t)=f d (t)-f e (t), then equation (44) simplifies to:

[0119]

[0120] From the adaptive control law shown in equation (38), we can see that:

[0121] b d Ω(t-λ)=b d Ω(t-(n-1)λ)+μΛ(t-(n-2)λ)+…+μΛ(t-2λ) (46)

[0122] If the initial value of the adaptive compensation is zero, i.e. Ω(t-(n-1)λ)=0, then equation (45) can be expressed as:

[0123]

[0124] Let ε(t) = f d (t)+f e Substituting (t) into equation (47), we get:

[0125]

[0126] Taking the Laplace transform of equation (48), we obtain the transfer functions for Λ(s) and ε(s):

[0127]

[0128] From equation (49), we can see that the characteristic equation of the system is:

[0129] m d s 2 +b d s+k e +μk e (e -(n-2)λs +…+e -λs )=0 (50)

[0130] In the formula, λ is the sampling rate, and the controller sampling period is 0.001s, which is approximately zero. Then, the sum of the series in formula (50) is expressed as:

[0131]

[0132] Substituting equation (51) into equation (50), we get:

[0133] m d λs 3 +b d λs 2 +k e λ(1-μ)s+μk e =0 (52)

[0134] According to the Routh criterion for linear systems, the Routh array corresponding to equation (52) is:

[0135]

[0136] When the coefficients of the characteristic equation have the same sign and the first column of the Routh array is all positive, the system is stable.

[0137]

[0138] Substituting c1 and c2, we get:

[0139]

[0140] Rearranging equation (55), the impedance parameter m d b d and k e All values ​​are positive. The conditions required for the system to be stable are:

[0141]

[0142] According to equation (56), the impedance control system based on parameter adaptation is stable when the system update rate μ satisfies the constraint described in equation (56).

[0143] Furthermore, step four specifically involves:

[0144] The tracking error of the steady-state force in the aforementioned parameter-adaptive impedance control system is analyzed. The tracking error of the steady-state force is expressed as:

[0145]

[0146] When the input signal is a step signal, that is Substituting into equation (57):

[0147]

[0148] When the input signal is a sinusoidal signal, that is Where ω represents the signal period, substituting it into equation (57):

[0149]

[0150] According to equations (58) and (59), when the input signal is a step signal or a sinusoidal signal, the tracking error of the force after the system reaches steady state is zero, thus achieving accurate tracking of the desired force.

[0151] Beneficial effects:

[0152] This invention is based on an improved particle swarm optimization algorithm. It improves the objective function by controlling the desired force deviation, position deviation and maximum overshoot of the system. Combined with an adaptive inertia factor, it optimizes the fitness index of the control system and obtains the optimal parameters for impedance control, thus realizing the tracking control requirements of normal pressure in robot-assisted sewing.

[0153] This invention relates to a fabric tension tracking control method based on parameter adaptation. On the basis of a fixed parameter impedance controller, an adaptive impedance controller is designed by dynamically adjusting the desired damping parameter. The adaptive update rate range is determined through system stability analysis, thereby realizing the tracking control requirements of fabric tension in robot-assisted sewing. Attached Figure Description

[0154] Figure 1This is a schematic diagram of a robot-assisted sewing feeding method based on normal pressure and fabric tension control according to the present invention.

[0155] Figure 2 This is a location-based impedance control block diagram of the present invention;

[0156] Figure 3 This is a flowchart of the impedance parameter optimization based on the improved particle swarm optimization algorithm of the present invention;

[0157] Figure 4 This is a schematic diagram of the force distribution during the robot-assisted sewing process according to an embodiment of the present invention. Detailed Implementation

[0158] To make the objectives, technical solutions, and technical effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0159] For example Figure 4 The robot-assisted sewing process shown in the diagram primarily involves normal pressure F acting on the robot. z and the fabric tension F on the plane x With F y The normal pressure is perpendicular to the sewing worktable. Under this force, the fabric is pressed onto the worktable. Because the coefficient of friction between the fabric and the sewing base plate is greater than that between the fabric and the sewing platform, the fabric and the sewing base plate do not slide relative to each other. The robot drives the fabric to move in a feeding motion through the sewing base plate. The fabric tension is a planar force, which can be divided into F... x With F y Under tension, the fabric remains taut throughout the sewing process, preventing deformation and bending at the edges.

[0160] like Figure 1 As shown, this embodiment of the invention proposes a robot-assisted sewing feeding method based on normal pressure and fabric tension control, specifically including:

[0161] Step 1: Establish a location-based impedance control model and analyze its stability. Specifically, establish a location-based impedance control model and analyze the influence of different impedance parameters on the response of the impedance control system. Determine the adjustment range of the impedance control parameters using the Routh stability criterion.

[0162] Step 2: Impedance control of normal pressure is achieved based on the improved particle swarm algorithm, that is: the objective function and adaptive inertia factor are improved based on the improved particle swarm algorithm to optimize the fitness index of the impedance control system, obtain the optimal impedance parameters, and achieve tracking control of normal pressure.

[0163] Step 3: Based on the idea of ​​dynamically adjusting the desired damping parameter, design an adaptive impedance controller and perform stability analysis to control the fabric tension. That is, design the robot's adaptive impedance controller by dynamically adjusting the desired damping parameter to dynamically compensate for environmental disturbances. Then, use the Routh stability criterion to analyze the stability of the adaptive impedance controller, determine the range of adaptive update rate, and achieve tracking control of the fabric tension.

[0164] Step four: Verify the accuracy of the adaptive impedance control system in tracking the force after steady state, that is: perform a steady-state force tracking error analysis and verification on the impedance control system after the parameter adaptive control adjustment in steps three and four.

[0165] Specifically, establishing the location-based impedance control model involves: Let X... d , X represents the reference desired position, velocity, and acceleration given by the impedance control model, respectively. c , θ represents the end effector position, velocity, and acceleration sent to the robot after impedance control model compensation. c θ represents the joint position to be input into the robot controller, obtained from inverse kinematics. m Indicates the actual joint position executed by the controller, X e X represents the given environmental location information. m F represents the actual position reached by the robot's end effector. e F represents the actual contact force with the environment. d Indicates the desired contact force, such as Figure 2 The impedance control block diagram shown is illustrated. The expression for the location-based impedance control model is as follows:

[0166]

[0167] Where M d B d K d Let F represent the desired inertia parameter matrix, desired damping parameter matrix, and desired stiffness parameter matrix in impedance control, respectively. Let ΔF represent the actual contact force F between the robot end effector and the environment. e and desired contact force F d deviation:

[0168] ΔF(t)=F e (t)-F d (t) (2)

[0169] Through Laplace transform, the impedance control model can be expressed in the frequency domain as:

[0170]

[0171] In the formula, E(s) = X m (s)-X d ΔF(s) represents the deviation between the actual and desired positions of the robot's end effector; ΔF(s) represents the deviation between the actual and desired contact forces of the robot's end effector, based on the robot's workspace dimension h and impedance parameter M. d B d K d The transfer function is set to an h×h positive definite diagonal matrix; the robot controller controls the robot's motion through discrete points, therefore the transfer function needs to be discretized.

[0172] make Discretizing equation (3) using the Tustin transform yields:

[0173]

[0174] In the formula, c1 = 4M d +2B d T s +K d T s 2 c2 = 2K d T s 2 -8M d c3 = K d T s 2 -2B d T s +4M d Let z be a complex variable. From equation (4), we obtain the impedance control difference equation, which can be expressed as:

[0175]

[0176] In the formula T s The robot controller instruction execution cycle is represented by E(t), the robot end position deviation at time t is represented by ΔF(t), and the robot end force deviation at time t is represented by ΔF(t). At the initial time, the position deviation and force deviation are set to be zero. Equation (5) is used for iterative calculation. The robot end position deviation is adjusted to compensate for the end force deviation, so as to ensure that the robot end contact force is always the expected value.

[0177] The stability of the analysis model is specifically as follows: the parameter matrix in the impedance control model is usually a positive definite diagonal matrix, that is, the forces of the robot in each direction in the task space are decoupled from each other. Taking the robot's single-direction force as an example for analysis, equation (1) can be expressed as:

[0178]

[0179] In the formula f e fd m d b d k d x m x d F e F d M d B d K d X m X d The unidirectional element, in the robot controller, is discretized by integral form of equation (6) to obtain:

[0180]

[0181] In the formula T s The value represents the robot controller instruction execution cycle, and n represents the nth control cycle. For a continuous impedance control system, the impedance control parameters m, b, and k are greater than zero. According to the Routh stability criterion, the impedance control system is always stable. However, when the continuous system is discretized, the stability of the impedance control system changes under the original conditions. When the impedance control parameters m, b, and k satisfy the relevant constraints, the impedance control system reaches stability.

[0182] Based on modern control theory, the state variables and output variables are determined as follows:

[0183]

[0184] Substituting equation (8) into equation (7), we get:

[0185]

[0186] Equation (9) can be rearranged to obtain:

[0187]

[0188] From equation (10), we can see that the state-space expression of the system is:

[0189]

[0190] In the formula, u represents the system's input vector, u n-1 =Δf(n-1), and from equation (11), we know that the system matrix A, control matrix b, and output matrix c are respectively:

[0191]

[0192] For a linear time-invariant system, when all eigenvalues ​​of the system matrix A have negative real parts, the system is asymptotically stable in equilibrium. However, from an engineering application perspective, the stability of the system output is more important. From equation (12), the characteristic equation of the system is:

[0193]

[0194] β is an eigenvalue, and equation (13) is expanded as follows:

[0195]

[0196] Let β = (s + 1) -1 Substituting (s-1) into equation (14), we get:

[0197] kT s 2 s 2 +2T s (b-kT s )s+(kT s 2 -2bT s +4m)=0 (15)

[0198] According to the Routh stability criterion for linear systems, the system is stable when all coefficients in the characteristic equation have the same sign and are not zero. Considering the practical meaning of the impedance control parameters, the condition for system output stability is as follows:

[0199]

[0200] Equation (16) can be further solved to obtain:

[0201]

[0202] When the impedance control parameters m, b, and k satisfy the conditions shown in equation (17), the system output is stable. Therefore, under the condition of satisfying system stability, different combinations of impedance control parameters m, b, and k can be selected to make the system have the desired dynamic performance.

[0203] The impedance control of normal pressure based on the improved particle swarm optimization algorithm is achieved by determining the optimal combination of impedance parameters through the improved particle swarm optimization algorithm, such as... Figure 3 As shown, the main steps in improving and optimizing the particle swarm optimization algorithm include:

[0204] Step 1: Particle Swarm Initialization: Based on the stability conditions of the impedance control system obtained in the above steps, set the impedance control parameter optimization range x. limit Randomly generate the initial velocity v0 and initial position x0 of the particles, and set the optimal position P for each individual particle. pos Individual optimal fitness Pbest Optimal position G of the group pos and the optimal fitness G of the population best Parameters such as these are used to complete particle swarm initialization;

[0205] Step 2: Calculation of the fitness index of the impedance control system: The particle fitness is the basis for algorithm optimization. It is necessary to use the objective function to calculate the system fitness value under the current particle and use it as the performance evaluation index of the impedance control system. Based on the input and output of the impedance control system, a quadratic objective function is designed to make the particle iteratively optimize in the direction of minimizing the combined input error and output energy.

[0206]

[0207] In the formula, e represents the input error of the impedance control system, u represents the system output, and the corresponding parameters are force deviation Δf and position deviation Δx in formula (6), respectively, and ρ1 is a constant between 0 and 1;

[0208] According to the impedance control application scenario of the present invention, considering the transition phase before the system reaches steady state, in order to prevent the robot from colliding with the sewing platform due to large position adjustments, the position adjustment should not be too large, i.e., the system overshoot M. p The value should not be too large. Therefore, based on this condition, the objective function is improved, and equation (18) becomes:

[0209]

[0210] In the formula M p This represents the maximum overshoot of the system. ρ2 is a weighting coefficient between 0 and 1. Particle values ​​are used to assign values ​​to the impedance parameters m, b, and k in sequence. Running the Simulink control model yields the system force deviation Δf, position deviation Δx, and system overshoot M. p Substituting into equation (19), the fitness value J of the control system under the current parameter combination is calculated. i ;

[0211] Step 3, Calculation of individual particle optimal value and population optimal value: Calculate the current particle fitness value J. i With the individual's optimal fitness P best Compare, if J i <P best Then P best =J i At the same time, update the optimal position P of the corresponding individual particle. pos J i With the optimal fitness G of the group best Compare, if J i <G best Then G best =J iAt the same time, update the corresponding optimal position G of the particle swarm. pos ;

[0212] Step 4, Particle Velocity and Position Update: Update particle velocity based on the optimal position of the individual particle and the optimal position of the group.

[0213] v i k+1 =ωv i k +c1rand1(P pos -x i k )+c2rand2(G pos -x i k (20)

[0214] In the formula This represents the position of the i-th particle in the k-th iteration. Let ω represent the velocity of the i-th particle in the (k+1)-th iteration, ω represent the inertia factor, c1 represent the individual learning factor, c2 represent the group learning factor, rand1 and rand2 represent random values ​​between 0 and 1, the superscript k represents the k-th iteration, and the subscript i represents the i-th particle. The inertia factor ω determines the algorithm's global optimization capability. A dynamic inertia factor has a better optimization effect than a fixed value, better balancing global and local optimization, and effectively avoiding the algorithm from getting trapped in local optima. An adaptive inertia factor is used to improve the fixed value, as expressed below:

[0215]

[0216] In the formula ω represents the inertia factor of the i-th particle in the k-th iteration. min ω max These represent the preset minimum inertia factor and maximum inertia factor, respectively. Let represent the minimum fitness value of all particles at the k-th iteration. This represents the average fitness value of all particles at the k-th iteration; combining equations (21) and (22), the particle positions are updated:

[0217]

[0218] Step 5, Iterative Loop: Apply boundary constraints to the updated particle positions and velocities. If the algorithm termination condition is met, output the optimization result, i.e., the optimal parameters of the impedance control system; otherwise, continue iterating until the algorithm termination condition is met.

[0219] The adaptive impedance controller designed based on the idea of ​​dynamically adjusting the desired damping parameter is specifically as follows:

[0220] The unidirectional impedance model of the robot in the task space is established as follows:

[0221]

[0222] In the formula, e = x m -x d Δf represents the deviation between the actual and desired positions of the robot's end effector in a single direction, and Δf represents the tracking error of the impedance control force in a single direction. The environmental model is equivalent to a linear spring system, such as... Figure 4 As shown, the contact force between the robot's end effector and the environment can be expressed as:

[0223] f e =k e (x e -x m ) (twenty four)

[0224] In the formula k e For the equivalent spring stiffness, x e Given the environmental reference position, from equation (3), let g(s) = 1 / (m d s 2 +b d s+k d From this, we can obtain e = g(s)Δf, that is:

[0225] x m =e+x d =g(s)Δf+x d (25)

[0226] Substituting equations (24) and (25) into equation (6), the force tracking error can be expressed as:

[0227] Δf=k e x e -k e (g(s)Δf+x d )-f d (26)

[0228] Let g(s) = 1 / (m d s 2 +b d s+k d Substituting into equation (26) and rearranging, we get:

[0229] Δf(m d s 2 +b d s+k d +k e )=(m d s 2 +bd s+k d (k) e (x e -x d )-f d (27)

[0230] When the system is stable, the tracking error of the force in steady state can be obtained:

[0231]

[0232] From equation (28), it can be seen that if the tracking deviation Δf of the desired force is in steady state of the system... ss It is zero, that is, the expression k e (x e -x d )-f d If the value is zero, then:

[0233]

[0234] From equation (29), it can be seen that if the tracking error of the force is zero in the steady state of the system, then the desired position x of the robot end effector is... d relative to environmental reference position x e The constraints must be strictly met, namely, accurate environmental position and environmental stiffness information are required. However, in practical applications, the stiffness information of the robot sewing environment is unknown, and it is difficult to obtain accurate environmental position information. Therefore, if the tracking error of the impedance control force is to be zero, a force tracking control method must be determined under the condition that the stiffness and position information of the robot-assisted sewing environment are unknown.

[0235] In robot-assisted sewing, given the desired contact force f at the robot's end effector... d ≠0, and the robot's base plate comes into contact with the environment (x). d ≠x e As can be seen from equation (29), the condition that the tracking error of the force is zero when the system is stable is not met;

[0236] When the environmental stiffness information k e When the information is unknown, to ensure the tracking error is zero when the system is stable, i.e., Δf ss =0, let the desired stiffness parameter k in equation (23) be 0. d =0, then equation (23) becomes:

[0237]

[0238] As can be seen from the analysis of equation (29), it is difficult to obtain accurate environmental information in practical applications, that is, it is difficult to determine the precise desired location x. d Therefore, let the initial environment position be x. e Replace x dThen the positional deviation e becomes e = x m -x e Substituting equation (24) into equation (30), we get:

[0239]

[0240] From equation (31), it can be seen that when the environmental stiffness information k e When the value is unknown, the desired stiffness parameter k in the impedance control system is set. d =0, adjust the desired inertia parameter m d With the desired damping parameter b d The above equation can be realized, that is, the tracking error Δf of the force in the steady state of the system. ss =0.

[0241] When environmental location information x e When the situation is unknown, there are multiple possibilities: the environment may be a plane, an inclined plane, or other irregular environments. Therefore, it is necessary to conduct targeted analyses for different scenarios. First, based on the conclusions obtained from the above analysis, let e = x m -x e Substituting into equation (30), we get:

[0242]

[0243] For a two-dimensional environment, the environment reference position. Substituting into equation (32), we get:

[0244]

[0245] From equation (33), it can be seen that when the system is stable, the force tracking error Δf ss A value of zero is achievable, meaning that force tracking can be achieved even in a planar environment where the location information is unknown.

[0246] For environments that are slopes or other irregular scenes. or From (32), it can be seen that after the system stabilizes, the force tracking error Δf ss ≠0.

[0247] In summary, in robot-assisted sewing scenarios, both environmental stiffness and position information are difficult to obtain accurately. Regarding the environmental stiffness k... d When the information is unknown, the desired stiffness parameter k is set. d =0, then select a suitable desired inertia parameter m d With the desired damping parameter b d To ensure that the force tracking error is zero; for environmental position information x eIn unknown situations, zero-error force tracking can be achieved in planar environments, but it is difficult to accurately track forces in inclined or other complex environments, requiring improvements to impedance control. The following analysis addresses the case where environmental location information is unknown. The accurate environmental location can be expressed as an estimated value:

[0248]

[0249] In the formula ξx e This represents the deviation from the estimated environmental position; the corresponding robot position deviation then becomes:

[0250]

[0251] Substituting equation (35) into equation (30), we get:

[0252]

[0253] In the formula f e f d Furthermore, since e varies with time, a force tracking error still exists even when the system is stable. To eliminate this steady-state error, this invention employs an adaptive control method, adjusting the damping parameter b by adding an adaptive term Δb(t). d To dynamically compensate for tracking errors, equation (36) becomes:

[0254]

[0255] The adaptive term Δb(t) in the formula is updated as the force error changes, and can be expressed as:

[0256]

[0257] In the formula, μ represents the update rate, λ represents the sampling rate, which depends on the controller sampling time, and ε is the denominator adjustment parameter, which is set to 10e-8.

[0258] Furthermore, after applying the adaptive control law shown in equation (38) to the impedance control system, it is necessary to consider whether the system stability changes, i.e., the stability analysis, specifically: substituting equation (38) into equation (37), we can obtain:

[0259]

[0260] By rearranging equation (39) and moving the position estimation term to the left side, we get:

[0261]

[0262] From the contact force model between the robot and the environment in equation (24), we can see that:

[0263]

[0264] From e = x m -x e Substituting into equation (41), we get:

[0265]

[0266] Substituting equation (42) into equation (40), we get:

[0267]

[0268] Add to both sides of equation (43) and

[0269] If the term is given, then equation (43) becomes:

[0270]

[0271] For ease of analysis, let Λ(t)=f d (t)-f e (t), then equation (44) simplifies to:

[0272]

[0273] From the adaptive control law shown in equation (38), we can see that:

[0274] b d Ω(t-λ)=b d Ω(t-(n-1)λ)+μΛ(t-(n-2)λ)+…+μΛ(t-2λ) (46)

[0275] If the initial value of the adaptive compensation is zero, i.e. Ω(t-(n-1)λ)=0, then equation (45) can be expressed as:

[0276]

[0277] Let ε(t) = f d (t)+f e Substituting (t) into equation (47), we get:

[0278]

[0279] Taking the Laplace transform of equation (48), we obtain the transfer functions for Λ(s) and ε(s):

[0280]

[0281] From equation (49), we can see that the characteristic equation of the system is:

[0282] m d s 2 +b d s+k e +μk e (e -(n-2)λs +…+e -λs )=0 (50)

[0283] In the formula, λ is the sampling rate. Under normal circumstances, the sampling period of the controller is 0.001s, which is close to zero. Then, the sum of the series in formula (50) can be expressed as:

[0284]

[0285] Substituting equation (51) into equation (50), we get:

[0286] m d λs 3 +b d λs 2 +k e λ(1-μ)s+μk e =0 (52)

[0287] According to the Routh criterion for linear systems, the Routh array corresponding to equation (52) is:

[0288]

[0289] When the coefficients of the characteristic equation have the same sign and the first column of the Routh array is all positive, the system is stable.

[0290]

[0291] Substituting c1 and c2, we get:

[0292]

[0293] Equation (55) is simplified, where the impedance parameter m d b d and k e All values ​​are positive. The conditions required for the system to be stable are:

[0294]

[0295] As can be seen from equation (56), when the system update rate μ satisfies the constraint described in equation (56), the impedance control system based on parameter adaptation is stable.

[0296] In an impedance control system with fixed impedance parameters, when the input signal is sinusoidal, a significant tracking error exists after the system reaches steady state. To verify whether the parameter adaptive control system can achieve accurate force tracking after steady state, the following analysis examines the force tracking error after steady state. The force tracking error after steady state can be expressed as:

[0297]

[0298] When the input signal is a step signal, that is Substituting into equation (57), we get:

[0299]

[0300] When the input signal is a sinusoidal signal, that is Where ω represents the signal period, substituting it into equation (57) yields:

[0301]

[0302] As can be seen from equations (58) and (59), when the input signal is a step signal or a sinusoidal signal, the tracking error of the force after the system reaches steady state is zero, thus achieving accurate tracking of the desired force.

[0303] In summary, the impedance control based on parameter adaptation can remain stable under certain constraints and can accurately track different forms of force in steady state.

[0304] The above-described method enables tracking and control of the normal pressure and fabric tension experienced during robot-assisted sewing.

[0305] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the implementation process of the present invention has been described in detail above, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robot-assisted sewing feeding method based on normal pressure and fabric tension control, characterized in that, Specifically, it includes the following: Step 1: Establish a location-based impedance control model and analyze the influence of different impedance parameters on the response of the impedance control system. Determine the adjustment range of the impedance control parameters using the Routh stability criterion. Step 2: Based on the improved particle swarm optimization algorithm, the objective function and adaptive inertia factor are improved to optimize the fitness index of the impedance control system, obtain the optimal impedance parameters, and achieve tracking control of the normal pressure. Step 3: Design the robot's adaptive impedance controller by dynamically adjusting the desired damping parameters to dynamically compensate for environmental disturbances. Then, use the Routh stability criterion to analyze the stability of the adaptive impedance controller, determine the range of adaptive update rate, and achieve tracking control of the fabric tension. Step four: Perform steady-state force tracking error analysis and verification on the impedance control system after parameter adaptive control adjustment in steps three and four. The establishment of the location-based impedance control model in step one specifically involves: assuming... , , These represent the desired reference position, velocity, and acceleration, respectively. , , These represent the end-effector position, velocity, and acceleration sent to the robot after impedance control model compensation, respectively. This represents the joint position obtained from inverse kinematics and to be input into the robot controller. This indicates the joint position actually executed by the controller. Indicates the given environmental location information, This indicates the actual location reached by the robot's end effector. Indicates the actual contact force with the environment. Let the desired contact force be represented by the position-based impedance control model, then the expression for the model is: (1) in , , Let them represent the desired inertia parameter matrix, desired damping parameter matrix, and desired stiffness parameter matrix in impedance control, respectively. This represents the actual contact force between the robot's end effector and the environment. and desired contact force deviation: (2) Through Laplace transform, the impedance control model can be expressed in the frequency domain as follows: (3) In the formula, This indicates the deviation between the actual position of the robot's end effector and the desired position. This represents the deviation between the actual contact force and the expected force at the robot's end effector, based on the robot's workspace dimension h and impedance parameters. , , The transfer function is set as an h×h positive definite diagonal matrix; the robot controller controls the robot's motion through discrete points, therefore the transfer function is discretized, as follows: make Discretizing equation (3) using the Tustin transform yields: (4) In the formula , , Let z be a complex variable. From equation (4), we obtain the impedance control difference equation, which is expressed as: (5) In the formula Indicates the robot controller instruction execution cycle. This represents the position deviation of the robot's end effector at time t. Let t represent the force deviation of the robot end effector at time t; initially, both the position deviation and the force deviation are set to zero. Equation (5) is used for iterative calculation. The position deviation of the robot end effector is adjusted to compensate for the force deviation at the end effector, so that the contact force of the robot end effector is always the desired value. The step one involves analyzing the impact of different impedance parameters on the response of the impedance control system, and determining the adjustment range of the impedance control parameters using the Routh stability criterion. Specifically: The parameter matrix in the impedance control model is a positive definite diagonal matrix, meaning that the forces of the robot in each direction in the task space are decoupled. Therefore, the analysis is performed on the force in a single direction of the robot, and equation (1) is expressed as: (6) In the formula They represent The unidirectional element, in the robot controller, is discretized by integral form of equation (6) to obtain: (7) In the formula This represents the robot controller instruction execution cycle, where n represents the nth control cycle; For a continuous impedance control system, the impedance control parameters m, b, and k are greater than zero. According to the Routh stability criterion, the impedance control system is always stable. However, when the continuous system is discretized, the stability of the impedance control system changes. When the impedance control parameters m, b, and k satisfy the relevant constraints, the impedance control system reaches stability. Specifically, based on modern control theory, the state variables and output variables are determined as follows: (8) Substituting equation (8) into equation (7), we get: (9) After rearranging equation (9), we get: (10) From equation (10), we can see that the state-space expression of the system is: (11) In the formula, u represents the system's input vector. From equation (11), we know that the system matrix A, control matrix b, and output matrix c are respectively: (12) For a linear time-invariant system, when all eigenvalues ​​of the system matrix A have negative real parts, the system is asymptotically stable in equilibrium. However, from an engineering application perspective, the stability of the system output is more important. From equation (12), the characteristic equation of the system is: (13) For the eigenvalues, equation (13) is expanded as follows: (14) make Substituting into equation (14), we get: (15) According to the Routh stability criterion for linear systems, the system is stable when all coefficients in the characteristic equation have the same sign and are not zero. Considering the practical meaning of the impedance control parameters, the condition for stable system output is as follows: (16) Solving equation (16) further, we get: (17) When the impedance control parameters m, b, and k satisfy the conditions shown in equation (17), the system output is stable. Then, different combinations of impedance control parameters m, b, and k can be selected to make the system have the desired dynamic performance.

2. The robot-assisted sewing feeding method based on normal pressure and fabric tension control as described in claim 1, characterized in that, Step two mainly includes the following sub-steps: Step 1: Particle Swarm Optimization: Based on the stability conditions of the control system, set the optimization range of the impedance control parameters. The initial velocity of randomly generated particles relative to the initial position of the particle Set the optimal position for each individual particle. Individual optimal fitness Optimal position of the group and the optimal fitness of the group Parameters are used to complete particle swarm initialization; Step 2: Calculation of the fitness index of the impedance control system: The particle fitness is the basis for algorithm optimization. The system fitness value under the current particle is calculated using the objective function and used as a performance evaluation index of the impedance control system. Based on the input and output of the impedance control system, a quadratic objective function is designed to iteratively optimize the particle in the direction of minimizing the combined input error and output energy. The expression is: (18) In the formula, e represents the input error of the impedance control system, and u represents the system output. The parameters corresponding to these two are the force deviation in formula (6). with positional deviation , A constant between 0 and 1; Based on the application scenario of impedance control, the objective function is improved, and equation (18) becomes: (19) In the formula This indicates the maximum overshoot of the system. The weighting coefficients are between 0 and 1. The impedance parameters m, b, and k are assigned values ​​sequentially using particle values. The Simulink control model is then run to obtain the force deviation of the system. Positional deviation and system overshoot Substituting into equation (19), the fitness value of the control system under the current parameter combination is calculated. ; Step 3, Calculation of individual particle optimal value and population optimal value: Calculate the current particle fitness value. With individual optimal fitness If a comparison is made, ,but At the same time, update the optimal position of the corresponding individual particle. ;Will optimal fitness of the group If a comparison is made, ,but At the same time, update the optimal position of the corresponding particle swarm. ; Step 4, Particle Velocity and Position Update: Update particle velocity based on the optimal position of the individual particle and the optimal position of the group. (20) In the formula This represents the position of the i-th particle in the k-th iteration. This represents the velocity of the i-th particle in the (k+1)-th iteration. Indicates the inertia factor. Represents individual learning factors. Represents the group learning factor. and Represents a random value between 0 and 1, with the superscript k indicating the k-th iteration and the subscript i indicating the i-th particle; Among them, inertia factor To determine the algorithm's global optimization capability, an adaptive inertia factor is used to improve the fixed value, as shown in the following expression: (21) In the formula This represents the inertia factor of the i-th particle in the k-th iteration. , These represent the preset minimum inertia factor and maximum inertia factor, respectively. Let represent the minimum fitness value of all particles at the k-th iteration. This represents the average fitness value of all particles at the k-th iteration; combining equations (21) and (22), the particle positions are updated: (22)； Step 5, Iterative Loop: Apply boundary constraints to the updated particle positions and velocities. If the algorithm termination condition is met, output the optimization result, i.e., the optimal parameters of the impedance control system; otherwise, continue iterating until the algorithm termination condition is met.

3. The robot-assisted sewing feeding method based on normal pressure and fabric tension control as described in claim 2, characterized in that, Step three, which involves designing an adaptive impedance controller by dynamically adjusting the desired damping parameters to dynamically compensate for environmental disturbances, specifically includes: The unidirectional impedance model of the robot in the task space is established as follows: (23) In the formula This indicates the deviation between the actual and desired positions of the robot's end effector in a single direction. The tracking error representing the impedance control force in one direction is represented by: If the environment model is equivalent to a linear spring system, then the contact force between the robot's end effector and the environment is expressed as: (24) In the formula For equivalent spring stiffness, Given the environmental reference position, it can be seen from equation (3) that, let , can be obtained ,Right now: (25) Substituting equations (24) and (25) into equation (6), the force tracking error is expressed as: (26) Will Substituting into equation (26) and rearranging, we get: (27) When the system is stable, the tracking error of the force in steady state is obtained: (28) According to equation (28), if the tracking deviation of the desired force in steady state is... It is zero, that is, the formula If it is zero, then we get: (29) According to equation (29), if the tracking error of the force is zero in steady state, then the desired position of the robot's end effector is... Environmental reference position The constraints must be met, which requires accurate information on the environmental location and environmental stiffness. When environmental stiffness information When the information is unknown, to ensure the tracking error is zero when the system is stable, i.e. Let the desired stiffness parameter in equation (23) be... Then equation (23) becomes: (30) Based on equation (29) and practical applications, let the environmental reference position be... Alternative Then the positional deviation Become Substituting equation (24) into equation (30), we get: (31) According to equation (31), when the environmental stiffness information When the value is unknown, the desired stiffness parameter in the impedance control system is set. Adjust the desired inertia parameter With desired damping parameters This causes the force tracking error in the steady state of the system to be reduced. ; When environmental location information When the situation is unknown, there are various different scene environments, including: the environment is a plane, an inclined plane, or other irregular environments. Therefore, a targeted analysis is performed for each different scene. First, [the analysis will begin with...] Substituting into equation (30), we get: (32) For a two-dimensional environment, the environment reference position. Substituting into equation (32), we get: (33) According to equation (33), when the system is stable, the force tracking error Zero error means achieving zero-error force tracking in a planar environment where the environmental position information is unknown. For environments that are slopes or other irregular scenes. or According to equation (32), after the system stabilizes, the force tracking error will be... If this is the case, impedance control needs to be improved. Next, we will analyze the situation where the environmental location information is unknown. The accurate environmental location can be expressed as an estimated value: (34) In the formula This represents the deviation from the estimated environmental position; the corresponding robot position deviation then becomes: (35) Substituting equation (35) into equation (30), we get: (36) In the formula , as well as The force tracking error varies over time, and even when the system is stable, there is still an error. Therefore, an adaptive control method is adopted, which involves adding an adaptive term. Adjusting damping parameters To dynamically compensate for tracking errors, equation (36) becomes: (37) In the formula, the adaptive term Updated as the force error changes, expressed as: (38) In the formula Indicates the update rate. The sampling rate depends on the controller's sampling time. Set the denominator adjustment parameter. .

4. The robot-assisted sewing feeding method based on normal pressure and fabric tension control as described in claim 3, characterized in that, Step three involves using the Routh stability criterion to analyze the stability of the adaptive impedance controller and determine the range of values ​​for the adaptive update rate. Specifically: Applying the adaptive control law shown in equation (38) to the control system, and substituting equation (38) into equation (37), we get: (39) Rearranging equation (39) and moving the position estimation term to the left side, we get: (40) Based on the contact force model between the robot and the environment (24), we obtain: (41) Depend on Substituting into equation (41), we get: (42) Substituting equation (42) into equation (40), we get: (43) Add to both sides of equation (43) and If the term is given, then equation (43) becomes: (44) For ease of analysis, let , Then equation (44) simplifies to: (45) From the adaptive control law shown in equation (38), we can see that: (46) The initial value for adaptive compensation is zero, that is... Then equation (45) can be expressed as: (47) make Substituting into equation (47), we get: (48) Taking a Laplace transform of equation (48), we obtain the following about and Transfer function: (49) From equation (49), we can see that the characteristic equation of the system is: (50) In the formula Given a sampling rate of 0.001s and a controller sampling period of approximately zero, the sum of series in equation (50) can be expressed as: (51) Substituting equation (51) into equation (50), we get: (52) According to the Routh criterion for linear systems, the Routh array corresponding to equation (52) is: (53) When the coefficients of the characteristic equation have the same sign and the first column of the Routh array is all positive, the system is stable. (54) Will , Substituting, we get: (55) Rearranging equation (55), the impedance parameter... , and All values ​​are positive. The conditions required for the system to be stable are: (56) According to equation (56), when the system update rate When the constraints described in equation (56) are satisfied, the impedance control system based on parameter adaptation is stable.

5. The robot-assisted sewing feeding method based on normal pressure and fabric tension control as described in claim 4, characterized in that, Step four specifically involves: The tracking error of the steady-state force in the aforementioned parameter-adaptive impedance control system is analyzed. The tracking error of the steady-state force is expressed as: (57) When the input signal is a step signal, that is Substituting into equation (57): (58) When the input signal is a sinusoidal signal, that is ,in Representing the signal period, substituting it into equation (57): (59) According to equations (58) and (59), when the input signal is a step signal or a sinusoidal signal, the tracking error of the force after the system reaches steady state is zero, thus achieving accurate tracking of the desired force.

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