Collaborative robot cooperative sewing control method based on model predictive control and disturbance observation technology

Abstract

The invention discloses a collaborative robot collaborative sewing control method based on a model predictive control and disturbance observation technology. The method comprises the steps of performing model equivalence and model discretization processing on a flexible joint collaborative robot; converting the discretization model into a standard output adjustment model; designing a reduced-order GPIO (general purpose input / output) disturbance observer by combining known disturbance information on the basis of the standard output model; and designing a model predictive control law based on the error system after the disturbance information is removed to realize control output. The method can effectively solve the problem that the flexible error cannot be eliminated due to the fact that the collaborative robot is controlled based on the rigid joint model, and the known disturbance information is removed from optimization, so that on the basis that the controller structure is reserved, the requirement for the control law calculation force is reduced, and the control efficiency is improved. The requirement for high-precision position servo of the robot in the sewing cooperation process can be met.

Description

Technical Field

[0001] This invention belongs to the field of advanced manufacturing technology for collaborative robots, and in particular relates to a collaborative sewing control method for collaborative robots based on model predictive control and disturbance observation technology. Background Technology

[0002] With the rapid development of intelligent manufacturing and human-machine collaboration technologies, collaborative robots are increasingly widely used in the textile and apparel industry, especially in automated processes such as sewing collaboration, fabric handling, and material conveying, demonstrating excellent flexibility and intelligent control potential. Collaborative sewing systems typically require multiple robots or robots working in conjunction with humans to complete sewing tasks, such as coordinated control of synchronous fabric feeding and sewing head feed, sewing path tracking, and dynamic adjustment of material tension. These tasks place extremely high demands on the real-time performance, robustness, and accuracy of the control system.

[0003] These technical bottlenecks manifest themselves in several ways: Faced with the nonlinear changes in the physical properties of sewing fabric, the periodic vibrations caused by the high-speed rotation of the sewing machine spindle, and the complex dynamic coupling effects of multi-robot collaborative operations, the response lag and insufficient robustness of traditional control strategies are significantly amplified. The resonance phenomenon caused by joint flexibility not only reduces the trajectory tracking accuracy of the end effector, but its energy transfer may also excite unstable modes in the fabric, exacerbating material deformation or fluctuations in thread tension. Simultaneously, the preset fixed trajectory cannot adapt to the minute slippage or deformation of the sewing fabric that occurs in real time during transport and sewing, leading to a cumulative deviation between the actual stitch and the desired path, affecting the flatness and aesthetics of the final product.

[0004] More importantly, existing methods have significant shortcomings in disturbance observation and compensation mechanisms. The dynamic disturbances inherent in the sewing process are complex and interconnected, including but not limited to abrupt changes in friction between the fabric and the presser foot / feed dogs, load variations caused by different materials or layers of fabric, and motion interference between the robot body and collaborating units. Traditional control architectures typically employ post-event feedback compensation, lacking the ability to effectively identify and model disturbance sources. This makes it difficult to proactively suppress disturbances in their early stages, causing the system to be prone to overshoot, oscillation, or even brief instability when dealing with sudden disturbances, thus hindering the realization of high-speed precision sewing.

[0005] In summary, there is currently a lack of a control method for sewing collaborative robots that can simultaneously handle multiple constraints, provide real-time disturbance compensation, and achieve high-precision predictive control. Summary of the Invention

[0006] Purpose of the Invention: The purpose of this invention is to overcome the technical problems of existing collaborative robot sewing control systems, such as low control accuracy, weak disturbance compensation capability, poor system stability, and imperfect constraint handling. It provides a collaborative robot sewing control method based on model predictive control and disturbance observation technology, achieving high-precision tracking of the sewing path, real-time compensation for multi-source disturbances, and effective constraints on control inputs and system states. This improves the stability, responsiveness, and intelligence of the system in complex dynamic sewing tasks.

[0007] Technical solution: The method described in this invention includes the following steps:

[0008] The elastic force of the collaborative arm itself, combined with its kinematic characteristics, is transformed into an equivalent torque expression of the joint actuator, resulting in an equivalent flexible joint collaborative robot model, which is then discretized.

[0009] Decompose the discrete model, establish an external system model based on known disturbance information, and combine the discrete model and the external system model to generate a standard output regulation model;

[0010] Based on the standard output regulation model, a reduced-order GPIO disturbance observer is designed using known disturbance information to estimate unmodeled disturbances. Combining the known disturbance model and the observed disturbance information, a standard output regulation model without disturbances is established for the observer design, namely the observation-compensated standard output regulation model.

[0011] Design a loss function to constrain the state of the standard output regulation model after observation compensation, and design a model predictive control law. Based on solving the model predictive control law, and combining the known disturbance model and the observed disturbance information, achieve optimal control.

[0012] Furthermore, the discrete model is as follows:

[0013] x1(k+1)=x1(k)+x2(k)△T

[0014]

[0015] Where, k represents the sampling time value, x1 is the joint angle matrix, x2 is the angular velocity matrix, ΔT is the discrete sampling interval time, x1(k+1) and x1(k) are the discrete equivalent angle matrices of the sewing flexible joint collaborative robot at time k+1 and time k, respectively, x2(k) and x2(k+1) are the discrete equivalent angular velocity matrices of the sewing flexible joint collaborative robot at time k and time k+1, respectively, C(x1(k),x2(k)) is the discrete equivalent Coriolis force matrix of the sewing flexible joint collaborative robot at time k, G(x1(k)) is the discrete equivalent gravity matrix of the sewing flexible joint collaborative robot at time k, and M(x1(k)) is the discrete equivalent inertia matrix of the sewing flexible joint collaborative robot at time k.

[0016] Furthermore, the external system model is represented as:

[0017] v(k+1)=A1v(k)

[0018]

[0019] Where, v(k)=[r0(k),r1(k),r2(k),d m (k),G(k),d ext (k)] T Let r0(k), r1(k), and r2(k) represent the external position command signal and its velocity and acceleration at time k, respectively. m (k) represents the disturbance torque experienced by the motor at time k, d ext (k) represents the disturbance torque experienced by the joint side at time k, G(k) represents the gravity torque matrix of the robot's self-weight and load gravity decomposed into the joint space at time k, v(k+1) represents the state value of the external system of the discrete model at the next time step, and ΔT represents the discrete sampling interval time.

[0020] Furthermore, the standard output adjustment model is expressed as:

[0021]

[0022] Where x(k+1) and x(k) are the state matrices of the standard output regulation model at time k+1 and time k, respectively; A is the state transition matrix of the standard output regulation model; B′ is the input transformation matrix of the standard output regulation model; E is the input transformation matrix of the external signal of the standard output regulation model; v(k+1) and v(k) are the external signal matrices of the standard output regulation model at time k+1 and time k, respectively; A1 is the system transition matrix of the external signal of the standard output regulation model; ε(k) is the output error matrix of the standard output regulation model at time k; C is the output transformation matrix of the standard output regulation model; F is the output matrix of the external signal of the standard output regulation model; and u(k) is the input matrix of the standard output regulation model at time k. The specific expressions of A, B′, A1, E, and F are as follows:

[0023]

[0024] Furthermore, based on the standard output regulation model and incorporating known disturbance information, a reduced-order GPIO disturbance observer is designed, including:

[0025] Design a new standard output regulation model based on the standard output regulation model, with state variable z(k) = [x(k)]. T v(k) T ] T The standard output regulation model output variable β(k) = [x(k)] T ε(k) T ] T The standard output regulation model used for observer design is expressed as:

[0026]

[0027] Where z(k+1) and z(k) are the standard output regulation models used for observer design at time k+1 and time k, respectively, and u(k) is the input matrix of the standard output regulation model used for observer design. A z B is the state transition matrix of the standard output regulation model used for observer design. z C is the input transformation matrix for the standard output conditioning model used in observer design. z The standard output adjustment model output transformation matrix is ​​used for observer design, where I is the identity matrix;

[0028] Based on the transformed standard output regulation model used for observer design, the reduced-order GPIO perturbation observer is designed as follows:

[0029]

[0030] Where φ(k+1) and φ(k) are the intermediate variables of the reduced-order GPIO disturbance observer at time k+1 and time k, respectively; P is the state transition matrix of the reduced-order GPIO disturbance observer; G is the observation error correction matrix of the reduced-order GPIO disturbance observer; Π is the input transformation matrix of the reduced-order GPIO disturbance observer; and L is the gain matrix of the reduced-order GPIO disturbance observer. and These are the perturbation matrices estimated by the reduced-order GPIO perturbation observer at time k+1 and time k, respectively.

[0031] Furthermore, the standard output adjustment model after observation compensation is expressed as:

[0032]

[0033] Where ξ(k+1) and ξ(k) are the state matrices of the standard output regulation model after observation compensation at time k+1 and time k, respectively, and x(k+1) and x(k) are the state matrices of the standard output regulation model at time k+1 and time k, respectively. and These are the perturbation matrices estimated by the reduced-order GPIO perturbation observer at time k+1 and time k, respectively. Let δ(k) be the perturbation error matrix of the time-degraded GPIO perturbation observer, and let δ(k) be the equivalent perturbation matrix of the standard output adjustment model.

[0034] Furthermore, the model predictive control law is expressed as:

[0035]

[0036] s.tξ(i+1|k)=Aξ(i|k)+Bμ(i|k)

[0037] ξ(i|k)∈{|ξ(i-1|k)+x r (k)|≤q max}

[0038] μ(i|k)∈{|μ(i-1|k)+u r (k)|≤τ max}

[0039] Where i is the prediction step, N is the prediction step size, J(ξ(k)) is the optimization objective value corresponding to the standard output regulation model state after observation compensation at time k, ξ(i|k) is the state matrix corresponding to the i-th step standard output regulation model state after observation compensation at time k, μ(i|k) is the input matrix corresponding to the i-th step standard output regulation model state after observation compensation at time k, l(ξ(i|k),μ(i|k)) is the loss function of the MPC control law corresponding to the i-th step standard output regulation model state after observation compensation at time k, ξ(i+1|k) is the state matrix corresponding to the (i+1)-th step standard output regulation model state after observation compensation at time k, ξ(i-1|k) is the state matrix corresponding to the (i-1)-th step standard output regulation model state after observation compensation at time k, x r (k) is the state matrix of the standard output conditioning model at time k, and μ(i-1|k) is the input matrix corresponding to the state of the standard output conditioning model at the (i-1)th step after observation compensation at time k. r (k) is the input matrix of the standard output adjustment model at time k.

[0040] Furthermore, optimal control is achieved by solving the model predictive control law, including:

[0041] (1) Discrete model prediction: Measure / estimate the state matrix ξ(k) corresponding to the current standard output regulation model state;

[0042] (2) Predicted output correction: The output error model is predicted based on the standard output adjustment model for observer design without disturbances;

[0043] (3) Calculate the model output: Calculate the output sequence based on the standard output adjustment model and the output error model designed by the observer;

[0044] (4) Optimize model constraints: Solve the optimization problem, i.e. model predictive control law, to obtain the optimal control sequence for the next N steps;

[0045] (5) Derive the control quantity at the next future time step: Apply the control matrix μ corresponding to the state of the adjustment model using the first standard output. * (k)=μ(0|k);

[0046] (6) Shift the time forward by k→k+1, and repeat the above steps; solve for the control signal μ. * (k);

[0047] The external disturbance model information is re-embedded into the controller to obtain the discrete equivalent control input u of the sewing flexible joint collaborative robot at time k. * (k) is:

[0048]

[0049] in, Let u be the perturbation matrix estimated by the reduced-order GPIO perturbation observer at time k. r (k) is the input matrix of the standard output regulation model at time k, and U is the input matrix of the standard output regulation model.

[0050] The system corresponding to the method described in this invention includes:

[0051] The model discretization unit is used to transform the elastic force of the collaborative arm itself, combined with its kinematic characteristics, into an equivalent torque expression of the joint actuator, thereby obtaining an equivalent flexible joint collaborative robot model, and then discretizing the model.

[0052] The model standardization unit is used to decompose the discrete model, establish the discrete model external system model based on known disturbance information, and generate a standard output regulation model by combining the discrete model and the external system model.

[0053] The observation compensation unit is used to design a reduced-order GPIO disturbance observer based on the standard output regulation model and combined with known disturbance information, and to estimate the unmodeled disturbance; combined with the known disturbance model and the observed disturbance information, it establishes a standard output regulation model output error model that does not contain the disturbance for the observer design, i.e., the standard output regulation model after observation compensation.

[0054] An optimized control unit is used to design the loss function, perform constraint transformation on the standard output regulation model state after observation compensation, and design the model predictive control law. Based on solving the model predictive control law, optimal control is achieved by combining the known disturbance model and the observed disturbance information.

[0055] An electronic device for storing and executing the method includes a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor, wherein the computer program / instructions, when executed by the processor, implement the steps of the collaborative robot sewing control method based on model predictive control and disturbance observation technology.

[0056] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are: (1) It can effectively improve the tracking accuracy of the sewing path, enhance the system's ability to suppress external disturbances, and realize the stability of system operation and the rationality of control input; (2) By introducing the model predictive control (MPC) strategy, it can realize the rolling prediction and optimization control of the future state of the collaborative robot, effectively reduce the sewing path error, and improve the trajectory following performance; (3) At the same time, a disturbance observer is designed to estimate the unknown disturbances caused by fabric deformation, tension fluctuations, friction changes, etc. during the sewing process in real time, and introduce them into the control quantity for compensation, thereby enhancing the robustness and anti-interference ability of the system; (4) It can also (5) Explicitly process system state and input constraints to prevent equipment instability caused by excessive control input; (6) Improve the dynamic response performance and steady-state accuracy of the system by using a hierarchical control architecture combined with optimal trajectory generation and feedback correction mechanism; (7) In addition, this method can be extended to output feedback scenarios to adapt to actual working conditions where the state cannot be fully measured, and has good engineering adaptability and deployment flexibility; In summary, this invention can be widely applied to high-precision control tasks such as sewing collaboration, fabric handling, and fabric transportation involving collaborative robots, providing an effective control solution for the textile and apparel industry to achieve intelligent and flexible manufacturing, and has significant practical value and industrial promotion prospects. Attached Figure Description

[0057] Figure 1 This is a flowchart of the method of the present invention;

[0058] Figure 2 This is a structural diagram of the joint of a harmonic reducer;

[0059] Figure 3 This is a diagram showing the composition of joint torques in a collaborative robot.

[0060] Figure 4 It is a model predictive control flowchart;

[0061] Figure 5 It is the overall control signal flow diagram. Detailed Implementation

[0062] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0063] As attached Figure 1 As shown, the collaborative robot sewing control method based on model predictive control and disturbance observation technology of the present invention includes the following steps:

[0064] (1) Equivalence of flexible joint collaborative robot model and model discretization processing.

[0065] First, the forces and kinematic characteristics experienced by the collaborative arm during actual sewing operations are transformed into equivalent torque expressions of joint actuators, thus achieving a unified description of force-motion coupling at the system modeling level. Subsequently, based on the established equivalent flexible joint collaborative robot model, a suitable discretization method (such as the forward Euler method) is used to transform the system into a discrete-time state-space representation to meet the real-time optimization requirements of the subsequent model predictive control law on a digital platform. Further steps include:

[0066] (11) The transmission torque of the flexible joint collaborative robot model is equivalent, and the rigid part and flexible disturbance part of the system are separated.

[0067] A mathematical model of a flexible joint collaborative robot is established based on the Euler-Lagrange method, such as... Figure 2 As shown, the model expression is:

[0068]

[0069] Where q is the angle matrix of the six joints of the collaborative robot, and M(q) is the joint inertia matrix of the collaborative robot. G(q) is the Coriolis force matrix resulting from joint rotation, G(q) is the gravitational torque matrix of the collaborative robot's own weight and load force decomposed into the joint space, and τ is the torque matrix of the harmonic reducer inside the collaborative robot. ext Let τ be the external disturbance torque acting on the joint, B be the inertia matrix of the collaborative robot's joint motors, and D be the damping matrix of the collaborative robot's joint motors. m This is the torque matrix for the joint motor output. This is the joint-side acceleration matrix. This is the joint-side angular velocity matrix. This is the angular acceleration matrix of the drive motor. Here is the angular acceleration matrix of the drive motor. After equivalent elimination of the transmission torque τ, the equivalent flexible joint collaborative robot model is obtained as follows:

[0070]

[0071] This equation can be divided into a rigid dynamic part and a flexible disturbance part caused by the flexibility of the harmonic reducer:

[0072]

[0073] Where, τ dis It is a flexible disturbance torque.

[0074] (12) Establish a discrete equivalent collaborative robot model for sewing flexible joints (referred to as the discrete model);

[0075] For the discrete equivalent collaborative robot model of a flexible joint sewing machine, define new state variables. Then, by using the forward Euler method with a zero-order hold and the discrete sampling interval ΔT, the discrete model of equation (2) can be obtained as follows:

[0076]

[0077] Where k represents the sampling time value, x1 is the joint angle matrix, x2 is the angular velocity matrix, ΔT is the discrete sampling interval time, x1(k+1) is the discrete equivalent angle matrix of the sewing flexible joint collaborative robot at time k+1, x1(k) is the discrete equivalent angle matrix of the sewing flexible joint collaborative robot at time k, x2(k) is the discrete equivalent angular velocity matrix of the sewing flexible joint collaborative robot at time k, x2(k+1) is the discrete equivalent angular velocity matrix of the sewing flexible joint collaborative robot at time k+1, C(x1(k),x2(k)) is the discrete equivalent Coriolis force matrix of the sewing flexible joint collaborative robot at time k, G(x1(k)) is the discrete equivalent gravity matrix of the sewing flexible joint collaborative robot at time k, and M(x1(k)) is the discrete equivalent inertia matrix of the sewing flexible joint collaborative robot at time k.

[0078] (2) Modeling with known disturbance information, converting the discrete model into a standard output adjustment model.

[0079] The discrete model is converted into a standardized output regulation model, simplifying control design by separating system dynamics from external disturbance information. An error state is defined, and a standard output regulation framework is constructed. Parameter design ensures that the system can progressively track external commands and effectively suppress disturbances, while also incorporating the known Coulomb friction τ. cf Viscous friction τ vf Gravity change τ c Flexibility variation τ of harmonic reducer g Disturbance information see Figure 3 By separating observations from computation, the complexity of the observer is reduced, thus decreasing the computational burden on the controller. This transformation provides theoretical support for achieving high-precision position control in collaborative robots, balancing control performance and computational efficiency. Further steps include:

[0080] (21) Decompose the discrete model and establish the discrete model external system model based on the known disturbance information;

[0081] Based on the discrete model established in step (1), the error state ε(k) = y(k) - v(k) is defined, where y(k) is the observed output signal, including the motor position and joint position, and v(k) = [r0(k), r1(k), r2(k), d m (k),G(k),d ext (k)] TThis represents the current state of the discrete model's external source system, specifically the state of the discrete model's external source system at time k, which is the external signal caused by external input or disturbance. Here, r0(k), r1(k), and r2(k) represent the external position command signal at time k, along with its velocity and acceleration, respectively. m (k) represents the disturbance torque experienced by the motor at time k, d ext Let G(k) be the disturbance torque experienced by the joint at time k, and G(k) be the gravitational torque matrix of the robot's self-weight and load gravity decomposed into the joint space at time k. Then the external signal satisfies:

[0082]

[0083] Where v(k+1) represents the state value of the external source system in the discrete model at the next time step, that is, the state of the external source system in the discrete model at time k+1.

[0084] (22) Generate a standard output regulation model based on discrete model and external system model;

[0085] Based on the known Denavit-Hartenberg parameters of the sewing collaborative arm DH, the gravitational torque data G(k) at time k and the command angle, angular velocity, and angular acceleration data r0(k), r1(k), and r2(k) at time k can be calculated using the joint angle data and the robot's forward dynamics in equation (5). The signal in equation (5) is an external signal that can be separated from the state variables, thereby establishing a discrete equivalent standard output adjustment model for a sewing flexible joint collaborative robot (referred to as the standard output adjustment model):

[0086]

[0087] Where x(k+1) and x(k) are the state matrices of the standard output regulation model at time k+1 and time k, respectively; A is the state transition matrix of the standard output regulation model; B′ is the input transformation matrix of the standard output regulation model; E is the input transformation matrix of the external signal of the standard output regulation model; v(k+1) and v(k) are the external signal matrices of the standard output regulation model at time k+1 and time k, respectively; A1 is the system transition matrix of the external signal of the standard output regulation model; ε(k) is the output error matrix of the standard output regulation model at time k; C is the output transformation matrix of the standard output regulation model; F is the output matrix of the external signal of the standard output regulation model; and u(k) is the input matrix of the standard output regulation model at time k. The specific expressions of A, B, A1, E, and F are as follows:

[0088]

[0089] Based on the standard output regulation model form, we can obtain the standard output regulation model equation (6) which satisfies:

[0090]

[0091] Where X is the state matrix of the standard output regulation model, and U is the input matrix of the standard output regulation model.

[0092] When equation (8) has a solution, we have:

[0093]

[0094] (3) Based on the standard output regulation model, a reduced-order GPIO (generalized proportional-integral observer) disturbance observer is designed in combination with known disturbance information.

[0095] By incorporating known disturbance information from the standard output regulation model, a reduced-order generalized proportional-integral (GPIO) observer is designed, focusing on estimating unmodeled disturbances. Its core lies in eliminating redundant calculations for known disturbances and dynamically adjusting the observer gain using the output error of the standard output regulation model to infer unknown disturbances on the motor or joint side in real time. This design, by reducing observer complexity, provides accurate disturbance compensation data to the controller while ensuring stability and fast convergence, significantly improving the system's anti-interference capability and control accuracy, meeting the high-precision position servo requirements of collaborative robots. Further steps include:

[0096] (31) Based on the standard output regulation model, design a reduced-order GPIO (generalized proportional-integral observer) disturbance observer;

[0097] In the external disturbance information, the command reference signal has cubic polynomial characteristics and can be directly obtained from the controller. Model uncertainty and external disturbance signals need to be obtained using an observer. Based on the standard output regulation model formula (6) established in step (22), a new standard output regulation model state variable z(k) = [x(k)] is designed. T v(k) T ] T The standard output regulation model output variable β(k) = [x(k)] T ε(k) T ] T Then there is a standard output regulation model for observer design:

[0098]

[0099] Where z(k+1) and z(k) are the standard output regulation models used for observer design at time k+1 and time k, respectively, and u(k) is the input matrix of the standard output regulation model used for observer design. A z B is the state transition matrix of the standard output regulation model used for observer design. zC is the input transformation matrix for the standard output conditioning model used in observer design. z Let I be the output transformation matrix of the standard output conditioning model used for observer design, and let I be the identity matrix. Then:

[0100]

[0101] Based on the transformed standard output regulation model (10) for observer design, a reduced-order GPIO (generalized proportional-integral observer) perturbation observer is designed:

[0102]

[0103] Where φ(k+1) and φ(k) are the intermediate variables of the reduced-order GPIO disturbance observer at time k+1 and time k, respectively; P is the state transition matrix of the reduced-order GPIO disturbance observer; G is the observation error correction matrix of the reduced-order GPIO disturbance observer; Π is the input transformation matrix of the reduced-order GPIO disturbance observer; and L is the gain matrix of the reduced-order GPIO disturbance observer. and These are the perturbation matrices estimated by the reduced-order GPIO perturbation observer at time k+1 and time k, respectively. The matrix definitions are as follows.

[0104]

[0105] (32) Combining the known disturbance model and the observed disturbance information, establish a standard output adjustment model for observer design that does not contain disturbances, i.e., the standard output adjustment model after observation compensation.

[0106] Through experiments, selecting the observer gain L allows the observation error to asymptotically converge to 0. This is achieved using the standard output regulation model system input and the standard output regulation model reference signal matrix for observer design. x r (k) is the reference signal matrix of the standard output regulation model used for observer design. Let u be the perturbation matrix estimated by the reduced-order GPIO perturbation observer at time k. r (k) is the input matrix of the standard output regulation model used for observer design. Furthermore, a new observation-compensated state variable for the standard output regulation model can be defined, and the observation-compensated state error matrix of the standard output regulation model is ξ(k) = x(k) - x. r (k), x(k) and x r (k) represents the state matrix and state reference matrix of the standard output regulation model, respectively, and the control error matrix of the standard output regulation model after observation compensation is μ(k) = u(k) - u r (k), u(k) and u r(k) represents the input matrix and input reference matrix of the standard output regulation model, respectively. The standard output regulation model after observation compensation is:

[0107]

[0108] Where ξ(k+1) and ξ(k) are the state matrices of the standard output regulation model after observation compensation at time k+1 and time k, respectively, and x(k+1) and x(k) are the state matrices of the standard output regulation model at time k+1 and time k, respectively. and These are the perturbation matrices estimated by the reduced-order GPIO perturbation observer at time k+1 and time k, respectively. Let δ(k) be the perturbation error matrix of the time-degraded GPIO perturbation observer, and let δ(k) be the equivalent perturbation matrix of the standard output adjustment model.

[0109] (4) Based on the standard output adjustment model after observation compensation, establish an error model and design a model predictive control law to finally realize the calculation control output.

[0110] Based on the error system after disturbance removal, a model predictive control law is designed to achieve precise control output. Its core lies in utilizing the observed and compensated standard output to adjust the model. By predicting the behavior of the adjusted standard output after future observations and continuously optimizing the control input, the output quickly tracks the target command. Since the disturbance information has been separated and compensated by the observer, the controller does not need to repeatedly process known disturbances, significantly reducing computational complexity while improving dynamic response speed and tracking accuracy. This method balances real-time performance and robustness, meeting the stringent requirements of collaborative robots for high-precision position servoing in complex tasks such as sewing. Further, the following steps are included:

[0111] (41) Establish an error model and adjust the constraint transformation of the model state based on its loss function and the standard output after observation compensation;

[0112] By transforming the state error, the output following problem is converted into a stabilization problem of the standard output-adjusted model state ξ(k) at time k after observation compensation. The control objective is designed as convergence of both the state error and the control error, so the loss function l(ξ(k), μ(k)) of the MPC (Model Predictive Control) control law can be designed as follows:

[0113]

[0114] The objective of the loss function is to minimize both the state error and the control input of the observation-compensated standard output regulation model. Here, Q and R are the weight matrices for the state error and control error of the observation-compensated standard output regulation model, respectively. Simultaneously, for the state of the discrete equivalent sewing flexible joint collaborative robot, there exists a constraint: the joints of the discrete equivalent sewing flexible joint collaborative robot must satisfy the maximum joint angle constraint q. max To ensure the end effector does not exceed the working space, the joint torque must be less than the motor's maximum output torque τ. max Therefore, the design optimization objective J is:

[0115]

[0116] Where i is the prediction step, N is the prediction step size, J(ξ(k)) is the optimization objective value corresponding to the standard output regulation model state after observation compensation at time k, ξ(i|k) is the state matrix corresponding to the i-th step standard output regulation model state after observation compensation at time k, μ(i|k) is the input matrix corresponding to the i-th step standard output regulation model state after observation compensation at time k, l(ξ(i|k),μ(i|k)) is the loss function of the MPC (Model Predictive Control) control law corresponding to the i-th step standard output regulation model state after observation compensation at time k, ξ(i+1|k) is the state matrix corresponding to the (i+1)-th step standard output regulation model state after observation compensation at time k, ξ(i-1|k) is the state matrix corresponding to the (i-1)-th step standard output regulation model state after observation compensation at time k, x r (k) is the state matrix of the standard output conditioning model at time k, and μ(i-1|k) is the input matrix corresponding to the state of the standard output conditioning model at the (i-1)th step after observation compensation at time k. r (k) is the input matrix of the standard output adjustment model at time k.

[0117] (42) Design the model predictive control law, solve for the control output and calculate the control output;

[0118] Based on the designed optimization objective J, the optimization problem is solved at each control time k, such as... Figure 4 As shown, it includes the following steps:

[0119] (1) Discrete model prediction: Measure / estimate the state matrix ξ(k) corresponding to the current discrete equivalent flexible joint collaborative robot standard output adjustment model state;

[0120] (2) Predicted output correction: The output error model is predicted based on the standard output adjustment model of the discrete equivalent sewing flexible joint collaborative robot for observer design without perturbation;

[0121] (3) Calculation model output: The standard output adjustment model of the discrete equivalent sewing flexible joint collaborative robot based on the observer design calculates the output sequence of the error model;

[0122] (4) Optimize model constraints: Solve the optimization problem equation (16) to obtain the optimal control sequence for the next N steps;

[0123] (5) Deriving the control quantity at a future moment: Apply the control matrix μ corresponding to the state of the standard output adjustment model of the first discrete equivalent sewing flexible joint collaborative robot. * (k)=μ(0|k);

[0124] (6) Move the time forward by k→k+1 and repeat the above steps.

[0125] Based on the design optimization objective (16), the control signal μ can be solved through the above steps (1)-(6), i.e., the MPC (Model Predictive Control) method. * (k). Furthermore, by re-embedding the discrete model of the external system into the control results, the discrete equivalent control input u of the collaborative sewing flexible joint robot at time k can be calculated. * (k) is:

[0126]

[0127] The final overall control structure of the system is as follows: Figure 5 As shown, the dynamic model of the flexible joint collaborative robot is first discretized and converted into a standard output regulation model, where X is the state matrix of the discrete equivalent standard output regulation model of the flexible joint collaborative robot and U is the input matrix of the discrete equivalent standard output regulation model of the flexible joint collaborative robot, in order to separate the system state from known disturbances (such as friction, gravity, and reference input r(k)); then, a reduced-order GPIO (generalized proportional-integral observer) is designed. The disturbance estimated by the reduced-order GPIO (Generalized Proportional-Integral Observer) disturbance observer at time k is used to estimate unknown disturbances such as fabric deformation and tension fluctuations in real time and perform dynamic compensation. Then, a prediction model is established based on the compensated error state, x(k) and x... r(k) The state error matrix ξ(k) of the standard output adjustment model of the discrete equivalent sewing flexible joint collaborative robot after observation compensation at time k is calculated using the state matrix and state reference matrix of the standard output adjustment model. The future multi-step trajectory is then optimized using Model Predictive Control Law (MPC) rolling optimization to solve for the optimal control sequence μ(k) under the constraints of joint angles and torques. Finally, the optimization result is embedded into the external system to generate the driving signal, achieving high-precision sewing path tracking and anti-interference collaborative operation of the collaborative robot. The entire process, through a closed-loop architecture of modeling to separate disturbances, real-time observer compensation, and MPC rolling optimization, significantly improves the accuracy and robustness of the system in dynamic sewing tasks.

[0128] The system corresponding to the method described in this invention includes:

[0129] The model discretization unit is used to transform the elastic force of the collaborative arm itself, combined with its kinematic characteristics, into an equivalent torque expression of the joint actuator, thereby obtaining an equivalent flexible joint collaborative robot model, and then discretizing the model.

[0130] The model standardization unit is used to decompose the discrete model, establish the discrete model external system model based on known disturbance information, and generate a standard output regulation model by combining the discrete model and the external system model.

[0131] The observation compensation unit is used to design a reduced-order GPIO disturbance observer based on the standard output regulation model and combined with known disturbance information, and to estimate the unmodeled disturbance; combined with the known disturbance model and the observed disturbance information, it establishes a standard output regulation model output error model that does not contain the disturbance for the observer design, i.e., the standard output regulation model after observation compensation.

[0132] An optimized control unit is used to design the loss function, perform constraint transformation on the standard output regulation model state after observation compensation, and design the model predictive control law. Based on solving the model predictive control law, optimal control is achieved by combining the known disturbance model and the observed disturbance information.

[0133] An electronic device for storing and executing the method includes a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor, wherein the computer program / instructions, when executed by the processor, implement the steps of the collaborative robot sewing control method based on model predictive control and disturbance observation technology.

[0134] It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technology.

Claims

1. A collaborative robot sewing control method based on model predictive control and disturbance observation technology, characterized in that, Includes the following steps: The elastic force of the collaborative arm itself, combined with its kinematic characteristics, is transformed into an equivalent torque expression of the joint actuator, resulting in an equivalent flexible joint collaborative robot model, which is then discretized. Decompose the discrete model, establish an external system model based on known disturbance information, and combine the discrete model and the external system model to generate a standard output regulation model; Based on the standard output regulation model, a reduced-order GPIO disturbance observer is designed using known disturbance information to estimate unmodeled disturbances. Combining the known disturbance model and the observed disturbance information, a standard output regulation model without disturbances is established for the observer design, namely the observation-compensated standard output regulation model. Design a loss function to constrain the state of the standard output regulation model after observation compensation, and design a model predictive control law. Based on solving the model predictive control law, and combining the known disturbance model and the observed disturbance information, achieve optimal control.

2. The collaborative robot sewing control method based on model predictive control and disturbance observation technology according to claim 1, characterized in that, The discrete model is: x1(k+1)=x1(k)+x2(k)△T Where, k represents the sampling time value, x1 is the joint angle matrix, x2 is the angular velocity matrix, ΔT is the discrete sampling interval time, x1(k+1) and x1(k) are the discrete equivalent angle matrices of the sewing flexible joint collaborative robot at time k+1 and time k, respectively, x2(k) and x2(k+1) are the discrete equivalent angular velocity matrices of the sewing flexible joint collaborative robot at time k and time k+1, respectively, C(x1(k),x2(k)) is the discrete equivalent Coriolis force matrix of the sewing flexible joint collaborative robot at time k, G(x1(k)) is the discrete equivalent gravity matrix of the sewing flexible joint collaborative robot at time k, and M(x1(k)) is the discrete equivalent inertia matrix of the sewing flexible joint collaborative robot at time k.

3. The collaborative robot sewing control method based on model predictive control and disturbance observation technology according to claim 1, characterized in that, The external system model is represented as: v(k+1)=A1v(k) Where, v(k)=[r0(k),r1(k),r2(k),d m (k),G(k),d ext (k)] T Let r0(k), r1(k), and r2(k) represent the external position command signal and its velocity and acceleration at time k, respectively. m (k) represents the disturbance torque experienced by the motor at time k, d ext (k) represents the disturbance torque experienced by the joint side at time k, G(k) represents the gravity torque matrix of the robot's self-weight and load gravity decomposed into the joint space at time k, v(k+1) represents the state value of the external system of the discrete model at the next time step, and ΔT represents the discrete sampling interval time.

4. The collaborative robot sewing control method based on model predictive control and disturbance observation technology according to claim 1, characterized in that, The standard output regulation model is expressed as: Where x(k+1) and x(k) are the state matrices of the standard output regulation model at time k+1 and time k, respectively; A is the state transition matrix of the standard output regulation model; B′ is the input transformation matrix of the standard output regulation model; E is the input transformation matrix of the external signal of the standard output regulation model; v(k+1) and v(k) are the external signal matrices of the standard output regulation model at time k+1 and time k, respectively; A1 is the system transition matrix of the external signal of the standard output regulation model; ε(k) is the output error matrix of the standard output regulation model at time k; C is the output transformation matrix of the standard output regulation model; F is the output matrix of the external signal of the standard output regulation model; and u(k) is the input matrix of the standard output regulation model at time k. The specific expressions of A, B′, A1, E, and F are as follows: F＝[-1 0 0 0]。 5. The collaborative robot sewing control method based on model predictive control and disturbance observation technology according to claim 1, characterized in that, Based on the standard output regulation model and incorporating known disturbance information, a reduced-order GPIO disturbance observer is designed, including: Design a new standard output regulation model based on the standard output regulation model, with state variable z(k) = [x(k)]. T v(k) T ] T The standard output regulation model output variable β(k) = [x(k)] T ε(k) T ] T The standard output regulation model used for observer design is expressed as: Where z(k+1) and z(k) are the standard output regulation models used for observer design at time k+1 and time k, respectively, and u(k) is the input matrix of the standard output regulation model used for observer design. A z B is the state transition matrix of the standard output regulation model used for observer design. z C is the input transformation matrix for the standard output conditioning model used in observer design. z The standard output adjustment model output transformation matrix is ​​used for observer design, where I is the identity matrix; Based on the transformed standard output regulation model used for observer design, the reduced-order GPIO perturbation observer is designed as follows: Where φ(k+1) and φ(k) are the intermediate variables of the reduced-order GPIO disturbance observer at time k+1 and time k, respectively; P is the state transition matrix of the reduced-order GPIO disturbance observer; G is the observation error correction matrix of the reduced-order GPIO disturbance observer; Π is the input transformation matrix of the reduced-order GPIO disturbance observer; and L is the gain matrix of the reduced-order GPIO disturbance observer. and These are the perturbation matrices estimated by the reduced-order GPIO perturbation observer at time k+1 and time k, respectively.

6. The collaborative robot sewing control method based on model predictive control and disturbance observation technology according to claim 1, characterized in that, The standard output adjustment model after observation compensation is expressed as: Where ξ(k+1) and ξ(k) are the state matrices of the standard output regulation model after observation compensation at time k+1 and time k, respectively, and x(k+1) and x(k) are the state matrices of the standard output regulation model at time k+1 and time k, respectively. and These are the perturbation matrices estimated by the reduced-order GPIO perturbation observer at time k+1 and time k, respectively. Let δ(k) be the perturbation error matrix of the time-degraded GPIO perturbation observer, and let δ(k) be the equivalent perturbation matrix of the standard output adjustment model.

7. The collaborative robot sewing control method based on model predictive control and disturbance observation technology according to claim 1, characterized in that, The model predictive control law is expressed as: Where i is the prediction step, N is the prediction step size, J(ξ(k)) is the optimization objective value corresponding to the standard output regulation model state after observation compensation at time k, ξ(i|k) is the state matrix corresponding to the i-th step standard output regulation model state after observation compensation at time k, μ(i|k) is the input matrix corresponding to the i-th step standard output regulation model state after observation compensation at time k, l(ξ(i|k),μ(i|k)) is the loss function of the MPC control law corresponding to the i-th step standard output regulation model state after observation compensation at time k, ξ(i+1|k) is the state matrix corresponding to the (i+1)-th step standard output regulation model state after observation compensation at time k, ξ(i-1|k) is the state matrix corresponding to the (i-1)-th step standard output regulation model state after observation compensation at time k, x r (k) is the state matrix of the standard output conditioning model at time k, and μ(i-1|k) is the input matrix corresponding to the state of the standard output conditioning model at the (i-1)th step after observation compensation at time k. r (k) is the input matrix of the standard output adjustment model at time k.

8. The collaborative robot sewing control method based on model predictive control and disturbance observation technology according to claim 1, characterized in that, Solving the model predictive control law to achieve optimal control includes: (1) Discrete model prediction: Measure / estimate the state matrix ξ(k) corresponding to the current standard output regulation model state; (2) Predicted output correction: The output error model is predicted based on the standard output adjustment model for observer design without disturbances; (3) Calculate the model output: Calculate the output sequence based on the standard output adjustment model and the output error model designed by the observer; (4) Optimize model constraints: Solve the optimization problem, i.e. model predictive control law, to obtain the optimal control sequence for the next N steps; (5) Derive the control quantity at the next future time step: Apply the control matrix μ corresponding to the state of the adjustment model using the first standard output. * (k)=μ(0|k); (6) Shift the time forward by k→k+1, and repeat the above steps; solve for the control signal μ. * (k); The external disturbance model information is re-embedded into the controller to obtain the discrete equivalent control input u of the sewing flexible joint collaborative robot at time k. * (k) is: in, Let u be the perturbation matrix estimated by the reduced-order GPIO perturbation observer at time k. r (k) is the input matrix of the standard output regulation model at time k, and U is the input matrix of the standard output regulation model.

9. A collaborative robot sewing control system based on model predictive control and disturbance observation technology, characterized in that, include: The model discretization unit is used to transform the elastic force of the collaborative arm itself, combined with its kinematic characteristics, into an equivalent torque expression of the joint actuator, thereby obtaining an equivalent flexible joint collaborative robot model, and then discretizing the model. The model standardization unit is used to decompose the discrete model, establish the discrete model external system model based on known disturbance information, and generate a standard output regulation model by combining the discrete model and the external system model. The observation compensation unit is used to design a reduced-order GPIO disturbance observer based on the standard output regulation model and combined with known disturbance information, and to estimate the unmodeled disturbance; combined with the known disturbance model and the observed disturbance information, it establishes a standard output regulation model output error model that does not contain the disturbance for the observer design, i.e., the standard output regulation model after observation compensation. An optimized control unit is used to design the loss function, perform constraint transformation on the standard output regulation model state after observation compensation, and design the model predictive control law. Based on solving the model predictive control law, optimal control is achieved by combining the known disturbance model and the observed disturbance information.

10. An electronic device, characterized in that, It includes a memory, a processor, and a computer program / instruction stored in the memory and executable on the processor, wherein the computer program / instruction, when executed by the processor, implements the steps of the collaborative robot cooperative sewing control method based on model predictive control and disturbance observation technology according to any one of claims 1-8.

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