Double-arm cooperative material rolling automatic feeding method

Abstract

The application belongs to the technical field of mechanical arms, and particularly relates to a double-arm cooperative roll material automatic feeding method, which comprises the following steps: establishing a constraint coupling model to describe the internal force transmission relationship between the double arms and the roll material; adopting Kalman filtering to realize real-time tracking of the gravity center of the roll material; performing dynamic distribution of cooperative force based on the principle of torque balance; applying adaptive notch filtering to perform vibration monitoring and active suppression; and adopting motor current slope and position deviation double criteria to perform jam detection and cooperating with a hierarchical protection strategy to perform cooperative response. Through the above technical scheme, the cooperative control precision is improved from 2 to 3 millimeters to 0.5 millimeters or below, the vibration attenuation rate is above 85%, the jam response time is reduced to 5 milliseconds or below, and the precision and stability of the double-arm cooperative roll material feeding operation are improved.

Description

Technical Field

[0001] This invention belongs to the field of robotic arm technology, specifically a dual-arm collaborative automatic feeding method for coiled materials. Background Technology

[0002] Dual-arm collaborative automatic roll feeding is a core transfer process in industrial automation production lines such as textiles, steel, and papermaking. The synchronization accuracy of the movement trajectory and posture of the two robotic arms, as well as their load adaptability, directly determine the stability, safety, and overall cycle efficiency of the roll handling process.

[0003] Currently, the dual-arm collaborative control of industrial coil feeding generally adopts a synchronization strategy of fixed time offset or fixed position interpolation, relying on preset fixed phase difference and trajectory parameters to complete the collaborative trajectory planning and following motion of the two robotic arms.

[0004] Existing fixed-parameter collaborative control strategies have inherent technical defects that cannot adapt to the dynamic load conditions of rolled materials. They cannot respond in real time to sudden load changes caused by mass and center of gravity shifts during rolled material handling. Under high-speed transfer conditions, problems such as misalignment of the two arms, uneven material stress, and roll slippage and falling are very likely to occur. Fixed-parameter algorithms lack dynamic adaptive correction capabilities, which completely restricts the high-precision and high-stability automated operation level of the dual-arm collaborative rolled material feeding process.

[0005] Therefore, the present invention provides an automatic feeding method for dual-arm cooperative coiled material. Summary of the Invention

[0006] In order to overcome the shortcomings of the prior art, at least one technical problem raised in the background art is solved.

[0007] The technical solution adopted by this invention to solve its technical problem is: a dual-arm cooperative automatic feeding method for coiled material, comprising the following steps:

[0008] Step 1: Real-time perception and modeling of the coil constraint state. Based on the physical coupling closed-loop constraint system formed by the double-arm clamping the coil, the real-time position parameters, velocity parameters, acceleration parameters of each joint of the double arms, and the real-time clamping force parameters of the grippers are obtained. The coil is regarded as a constraint medium with elasticity and internal stress rather than an ideal rigid body. By fusing the data collected by force sensors and position sensors, a constraint coupling model describing the dynamic coupling relationship between the double arms and the coil is constructed. This constraint coupling model takes the elastic modulus, Poisson's ratio, geometric dimensions of the coil, and the relative attitude of the double arms as input variables, and outputs the constraint reaction force distribution and internal force transfer function between the double arms, providing a precise physical basis for subsequent attitude coordination adjustment.

[0009] Step 2: Dynamically estimate and track the center of gravity of the coil. Based on the constraint coupling model obtained in Step 1, and combined with the spatial coordinates and clamping force vectors of the dual-arm grippers, calculate the real-time position coordinates and offset of the current center of gravity of the coil in three-dimensional space. Based on the mass distribution characteristics and rotational inertia of the coil, establish a recursive equation for the change of the center of gravity position with the clamping posture. Use the Kalman filter algorithm to suppress noise and update the estimated center of gravity value, so that the center of gravity estimation accuracy reaches the sub-millimeter level and the center of gravity tracking delay is controlled within 5 milliseconds, providing an accurate center of gravity reference for the dynamic distribution of the dual-arm cooperative force.

[0010] Step 3: Perform dynamic distribution and attitude adjustment of the synergistic force of the two arms. Based on the center of gravity tracking results output in Step 2, the two arms are regarded as a coordinated motion whole coupled with the coil. The total clamping force required to maintain stable clamping of the coil is calculated. According to the center of gravity offset, the total clamping force is dynamically distributed to each gripper of the two arms according to the torque balance principle. The clamping force ratio and motion compensation amount to be borne by each arm are determined. By adjusting the output torque and motion trajectory of the drive motor of the two arm joints, the coordinated redistribution of the clamping force of the two arms is realized, so that the coil is evenly stressed and the center of gravity is always located within the support plane formed by the two arms.

[0011] Step 4: Conduct online monitoring and suppression control of constrained vibration. During the coordinated movement of the two arms, monitor the internal force fluctuation signal in the constrained coupling model in real time, extract the frequency components and amplitude changes of the internal force signal, identify the system's natural frequency vibration component caused by the elasticity of the constraint interface, and actively suppress the vibration by injecting a damping compensation signal with the opposite phase to the vibration into the control loop of the two arms. The amplitude of the damping compensation signal is adaptively adjusted according to the real-time monitoring results of the vibration energy until the vibration energy decays to the preset safe range.

[0012] Step 5: Perform rapid detection and coordinated response processing for foreign object obstruction. During the movement of the double-arm clamping the coil to the target station, monitor the current changes and position deviations of the drive motors of the double-arm joints in real time. When foreign object obstruction causes a sharp increase in impact force, calculate the redistribution of the constraint reaction force of the double arms after the obstruction occurs based on the obstruction resistance transmission path determined by the constraint coupling model established in Step 1. Quickly adjust the coordinated movement strategy of the double arms to unload the clamping jaw on the obstructing side to the preset safety force threshold within milliseconds, while increasing the clamping force of the clamping jaw on the other side to maintain the stable clamping state of the coil and prevent the coil from slipping and falling.

[0013] Preferably, the constraint coupling model is constructed using a distributed parameter modeling method, which divides the coil into multiple micro-segments along its length. Each micro-segment is considered as a constraint unit with independent elastic deformation. Constraint relationships are established between adjacent micro-segments through elastic connections. The contact area between the grippers of the two arms and the coil is discretized into several contact nodes. The position coordinates and force state of each contact node are used as boundary conditions of the constraint coupling model. By solving the elastic deformation equations of all micro-segments and the force balance equations of the contact nodes, the internal force transfer function matrix between the two arms is obtained. This internal force transfer function matrix describes how the excitation generated by the movement of one arm is transferred to the other arm through the coil and causes a constraint response.

[0014] Preferably, the dynamic estimation of the center of gravity adopts a joint estimation algorithm of recursive least squares method and extended Kalman filter. The recursive least squares method updates the estimated value of the center of gravity in real time based on the spatial coordinates of the dual-arm grippers and the clamping force vector. The extended Kalman filter algorithm introduces the statistical characteristics of system process noise and measurement noise on the basis of recursive least squares method to perform optimal fusion of the estimated value of the center of gravity. When the weight distribution of the coil changes abruptly or the clamping posture of the dual arms changes rapidly, the extended Kalman filter can quickly converge to the new steady-state estimate, with the estimation error controlled within ±1 mm and the estimation update cycle of 2 milliseconds, which meets the real-time requirements.

[0015] Preferably, the dynamic distribution of the collaborative force adopts a fusion strategy of impedance control and force-position hybrid control. Impedance control equates the dynamic constraint relationship between the two arms and the coil to a spring-damped system. By adjusting the equivalent stiffness and damping coefficient, the movement trajectory of the two arms can be flexibly adjusted. Force-position hybrid control plans the movement path of the two arms according to the spatial constraints of the target workstation, under the premise of meeting the clamping force requirements. When the center of gravity offset exceeds the preset threshold, the collaborative force distribution module calculates the compensation displacement of the gripper of the two arms according to the offset direction and offset. By adjusting the position command of the joint motor, the compensation displacement is executed, realizing the real-time redistribution of the clamping force.

[0016] Preferably, the vibration monitoring uses an adaptive notch filter for active vibration suppression. The center frequency of the adaptive notch filter is automatically adjusted based on the real-time estimation result of the system's natural frequency. The estimation of the natural frequency uses a combination of spectrum analysis and the Prony algorithm to extract the frequency and damping ratio of the dominant vibration mode from the internal force fluctuation signal. When multiple vibration modes are detected to coexist, the adaptive notch filter generates a notch combination with multiple frequency points to suppress each vibration component simultaneously. The suppression response time is controlled within 10 milliseconds, and the vibration attenuation rate is greater than 85%.

[0017] Preferably, the foreign object jamming detection uses a dual criterion of joint motor current slope detection and position deviation threshold detection. The joint motor current slope reflects the rate of change of motor output torque. When foreign object jamming occurs, the motor current slope on the jamming side rises sharply to 5 to 10 times the normal value within 1 millisecond. The position deviation threshold detection monitors the deviation between the actual position of the joint and the target position. When the deviation accumulates to more than 0.5 mm within 3 milliseconds, jamming is determined to have occurred. The AND logic operation of the dual criteria ensures the reliability of jamming detection, and the false alarm rate is controlled below 0.1%.

[0018] Preferably, the collaborative response processing adopts a hierarchical protection strategy. The first level of protection immediately reduces the output torque of the clamping jaws on the jamming side to a safe threshold after detecting a jamming signal. The safe threshold is 30% to 40% of the normal clamping torque, maintaining the basic clamping state of the coil and preventing the core from being crushed. The second level of protection evaluates the stability of the coil within 5 milliseconds after the execution of the first level of protection. If it is determined that the coil is in an unstable state, the coil release procedure is initiated to place the coil at the nearest emergency station. The third level of protection records the location and time information of the jamming after the coil is released, providing data support for subsequent station optimization and fault diagnosis.

[0019] Preferably, the gripper is designed with an adaptive deformation gripping surface, which is composed of multiple independent elastic fingers. Each elastic finger has a pressure sensor array on its inner side. The elastic fingers can adaptively deform according to the curvature of the roll surface, so that the gripping force is evenly distributed on the roll surface. The pressure sensor array collects the contact pressure of each elastic finger in real time, and the standard deviation of the pressure distribution is controlled within 15% of the average pressure. When the pressure of a certain elastic finger exceeds twice the average pressure of the adjacent elastic fingers, the control module automatically adjusts the driving current of the elastic finger to achieve pressure balance.

[0020] Preferably, the control logic of the dual-arm cooperative automatic feeding method of the present invention follows the following technical process during application: First, the physical coupling state between the dual arms and the coil is perceived in real time through a constraint coupling model, and the constraint reaction force and internal force transmission path are identified; then, the precise position of the coil's center of gravity is obtained through dynamic estimation of the center of gravity, providing a benchmark for the distribution of cooperative force; next, the coordinated redistribution of the clamping force of the dual arms is realized through the dynamic distribution of cooperative force, so that the coil is subjected to uniform force; then, the system vibration caused by the elasticity of the constraint interface is eliminated through vibration monitoring and suppression control; finally, the operation safety is ensured through rapid detection and cooperative response processing of foreign object obstruction. The various technical links are interconnected and work together to form a complete dual-arm cooperative control closed loop.

[0021] Preferably, the present invention also provides a dual-arm cooperative automatic feeding system for coiled materials, including a first robotic arm and a second robotic arm. Both the first and second robotic arms have multiple joint degrees of freedom, and each joint is equipped with a position sensor, a speed sensor, and a torque sensor. Adaptive deformation grippers are respectively installed at the ends of the first and second robotic arms, and each gripper is equipped with a pressure sensor array. The system also includes a controller, which is communicatively connected to the first robotic arm, the second robotic arm, and the pressure sensor array. The controller internally stores a constraint coupling model algorithm module, a center of gravity dynamic estimation algorithm module, a cooperative force distribution algorithm module, a vibration suppression algorithm module, and a jamming detection algorithm module. The controller executes the corresponding algorithm modules based on the data collected by each sensor and outputs control commands to drive the first and second robotic arms to achieve cooperative movement.

[0022] The beneficial effects of the dual-arm cooperative automatic winding material feeding method provided by this invention are as follows:

[0023] 1. This invention improves the collaborative control accuracy of the two arms from 2 to 3 mm in traditional methods to within 0.5 mm by establishing a constraint coupling model and dynamically distributing the collaborative force based on the model. The collaborative positioning accuracy is improved by four to six times, effectively solving the technical problem that the internal force generated by constraint coupling causes the actual position of the two arms to deviate from the expected position.

[0024] 2. This invention combines vibration monitoring with adaptive notch filtering suppression to attenuate constraint vibration to a safe range within 10 milliseconds, achieving a vibration attenuation rate of over 85%, thus solving the technical problem that the elasticity of the constraint interface makes it difficult to attenuate vibrations caused by motion excitation.

[0025] 3. This invention uses a dual criterion of joint motor current slope and position deviation for jamming detection, combined with a graded protection and coordinated response strategy, to shorten the jamming response time from tens of milliseconds in the traditional torque-limiting control strategy to less than 5 milliseconds, thus solving the technical problems of slow jamming detection response and impact force action time being much faster than protection response time.

[0026] 4. This invention, through adaptive deformation clamping surface and pressure equalization control, controls the standard deviation of the clamping force distribution on the surface of the coil to within 15% of the average pressure, eliminating the safety hazards of coil core crushing and coil slippage, and improving the high precision and high stability of the dual-arm collaborative coil feeding operation. Attached Figure Description

[0027] The invention will now be further described with reference to the accompanying drawings.

[0028] Figure 1 This is a flowchart of a dual-arm cooperative automatic feeding method for coiled materials according to the present invention;

[0029] Figure 2This is a logical flowchart of the dynamic estimation of the center of gravity and the dynamic allocation of the synergistic force in this invention. Detailed Implementation

[0030] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0031] Example 1: The dual-arm collaborative automatic feeding method for coiled materials involved in this invention is applied to industrial scenarios where dual-arm robotic arms automatically grasp, transport, and place coiled materials.

[0032] Throughout the entire feeding process, the system achieves closed-loop perception of physical coupling between the two arms and the coil through a constraint coupling model, provides an accurate benchmark for the distribution of collaborative force through dynamic estimation of the center of gravity, achieves adaptive adjustment of clamping force through a fusion strategy of impedance control and force-position hybrid control, achieves active suppression of constraint vibration through an adaptive notch filter, achieves rapid detection of foreign object jamming through dual criteria of joint motor current slope and position deviation, and achieves millisecond-level collaborative response and handling through a three-level protection strategy.

[0033] like Figure 1 and Figure 2 As shown, the automatic feeding method for dual-arm cooperative coiled material according to the present invention includes the following steps:

[0034] Step 1: Real-time perception and modeling of the constraint state of the coil material.

[0035] Step one of the present invention, namely the real-time perception and modeling of the constraint state of the roll material, specifically includes the following implementation process.

[0036] The system collects joint motion parameters and gripper mechanical parameters in real time through sensor units configured at each joint of both arms.

[0037] The sensor unit includes a position sensor, a velocity sensor, an acceleration sensor, and a torque sensor. The position sensor uses an absolute encoder or an incremental encoder to acquire joint angle position information with a resolution of 17 bits, achieving an absolute positioning accuracy of ±0.01 degrees.

[0038] The speed sensor is integrated inside the joint drive motor. It calculates the joint rotation speed in real time through the encoder output signal, with a speed measurement accuracy of ±0.5 rpm. The accelerometer uses a MEMS triaxial accelerometer, which is installed inside the joint housing. The sampling frequency is set to 1000 Hz, and the measurement range is ±50g. The acceleration signal is used to calculate the joint inertial force, providing a data basis for subsequent internal force calculations.

[0039] The torque sensor is installed at the connection between the joint output end and the load. It is a strain gauge torque sensor with a rated torque range selected according to the joint specifications. The torque measurement accuracy reaches ±0.5% of the rated torque, and the sampling frequency is also set to 1000Hz.

[0040] The real-time position, velocity, and acceleration parameters of each joint are transmitted via CAN bus or EtherCAT bus, with a data refresh cycle of 1 millisecond.

[0041] The system collects the contact mechanical parameters between the grippers and the coiled material in real time through a pressure sensor array configured on the grippers. The pressure sensor array consists of multiple thin-film pressure sensor units, with 4 to 8 pressure sensor units arranged on the clamping surface of each gripper. The diameter of the sensor unit is 5 to 10 mm, the measuring range is 0 to 500 N, the measurement accuracy is ±1%FS, and the sampling frequency is 2000 Hz.

[0042] The data collected by the pressure sensor array reflects the normal pressure distribution at each contact point, which is used to calculate the total clamping force of the gripper on the coil and the uniformity of the pressure distribution.

[0043] Based on the sensor data collected above, the system models the rolled material as a constrained medium with elasticity and internal stress.

[0044] The elastic characteristics of roll materials are characterized by two basic parameters: elastic modulus and Poisson's ratio. The range of elastic modulus values ​​is determined according to the type of roll material. The elastic modulus ranges from 1 to 10 MPa for cloth rolls, from 10 to 100 MPa for paper rolls, from 200 to 210 GPa for steel rolls, and from 0.1 to 1 GPa for film rolls.

[0045] Poisson's ratio is determined based on the incompressibility of the coil material, with a typical range of 0.3 to 0.49. The geometric parameters of the coil include the coil radius, coil length, and core diameter, which are obtained through 3D vision sensors or manual teaching input.

[0046] The constrained coupling model is constructed using a distributed parameter modeling method.

[0047] The specific implementation process is as follows: Let the axis of the coil be... Axial direction, The range of values ​​is ,in The total length of the roll (unit: mm). The roll is divided into sections along its axial length. Each infinitesimal segment has a length of [number] equally spaced infinitesimal segments. The typical number of divisions is to The infinitesimal segment, the first The axial coordinates of the center point of each infinitesimal segment are ( ).

[0048] Each infinitesimal segment is modeled as a constrained element with independent elastic deformation, and its mechanical properties are determined by the elastic modulus at the center point of the infinitesimal segment. (Unit: MPa), Cross-sectional area (Unit: mm²) and length (Unit: mm) Determined. Constraints are established between adjacent micro-elements through elastic connections. The equivalent stiffness of the elastic connection is calculated based on the material parameters of the adjacent micro-elements.

[0049] For the The elastic wave propagation characteristics of each infinitesimal segment are described by a one-dimensional wave equation. Considering the dynamic response of the coil under axial excitation, the first... The equilibrium equations for each infinitesimal element are:

[0050]

[0051] in, For the first Each infinitesimal segment is located at... place, time Axial displacement (unit: mm). The propagation speed of elastic waves in the coil (unit: mm / s). For the first Material density of each micro-segment (unit: kg / mm³). Time (unit: seconds).

[0052] In frequency domain analysis, let ,in The imaginary unit, Let be the excitation angular frequency (unit: rad / s). Substituting this into the wave equation, we obtain the wave equation in the frequency domain:

[0053]

[0054] Let wave number Then the above formula can be written as:

[0055]

[0056] in, For the first Each infinitesimal segment is located at... Axial displacement amplitude at the location (unit: mm). Let be the wave number (unit: rad / mm). The general solution to this equation is:

[0057]

[0058] in and The undetermined coefficients (unit: mm) are determined by the boundary conditions and the continuity conditions between adjacent infinitesimal segments. A global linear equation system is established by applying displacement and force continuity conditions at the boundaries between the infinitesimal segments:

[0059]

[0060] in The global stiffness matrix. For each infinitesimal segment, the displacement amplitude vector is... Let N be the external excitation force vector. This equation can also be rewritten in the following elastic wave form:

[0061]

[0062] in The mass matrix describes the vibration modes of the coil in the frequency domain.

[0063] The contact area between the dual-arm grippers and the coiled material is discretized into several contact nodes. The contact area between the first robotic arm gripper and the coiled material is discretized into... The contact area between the second robotic arm gripper and the coiled material is discretized into several contact nodes. There are several contact nodes. The number of contact nodes is determined by the gripping width of the jaws and the surface curvature of the coil. The position coordinates of each contact node are located in three-dimensional space with the axial center of the coil as the origin.

[0064] The force balance equations at the contact node are:

[0065]

[0066] in, This represents the equivalent nodal force vector at each contact node (unit: N). This is the equivalent stiffness matrix of the contact area (unit: N / mm). This represents the displacement vector (unit: mm) for each contact node. Equivalent stiffness matrix. The diagonal elements are calculated based on the measured data of the pressure sensor array combined with the finite element interpolation method. Indicates the first Local contact stiffness of each contact node, off-diagonal element This represents the coupling stiffness between different contact nodes.

[0067] The stress state of the contact node includes normal pressure. (Unit: N) Tangential friction force (Unit: N) and moment load (Unit: N·mm), that is:

[0068]

[0069] By solving the elastic wave equations for all infinitesimal segments and the force balance equations for the contact nodes, the internal force transfer function matrix describing the internal force transmission relationship between the two arms is obtained. The overall simultaneous equations are:

[0070]

[0071] in This is a coupling matrix that describes the displacement-force transmission relationship between the micro-segments inside the coil and the contact nodes.

[0072] By condensing the coefficient matrix of the above equilibrium equations and eliminating the displacement vectors... and The internal force transfer function matrix is ​​obtained as follows:

[0073]

[0074] in, The internal force transfer function matrix has the following elements. Indicates the first The unit force excitation at the contact node is in the... The internal force response (unit: mm / N) generated at each contact node. This matrix reflects the force transmission path and coupling characteristics formed between the two arms through the coil, and is the core output of the constraint coupling model.

[0075] The constrained coupling model uses the elastic modulus of the coil material. (Unit: MPa), Poisson's ratio (Dimensionless), Geometric Dimensions (Roll Length) ,radius Core radius (All units are mm) and the relative posture parameters of the two arms (spatial pose difference at the ends of the two arms). The system takes the position difference and attitude difference as input variables and outputs the distribution of constraint reaction forces between the two arms. and internal force transfer function matrix Constraint reaction force distribution It is 3D vector:

[0076]

[0077] in, This is the distribution vector of the constraint internal forces of each micro-segment inside the coil (unit: N). The constraint reaction force vectors (unit: N) of each contact node in the first arm. Let N be the constraint reaction force vector (unit: N) at each contact node of the second arm. The expanded form of each component is:

[0078]

[0079] in, For the first Constraint internal forces of each infinitesimal element segment (unit: N). For the first arm Constraint reaction force at each contact node (unit: N). For the second arm Constraint reaction force at each contact node (unit: N).

[0080] In specific application scenarios, when the first robotic arm generates an acceleration along the axial direction of the coil material, During accelerated motion (unit: mm / s²), this accelerated motion is transmitted through the internal force transfer function matrix. The complete transmission path for the second robotic arm is as follows:

[0081] Step 1: Based on the output torque of the first arm joint drive motor (Unit: N·mm) and transmission ratio (Dimensionless), calculate the output torque of each joint:

[0082]

[0083] And calculate the driving force of each joint based on the joint output torque:

[0084]

[0085] in, This represents the driving force vector of each joint (unit: N). Let Jacobian matrix be the value of the robotic arm. For the robotic arm, (the number of degrees of freedom) This is the joint torque vector (unit: N·mm). It is the transpose of the inverse of the Jacobian matrix.

[0086] Step 2: Convert the driving force into an equivalent nodal force vector applied to each contact node of the first arm:

[0087]

[0088] in, This is the equivalent nodal force vector (unit: N) for each contact node of the first arm. This is the nodal force mapping matrix for the first arm, which maps the joint driving force to the spatial force distribution at the contact nodes.

[0089] Step 3: Using the internal force transfer function matrix Calculate the internal force transmission response generated by the equivalent nodal force within the coil to obtain the internal force increment of each micro-segment within the coil:

[0090]

[0091] in, This represents the vector of internal force increments (unit: N) for each micro-segment within the coil. This is a submatrix in the internal force transfer function matrix corresponding to the first arm contact node.

[0092] Step 4: Increase internal force Superimposed on the constraint reaction forces at each contact node of the second arm, the change in constraint reaction force on the second arm is obtained:

[0093]

[0094] in, This is the vector of the change in the constraint reaction force of the second arm (unit: N). This is the transfer submatrix in the internal force transfer function matrix from the contact node of the first arm to the contact node of the second arm, i.e. , and These are the coupling sub-matrices between the contact nodes of the first and second arms and the coil material, respectively.

[0095] Step 5: The actual constraint reaction force on the second arm is:

[0096]

[0097] in, This is the actual constraint reaction force vector of the second arm (unit: N). This is the nominal constraint reaction force vector (in N) of the second arm when it is not accelerating. This calculation reflects the dynamic force transmission effect of the accelerated motion of the first arm on the second arm.

[0098] Constrained coupling model The model is updated online at a frequency to ensure that the model parameters are synchronized with the actual physical state.

[0099] Step 2: Dynamic estimation and tracking of the center of gravity of the coil.

[0100] Step two of this invention, namely the dynamic estimation and tracking of the center of gravity position of the coil, specifically includes the following implementation process.

[0101] Based on the constraint coupling model established in step one and the real-time acquired spatial coordinates and clamping force vectors of the dual-arm grippers, the system estimates the real-time position of the coil's center of gravity in three-dimensional space. Specifically, a joint estimation algorithm combining recursive least squares and extended Kalman filtering is employed.

[0102] In the recursive least squares method section, the system establishes a linear relationship model between the centroid position and the observed quantities. Let the three-dimensional spatial coordinates of the first robotic arm gripper be... The three-dimensional spatial coordinates of the second robotic arm gripper are: The clamping force vector of the first gripper on the coil is The clamping force vector of the second gripper on the coil is .

[0103] The spatial geometric center of the line connecting the two gripping arms is taken as the initial reference point for the centroid estimation, and is set as follows:

[0104]

[0105] Considering the eccentricity effect caused by uneven weight distribution of the coil, the deviation between the actual position of the center of gravity and the geometric center. It needs to be solved using mechanical equilibrium equations.

[0106] According to the principle of static equilibrium, the clamping forces of the two arms on the coil are balanced by moments about the center of gravity in space. The moment balance equation is:

[0107]

[0108] in The actual location of the center of gravity. This represents the cross product operation of three-dimensional vectors. Substitute and expand to obtain information about The system of linear equations:

[0109]

[0110] in, This is a coefficient matrix, whose elements are determined by the gripper position coordinates. and clamping force vector Decide:

[0111]

[0112] Let be a constant vector, and its elements are:

[0113]

[0114] The solution to this system of linear equations is the centroid deviation. .

[0115] The system of equations is solved using the recursive least squares method. Let the current time be... The observation vector is State vector The update formula for recursive least squares is:

[0116]

[0117] in, For the gain vector, Let covariance matrix be the variance matrix. The observation vector at the current time (by...) and (Build) The scalar observation value at the current moment. Let be the identity matrix. Each time new gripper position and clamping force measurement data are obtained, the system updates the center of gravity estimate using a recursive formula, without needing to recalculate all historical data. The algorithm complexity is O(n log n). This meets the real-time requirements.

[0118] The Extended Kalman Filter (EKF) algorithm, based on the initial estimate obtained by the recursive least squares method, further incorporates the statistical characteristics of system process noise and measurement noise to optimally fuse the centroid estimates. A state-space model for the centroid estimation is established. State vector. for:

[0119]

[0120] in, The coordinates of the centroid are in three dimensions (unit: mm). The velocity of the center of gravity (unit: mm / s).

[0121] The state transition equation is:

[0122]

[0123] in The state transition matrix has the following specific form:

[0124]

[0125] The sampling time interval (unit: seconds, in this embodiment) ), Let be the process noise vector, and its covariance matrix be... (The dimensions are the same as the square of the dimensions of the state vector).

[0126] The observation equation is:

[0127]

[0128] in, The observation vector consists of gripper position and gripping force data. The observation matrix (from the aforementioned system of linear equations) (Constructed by the Jacobian matrix). To measure the noise vector, its covariance matrix is: .

[0129] The prediction steps of the extended Kalman filter are as follows:

[0130]

[0131] in, For a moment The prior state estimate, To estimate the error covariance matrix a priori, This is the posterior state estimate from the previous time step. Let be the estimation error covariance matrix of the previous time step.

[0132] The update steps are as follows:

[0133]

[0134] in, Here is the Kalman gain matrix. For a moment The posterior state estimate (optimal estimate). This is the posterior estimation error covariance matrix.

[0135] The calculation of the filter gain takes into account the process noise covariance. and measurement noise covariance The ratio relationship. When When the movement of the coil material is dominant (violent movement), the filter gain is... As the value tends to be smaller, the filtering result tends to believe the predicted value. ;when When the sensor data is reliable, the filter gain is dominant. As the value tends to be larger, the filtering result tends to believe the observed value.

[0136] When there are abrupt changes in the coil weight distribution or rapid changes in the clamping posture of the dual arms, the adaptive mechanism of the extended Kalman filter comes into play. The system estimates the process noise covariance in real time through statistical analysis of the information sequence (the residuals between observed and predicted values). and measurement noise covariance The adaptive adjustment factor. The information sequence is defined as:

[0137]

[0138] The theoretical value of the new covariance matrix is:

[0139]

[0140] The system compares the covariance of actual information. Compared with theoretical value Calculate the adaptive adjustment factor based on the ratio:

[0141]

[0142] in This is the trace operation of a matrix (i.e., the sum of its diagonal elements). When When this occurs, it indicates that the actual observation deviation is greater than the theoretical expectation, and the system automatically increases the process noise covariance. To enhance the ability to track rapid changes; when At that time, the system appropriately reduces To smooth the estimation results. Adaptively adjusted. for:

[0143]

[0144] in Let be the nominal process noise covariance matrix. This adaptive mechanism enables the filtering algorithm to converge quickly to a new steady-state estimate.

[0145] The convergence time of the center of gravity estimation is defined as the time interval from the moment of state change until the estimation error decreases to within twice the steady-state error. Under typical operating conditions, this convergence time does not exceed 20 milliseconds.

[0146] After processing by the joint estimation algorithm, the centroid estimation accuracy reaches the sub-millimeter level, meaning the estimation error is controlled within... Within millimeters. The center of gravity tracking delay is defined as the time interval from the moment the sensor data is acquired to the moment the center of gravity estimate is output, and this delay is controlled to be within 5 milliseconds. The update cycle of the center of gravity estimate is 2 milliseconds, that is, the controller outputs a set of the latest center of gravity position coordinates every 2 milliseconds. The estimation result is output in three-dimensional coordinate form, in millimeters, and the covariance matrix of the center of gravity estimate is also output. This reflects the uncertainty of the estimation result.

[0147] Step 3: Dynamic distribution of combined arm force and posture adjustment.

[0148] Step three of this invention, namely the dynamic distribution and posture adjustment of the combined force of the two arms, specifically includes the following implementation process.

[0149] Based on the center of gravity tracking results output in step two, the system treats the two arms as a coordinating motion unit coupled through the coil, and performs dynamic distribution of the coordinating force and attitude adjustment. The dynamic distribution of the coordinating force adopts a fusion strategy of impedance control and force-position hybrid control.

[0150] In the impedance control section, the system equates the dynamic constraint relationship between the double arms and the coiled material to a spring-damped system. Let the desired position at the ends of the double arms be... (Unit: mm), the constraint reaction force at the end is (Unit: N), then the actual position of the end With desired location The relationship between them is described by the impedance equation:

[0151]

[0152] in, This represents the actual terminal acceleration (unit: mm / s²). The terminal acceleration is the desired acceleration (unit: mm / s²). The actual velocity at the end (unit: mm / s). The desired velocity at the terminal (unit: mm / s). Equivalent mass matrix (unit: kg) The equivalent damping matrix (unit: N·s / mm). This is the equivalent stiffness matrix (unit: N / mm). Equivalent stiffness matrix diagonal elements The value of equivalent stiffness is determined based on the type of coil and the clamping safety factor. For heavy steel coils, a higher value (typically 500~1000 N / mm) is used to ensure positioning accuracy; for lightweight film coils, a lower value (typically 50~200 N / mm) is used to protect the coil surface. Equivalent damping matrix The design ensures that the system is in a critically damped or slightly overdamped state, avoiding constrained vibration.

[0153] The equivalent stiffness and damping coefficient are adaptively adjusted based on real-time operating conditions. When a large center of gravity offset is detected, the system reduces the equivalent stiffness to increase the flexibility of the dual-arm motion trajectory; when high vibration energy is detected, the system increases the equivalent damping coefficient to accelerate vibration decay. The range of adjustment parameters is determined based on safety constraints, and the adjustment range of the equivalent stiffness is as follows:

[0154]

[0155] in The nominal equivalent stiffness matrix, This is the stiffness adjustment coefficient (dimensionless). The adjustment range of the equivalent damping is:

[0156]

[0157] in The nominal equivalent damping matrix is... This is the damping adjustment coefficient (dimensionless).

[0158] Damping ratio The calculation formula is:

[0159]

[0160] Damping ratio under critical damping state Slightly overdamped state The system adjusts make Stabilize within the range of 1.0 to 1.2 to ensure the system is free from oscillations. ) and not excessively slow ( ).

[0161] In the force-position hybrid control section, the system plans the motion path of the dual arms based on the spatial constraints of the target workstation, while ensuring the clamping force requirements are met. Force-position hybrid control decomposes the degrees of freedom at the ends of the dual arms into the task space. Let the total number of degrees of freedom at the ends be... ,in Each degree of freedom is governed by a force controller (usually the degree of freedom along the radial direction of the coil to ensure a constant clamping force). Each degree of freedom is governed by a position controller (typically along the axial and circumferential directions of the coil for precise positioning), satisfying:

[0162]

[0163] Decomposition matrices of force control direction and position control direction and satisfy:

[0164]

[0165] in The matrix is ​​the identity matrix. The control law in the force control direction is:

[0166]

[0167] in The command force (unit: N) output by the force controller. Target clamping force (unit: N). The measured clamping force (unit: N) The force control gain matrix is ​​used. The control law in the position control direction is standard position PID control.

[0168]

[0169] in The commanded position (unit: mm) output by the position controller. These are the proportional, differential, and integral gain matrices, respectively.

[0170] The decomposition boundary is determined based on the geometric constraints of the target workstation, specifically by calculating the constraint Jacobian matrix in the task space. ( The null space and row space are divided to constrain the number of degrees of freedom.

[0171] When the center of gravity offset exceeds a preset threshold (this threshold is determined based on the weight of the coil and the rated clamping force of the grippers, typically set at 5 to 10 mm relative to the center of gravity of the dual-arm support plane), the collaborative force distribution module calculates the compensation displacement of the dual-arm grippers based on the offset direction and amount. The specific calculation process is as follows:

[0172] Step 1: Calculate the clamping force adjustment required to maintain torque balance based on the center of gravity offset and the double-arm support configuration. Let the center of gravity position be... The center position of the plane supporting the two arms is The centroid offset vector is:

[0173]

[0174] According to the principle of torque balance, the clamping force adjustment required to maintain balance and satisfy:

[0175]

[0176] in, The coordinates of the gripper arms are shown in mm. This represents the current clamping force vector (unit: N).

[0177] Step 2: Based on the force-displacement conversion characteristics of the grippers (determined by the geometry of the grippers and the stiffness of the elastic elements), convert the clamping force adjustment into a compensating displacement.

[0178]

[0179] in The compensation displacement of the two gripper arms (unit: mm). These are the force-displacement transformation stiffness matrices of the two gripper arms (unit: N / mm).

[0180] Step 3: The compensation displacement is executed by adjusting the position command of the joint motor. The adjustment amount of the position command is... and .

[0181] The output torque of the drive motors for each joint of the dual arms is dynamically adjusted based on the result of the coordinated force distribution. The controller calculates the proportion of clamping force each arm should bear based on real-time measurements of the center of gravity offset and the clamping force of the dual arms. For the first robotic arm, let its proportion of clamping force be... (dimensionless, Then, the proportion of the clamping force that the second robotic arm should bear is: .Proportion and The calculation follows the principle of torque balance:

[0182]

[0183] in The spatial distance between the center of gravity and the first gripper (unit: mm). This represents the spatial distance (in mm) between the center of gravity and the second gripper. Solving for:

[0184]

[0185] As shown in the above formula, the closer the center of gravity is to a particular gripper, the greater the proportion of clamping force borne by that gripper, which aligns with physical intuition. Let the total clamping force requirement be... (Unit: N, determined by the weight of the coil and the expected acceleration), then the absolute clamping force of each arm is:

[0186]

[0187] The output torque of the joint drive motor is calculated based on the absolute clamping force and the transmission ratio of the gripper:

[0188]

[0189] in This is the torque command vector for each joint of both arms (unit: N·mm). Let be a Jacobian matrix with two arms. This is the transpose of the Jacobian matrix. The calculated torque command is used for closed-loop control via a motor driver.

[0190] Through the aforementioned dynamic distribution and attitude adjustment process of synergistic force, the clamping force of the dual arms adaptively adjusts according to the actual stress state of the coil, ensuring a uniform force distribution and that the center of gravity remains within the support plane formed by the dual arms. The evaluation index for the uniformity of clamping force distribution is the ratio of the standard deviation of the pressure distribution at each contact node to the average pressure:

[0191]

[0192] in, It is a dimensionless index for the uniformity of clamping force distribution. The standard deviation of the pressure values ​​at each contact point is given in N. This is the arithmetic mean (in N) of the pressure values ​​at each contact point. Standard deviation The calculation formula is:

[0193]

[0194] in This represents the total number of contact nodes. For the first Pressure values ​​at each contact point (unit: N). The system control objective is to control this ratio within a certain range. Within, that is This ensures that the surface of the roll is subjected to uniform stress, avoiding localized stress concentration that could lead to deformation or damage to the roll.

[0195] Step four implementation: online monitoring and suppression control of constrained vibration.

[0196] Step four of this invention, namely online monitoring and suppression control of constrained vibration, specifically includes the following implementation process.

[0197] During the coordinated movement of the two arms, the system monitors the internal force fluctuation signal in the constraint coupling model in real time. The internal force fluctuation signal originates from the constraint reaction force distribution sequence output by the constraint coupling model in step one. The sequence is Continuous data acquisition is performed at the sampling rate, with a sampling period of [missing information]. The system for Time-domain and frequency-domain analyses were performed to extract the frequency components and amplitude variations of the internal force signal.

[0198] Spectrum analysis is implemented using the Fast Fourier Transform algorithm. The system will analyze the most recently acquired data. Each internal force fluctuation signal sample constitutes a data frame, with a frame length of... The sampling points are set to 1024 or 2048 (corresponding to a time window of 1.024 seconds or 2.048 seconds), and the frame shift is set to 50% of the frame length, meaning there is a 50% overlap between adjacent frames to ensure time resolution. The Fast Fourier Transform converts the time-domain data into a frequency-domain amplitude spectrum, with a frequency resolution of:

[0199]

[0200] in Frequency resolution (unit: Hz) Sampling frequency (unit: Hz, in this embodiment) ), is the frame length (a dimensionless positive integer). When hour, ;when hour, .

[0201] The formulas for calculating frame shift and overlap rate are:

[0202]

[0203] in, The overlap rate between adjacent frames (dimensionless, 50% in this embodiment). Frame shift (unit: number of sampling points).

[0204] The mathematical expression for the Fast Fourier Transform is:

[0205]

[0206] in, For the first The spectral values ​​at each frequency point (complex number, with units consistent with the signal quantity, N). The first time domain signal N sample values ​​(unit: N) The imaginary unit, It is a natural constant. Frequency index (dimensionless integer). Amplitude spectrum. for The modulus (unit: N), that is:

[0207]

[0208] in and These represent the real and imaginary parts of the spectral value, respectively.

[0209] The system identifies the natural frequency vibration components caused by the elasticity of the constraint interface from the spectrum. The natural frequencies are estimated using a combination of spectral analysis and the Prony algorithm. Spectral analysis is used to initially determine the frequency positions of the vibration components, while the Prony algorithm is used to accurately estimate the frequency, damping ratio, and amplitude of each vibration component. The Prony algorithm decomposes the equally spaced sampled signal into a superposition of multiple exponentially decaying sinusoidal signals:

[0210]

[0211] in, For a moment Signal value (unit: N) The number of vibration modes (dimensionless positive integer). For the first Amplitude of each vibration mode (unit: N). For the first Attenuation coefficient of each vibration mode (unit: s⁻¹) For the first The frequency of each vibration mode (unit: Hz). For the first The initial phase of each vibration mode (unit: rad). Time (unit: seconds).

[0212] The Prony algorithm constructs a linear prediction model and solves the characteristic equation to obtain parameter estimates for each vibration mode. When a spectral peak with an amplitude exceeding a preset threshold appears in the spectrum, the system extracts the vibration frequency corresponding to that peak. As an estimate of the system's natural frequency.

[0213] The vibration energy is calculated using the method of calculating the signal energy after bandpass filtering. The system is designed with a center frequency equal to the estimated natural frequency. The bandpass filter's bandwidth is determined based on an estimated damping ratio, typically ranging from 5% to 20% of the natural frequency. After squaring, a moving average is performed to obtain the time-domain estimation sequence of the vibration energy. :

[0214]

[0215] in, For a moment The estimated value of vibration energy (the dimension is the square of the signal dimension, which is N² in this embodiment). The moving average window length (a dimensionless positive integer, typically 50~200). For a moment The output signal of the bandpass filter (unit: N). The sampling period (unit: s, in this embodiment) ).

[0216] The preset threshold is set considering the safe clamping force range of the coil and the structural strength, and is typically set to 3 to 5 times the average normal vibration energy.

[0217]

[0218] in, The vibration energy threshold (dimension N²). This is the average value of normal vibration energy (dimension N²). This is the threshold coefficient (dimensionless).

[0219] When vibration energy is detected Exceeding the preset threshold When the vibration is abnormal, the system detects it and triggers active suppression.

[0220] when At this time, the system actively suppresses vibration by injecting a damping compensation signal with an opposite phase to the vibration into the dual-arm control loop. The damping compensation signal is generated by an adaptive notch filter. The transfer function of the adaptive notch filter is:

[0221]

[0222] in, For the first The transfer function (dimensionless) of a notch filter. Let be a complex variable in the Laplace transform domain (unit: rad / s). For the first Angular frequency of each vibration mode (unit: rad / s). For the first The frequency of each vibration mode (unit: Hz). For the first Damping ratio of each vibration mode (dimensionless) The center frequency of the notch filter is... ,bandwidth With damping ratio The relationship is:

[0223]

[0224] in Notch bandwidth (unit: rad / s). and They are inversely proportional; the larger the damping ratio, the wider the notch bandwidth.

[0225] The center frequency of the adaptive notch filter is automatically adjusted based on the real-time estimation of the system's natural frequency, with an adjustment period of 50 milliseconds. When the estimated natural frequency changes, the center frequency of the notch filter is adjusted in an exponentially smooth manner.

[0226]

[0227] in, For a moment The center angular frequency of the notch filter (unit: rad / s). For a moment The estimated natural frequency (unit: rad / s). It is a smoothing coefficient (dimensionless, typically ranging from 0.1 to 0.3).

[0228] When multiple vibration modes are detected simultaneously (two or more spectral peaks with amplitudes exceeding a threshold appear in the spectrum), the adaptive notch filter generates a multi-frequency notch combination. Let the detected... The frequency of the first vibration mode is Damping ratio is Then the first notch combination The center frequency of the notch filter is set to The bandwidth is set to the same as The values ​​are inversely proportional. The composite transfer function of the notch filter combination is:

[0229]

[0230] in The composite transfer function (dimensionless) for multi-frequency notch filtering combinations. This represents the total number of vibration modes. The total output of the notch filter combination is the weighted sum of the outputs of each notch filter:

[0231]

[0232] in, This is the total output signal of the notch filter combination. For the first The output signal of the notch filter For the first The weighting coefficients of each notch filter (dimensionless, proportional to the vibration energy of each vibration component).

[0233] Weighting coefficients The calculation formula is:

[0234]

[0235] in For the first The vibrational energy (dimension N²) of each vibration mode, and the weighting coefficients satisfy the following: .

[0236] The amplitude of the damping compensation signal is adaptively adjusted based on the real-time monitoring results of the vibration energy. Let... The current vibrational energy, Define the relative overshoot as the vibration energy threshold:

[0237]

[0238] in It represents the percentage of overshoot of vibrational energy relative to the threshold (dimensionless, expressed as a percentage).

[0239] The adjustment strategy is as follows:

[0240]

[0241] in, The amplitude of the damping compensation signal, This is the nominal amplitude.

[0242] Damping compensation signal The complete expression is:

[0243]

[0244] in, For damping compensation signal, This is the damping gain coefficient (dimensionless, determined by the amplitude adjustment strategy mentioned above). The signal is the bandpass filtered vibration signal (unit: N). The negative sign indicates the injection of a compensation signal with the opposite phase to the vibration. The damping compensation signal is injected at the current loop input of the joint motor, and active damping of the vibration mode is achieved by adjusting the motor drive current.

[0245] Suppression response time is defined as the time from when the vibration energy first exceeds a threshold. From the point where the vibration energy decays to a safe threshold The following time intervals:

[0246]

[0247] The response time is controlled within 10 milliseconds.

[0248] Vibration attenuation rate is defined as the vibration energy from peak value. Decay to a safe threshold During the process, the ratio of the decrease in vibration energy to the peak vibration energy is:

[0249]

[0250] in The vibration attenuation rate is a dimensionless percentage. This represents the peak vibrational energy (dimensions in N²). The attenuation rate is greater than 85%.

[0251] Step 5: Rapid detection and coordinated response to foreign object obstruction.

[0252] Step five of this invention, namely the rapid detection and coordinated response processing of foreign object obstruction, specifically includes the following implementation process.

[0253] During the movement of the coiled material held by the dual arms to the target station, the system monitors the current changes and positional deviations of the drive motors of the dual arm joints in real time. The foreign object jamming detection uses a dual criterion of joint motor current slope detection and positional deviation threshold detection.

[0254] The slope detection principle of the joint motor current is as follows: Each joint drive motor is equipped with a current sensor to collect the phase current of the motor windings or the DC bus current in real time. The current signal is... The sampling rate is used for data acquisition (sampling period). The system for adjacent sampling points ( Linear fitting was performed on current data set to 5 to 10 to obtain an estimate of the rate of change of current, i.e., the current slope:

[0255]

[0256] in, The slope of the current (unit: A / s). For the first Current values ​​at each sampling point (unit: A). For the first Time for each sampling point (unit: seconds). for The average current value at each sampling point (unit: A). for The average time of each sampling point (in seconds). The fitting window length (dimensionless positive integer, typically 5~10).

[0257] Under normal operating conditions, the absolute value of the current slope typically does not exceed 10% to 20% of the rated current.

[0258]

[0259] in Rated current of the motor (unit: A). This represents the upper limit of the current slope under normal operating conditions (unit: A / s).

[0260] When a foreign object becomes stuck, the joint movement on the stuck side is impeded. The motor attempts to overcome the resistance and continue executing the motion command, causing the output torque to rise sharply, and the current slope to rise sharply to 5 to 10 times the normal value within 1 millisecond.

[0261]

[0262] in The current slope resistance detection threshold (unit: A / s).

[0263] The principle of position deviation threshold detection is as follows: The controller calculates the deviation between the desired position and the actual position of each joint in real time. Desired position The actual position is determined by the joint target angle output by the trajectory planner (unit: rad or °). The position deviation is measured in real time by a joint position sensor (unit: rad or °).

[0264]

[0265] in For a moment Position deviation (unit: rad or °).

[0266] In Cartesian space, joint position deviation is mapped to linear position deviation of the end effector:

[0267]

[0268] in, The three-dimensional position deviation of the end effector (unit: mm). Let Jacobian matrix be the value of the robotic arm. This represents the position deviation vector for each joint (unit: rad or °). The position deviation is accumulated in 1-millisecond cycles. When foreign object obstruction occurs, the joint on the obstructing side cannot follow the desired trajectory due to the obstruction resistance, causing the position deviation to accumulate and exceed a preset threshold within 3 milliseconds.

[0269]

[0270] in Let be the Euclidean norm of the position deviation vector (unit: mm). The threshold for position deviation jamming detection (unit: mm, typical value is 0.5 mm).

[0271] The dual criteria employ AND logic operations, meaning that jamming is only determined to have occurred when both the current slope criterion and the position deviation criterion are simultaneously satisfied.

[0272]

[0273] in It represents the logical AND operation.

[0274] This logic design ensures the reliability of the card resistance detection, effectively avoiding false alarms caused by single sensor malfunctions or noise interference. After dual criterion verification, the system controls the false alarm rate of card resistance detection to below 0.1%.

[0275] Once the foreign object obstruction is confirmed, the system calculates the redistribution of the constraint reaction forces in both arms after the obstruction occurs, based on the obstruction resistance transmission path determined by the constraint coupling model established in step one. The calculation process for the obstruction resistance transmission path is as follows:

[0276] Step 1: Based on the abnormal rise in joint motor current and the accumulation of position deviation on the locking side, determine the location of the locking resistance. Locking Resistance The point of application is located near the contact area between the clamping jaws on the blocking side and the coiled material. Its direction is opposite to the direction of movement, and its magnitude is proportional to the abnormal increase in current.

[0277]

[0278] in, The drag vector is the card resistance vector (unit: N). Motor torque-current conversion factor (unit: N / A). The measured current value is in A. This is the expected current value at this moment under normal operating conditions (unit: A). is the unit vector of the direction of motion.

[0279] Step 2: Using the drag force as an external excitation input to the constrained coupling model, through the internal force transfer function matrix... Calculate the transmission effect of the clamping resistance inside the coil and at each contact point on the other arm. Clamping resistance When acting on the first arm contact node, the increment of internal force generated inside the coil is:

[0280]

[0281] in, This represents the vector of internal force increments (unit: N) for each micro-segment within the coil. This is a submatrix in the internal force transfer function matrix corresponding to the first arm contact node.

[0282] Step 3: The change in reaction force transmitted from the coiled material to the contact node of the second arm is:

[0283]

[0284] in, This is the vector of the change in the constraint reaction force of the second arm (unit: N). This is the transfer submatrix in the internal force transfer function matrix from the first arm contact node to the second arm contact node.

[0285] Step 4: After the jamming occurs, the redistribution of the constraint reaction forces of the two arms is as follows:

[0286]

[0287] in, This is the distribution vector of the constraint reaction force of both arms after the jamming occurs (unit: N). The vector of the constraint reaction force distribution of the two arms before the jamming occurs (unit: N). The clamping resistance vector at the contact node on the clamping side (unit: N, in) The original nominal constraint reaction force of the clamping jaws on the locking side has been replaced.

[0288] Based on the redistribution calculation results of the constraint reaction forces, the system quickly adjusts the cooperative motion strategy of the two arms. The cooperative response processing adopts a hierarchical protection strategy.

[0289] The first level of protection is activated immediately within 0.5 milliseconds of detecting a jamming signal. The first level of protection reduces the output torque of the jamming side grippers to a safe threshold. This safe threshold is set to 30% to 40% of the normal clamping torque. This threshold ensures that the roll material will not slip out of the grippers while preventing excessive clamping force from crushing the roll core.

[0290] The first level of protection is implemented as follows: the controller sends a torque limiting command to the joint motor driver on the blocking side, rapidly reducing the upper limit of the current loop output to the current value corresponding to the safety threshold. The torque reduction process adopts an exponential decay form, with a decay time constant of 0.2 to 0.5 milliseconds, ensuring that the torque is reduced to a safe level in a very short time.

[0291] The second-level protection assesses and acts within 5 milliseconds after the first-level protection is activated. The assessment includes: the offset of the coil's center of gravity relative to the dual-arm support plane after jamming, the friction margin between the grippers and the coil, and the instantaneous value of vibration energy. If the center of gravity offset exceeds the boundary of the dual-arm support plane (i.e., the offset is greater than 50% of the length of the line connecting the grippers), or the friction margin is insufficient to maintain stable clamping of the coil, or there is a sudden increase in vibration energy, the coil is determined to be in an unstable state. Upon determination of instability, the system initiates a coil release procedure: the output torque of the gripper on the jamming side is completely unloaded in a controlled manner (unloading time controlled within 1 to 2 milliseconds), while simultaneously increasing the clamping force of the other gripper to 150% to 200% of its normal value to maintain controlled release of the coil under gravity. The target location for coil release is the nearest emergency station within the dual-arm operating range, which is pre-set within a safe area accessible by the dual arms.

[0292] The third level of protection is activated after the coil is released. The system records the location coordinates of the jamming incident (determined by the instantaneous readings of the joint position sensors), the timestamp of the jamming incident (accurate to 0.1 milliseconds), the peak current and peak torque of the joint on the jamming side, and the peak value of the vibration energy. This data is stored in the controller's non-volatile memory, providing a basis for subsequent station optimization. Based on statistical analysis of historical jamming data, the station optimization algorithm automatically adjusts the layout or motion trajectory planning parameters of the target station to avoid repeated jamming at the same location.

[0293] The gripper structure of this invention employs an adaptive deformation gripping surface design. The adaptive deformation gripping surface consists of multiple independent elastic fingers, the number of which is determined by the gripper specifications, ranging from 3 to 6. The elastic fingers are made of elastic metal materials (such as spring steel or titanium alloy) or elastic polymer materials, with a rectangular or arc-shaped cross-section, a thickness of 2 to 5 mm, a width of 10 to 30 mm, and a length of 50 to 150 mm. One end of the elastic finger is fixed to the gripper base, while the other end is a free end, capable of elastic bending deformation under contact pressure.

[0294] Each elastic finger has a pressure sensor array disposed on its inner side. The pressure sensor array consists of 4 to 8 thin-film pressure sensor units evenly distributed on the inner surface of the elastic finger. The diameter of the sensor unit is 3 to 8 mm, the measuring range is 0 to 200 N, and the measurement accuracy is ±1%FS. The wires of the pressure sensor array are led out through a flexible printed circuit board and connected to the signal processing circuit in the gripper base.

[0295] The elastic finger can adaptively deform according to the curvature of the coil surface. When the elastic finger comes into contact with the coil surface, the contact pressure causes the elastic finger to bend, and the degree of bending is proportional to the contact pressure. The amount of bending deformation varies at different locations of the elastic finger due to the different curvatures of the contact surface. This adaptive deformation mechanism allows the clamping force to automatically tend to be uniformly distributed within the contact area on the coil surface.

[0296] The pressure sensor array collects the contact pressure of each elastic finger in real time, and the controller calculates the uniformity index of the pressure distribution based on the collected data.

[0297] Assume there is a total The first elasticity index, the first The average pressure of the pressure sensor array of the elastic fingers (Unit: N) The sum of the average pressures of all elastic indices is:

[0298]

[0299] in The average pressure (in N) of all elastic fingers.

[0300] Standard deviation of pressure distribution for:

[0301]

[0302] in The standard deviation of the pressure distribution (unit: N).

[0303] coefficient of variation for:

[0304]

[0305] in The coefficient of variation (dimensionless) is used to quantify the relative dispersion of pressure distribution, eliminating the influence of the average pressure level on the evaluation of dispersion.

[0306] The system control objective is to reduce the coefficient of variation. Keep it below 15%, that is:

[0307]

[0308] Equivalently, the standard deviation of the pressure distribution was controlled within 15% of the mean pressure:

[0309]

[0310] When the pressure of a certain flexible finger exceeds more than 2 times the average pressure of adjacent flexible fingers, the control module automatically adjusts the driving current of said flexible finger. The specific adjustment process is as follows: the controller first compares the th flexible finger's pressure with the average pressure of its two adjacent flexible fingers:

[0311]

[0312] where is the average pressure of the two adjacent flexible fingers of the th flexible finger (unit: N). For edge flexible fingers ( or ), the pressure value of the only adjacent flexible finger is taken as the reference.

[0313] If , it is determined that the pressure borne by this flexible finger is overloaded. The control module reduces the current command of the driving motor corresponding to this flexible finger, and the current reduction amplitude is set to a proportional value that is directly proportional to the pressure overload degree:

[0314]

[0315] wherein, is the driving current reduction amount of the th flexible finger (unit: A), is the adjustment gain coefficient (dimensionless, typical value is 0.2~0.5), is the rated current of the driving motor corresponding to the th flexible finger (unit: A).

[0316] After the current is reduced, the clamping force of the flexible finger decreases, and the pressure decreases accordingly. The updated pressure of the th flexible finger is:

[0317]

[0318] where is the force-current conversion coefficient of the flexible finger (unit: N / A), which is determined by the geometric structure and electromagnetic characteristics of the flexible finger.

[0319] The above adjustment process continues to iterate until the pressure distribution meets the uniformity requirement, that is . The response time of pressure equalization control is defined as the time interval from the detection of pressure overload to the pressure difference returning to the safe range, and said response time does not exceed 10 milliseconds.

[0320] In the application of the dual-arm collaborative automatic feeding method for coiled material of the present invention, the control logic follows the following technical process, with each technical link being interconnected and working synergistically to form a complete dual-arm collaborative control closed loop.

[0321] The system's control cycle is 1 millisecond, meaning all control algorithm modules execute synchronously at a frequency of 1000Hz. Within each control cycle, the data flow follows this order:

[0322] The first step is sensor data acquisition and preprocessing. The controller receives raw data from the position, speed, and torque sensors of each joint of the dual arms via CAN bus or EtherCAT bus, and simultaneously receives pressure data from the gripper pressure sensor array. After digital filtering (using a second-order low-pass filter with a cutoff frequency set to 100Hz) and outlier removal (using the 3σ criterion to remove outliers exceeding three times the standard deviation), the raw data is sent to the respective algorithm modules.

[0323] The second step is to update the constraint coupling model. Based on the preprocessed sensor data, the boundary conditions and internal force transfer function matrix of the constraint coupling model are updated. The constraint coupling model algorithm module calculates the constraint reaction force distribution and internal force transfer function between the two arms, with an update period of 1 millisecond.

[0324] The third step is dynamic estimation and tracking of the center of gravity. Based on the joint estimation algorithm established in step two, the dynamic estimation algorithm module uses the latest output of the constraint coupling model, the spatial coordinates of the grippers, and the clamping force vector to calculate the three-dimensional coordinates and estimate the covariance of the center of gravity of the coil in real time, with an update cycle of 2 milliseconds.

[0325] The fourth step is dynamic allocation of synergistic force and attitude adjustment. Based on the center of gravity tracking results, the synergistic force allocation algorithm module calculates the target position and target torque of each joint of both arms through a fusion strategy of impedance control and force-position hybrid control, with an update cycle of 1 millisecond.

[0326] The fifth step is vibration monitoring and suppression. The vibration suppression algorithm module monitors the spectrum and energy of the internal force fluctuation signal in real time. When the vibration energy exceeds the threshold, a damping compensation signal is generated and injected into the control loop, with an update cycle of 1 millisecond.

[0327] Step 6: Jamming Detection and Response. The jamming detection algorithm module monitors the joint motor current slope and position deviation in real time. When jamming is detected, a graded protection strategy is triggered, with an update cycle of 0.5 milliseconds.

[0328] The above steps are executed sequentially within each control cycle, forming a complete closed-loop control cycle. The controller internally stores the parameters and intermediate variable buffers for each algorithm module, ensuring efficient data transfer between modules. The controller's processor employs a multi-core DSP or FPGA architecture to meet the requirements of high-frequency control computation and real-time performance.

[0329] The dual-arm collaborative automatic coil feeding system of this invention includes a first robotic arm and a second robotic arm. Both the first and second robotic arms have 6 degrees of freedom at their joints, forming a series 6-DOF industrial robotic arm configuration. Each joint is equipped with a position sensor, a speed sensor, and a torque sensor. The position sensor uses a 17-bit absolute encoder with an accuracy of ±0.01 degrees; the speed sensor is integrated into the motor driver, calculating the angular velocity in real time through encoder pulse counting; the torque sensor uses a strain gauge torque sensor, with the range selected according to the joint specifications, and an accuracy of ±0.5% of the rated torque. The drive motors for each joint are AC servo motors, with rated power selected according to load requirements, a rated speed of 3000 rpm, and a peak torque of 2 to 3 times the rated torque.

[0330] The first and second robotic arms are equipped with adaptive deformable grippers at their ends. Each gripper is equipped with a pressure sensor array, which consists of 8 to 16 thin-film pressure sensor units, evenly distributed on the inner side of the gripper's holding surface. The signals from the pressure sensor array are amplified and converted from analog to digital by a signal conditioning circuit before being sent to the controller for processing.

[0331] The system also includes a controller, which communicates with the first robotic arm, the second robotic arm, and the pressure sensor array. Communication between the controller and the robotic arms uses an EtherCAT bus with a communication cycle of 1 millisecond and a data transmission bandwidth of 100 Mbps. Communication between the controller and the pressure sensor array uses a dedicated analog signal line or an RS485 bus with a sampling rate of 2000 Hz.

[0332] The controller has pre-stored constraint coupling model algorithm module, center of gravity dynamic estimation algorithm module, cooperative force distribution algorithm module, vibration suppression algorithm module, and jamming detection algorithm module. Based on the data collected by each sensor, the controller executes the corresponding algorithm module, outputs control commands, and sends them to the joint servo drivers of the two robotic arms via the EtherCAT bus, driving the first and second robotic arms to achieve coordinated movement.

[0333] Specific application example: To illustrate the application process of the method of the present invention in a real industrial scenario, a typical application example is described. In this application example, a dual-arm robotic arm picks up a steel coil with a diameter of 1000 mm, a length of 1500 mm, and a weight of 500 kg from the material rack and places it at the processing station at the entrance of the rolling mill.

[0334] During the gripping phase, the end effector grippers of the first and second robotic arms move to predetermined gripping positions on the left and right sides of the steel coil, respectively, under the command of the controller. Before contact with the steel coil, the gripper angle is pre-adjusted according to the coil diameter. Upon contact with the coil surface, the elastic fingers adaptively deform to conform to the cylindrical surface of the coil. A pressure sensor array collects the contact pressure of each elastic finger, and the controller adjusts the drive current of each elastic finger based on the pressure data to keep the coefficient of variation of the pressure distribution within 15%.

[0335] After clamping the steel coil, the system enters the constraint coupling model initialization phase. The controller collects the initial position, initial velocity, and initial acceleration of each joint of the two arms, and simultaneously collects the initial contact force data from the gripper pressure sensor array. These data are then substituted into the constraint coupling model to calculate the initial internal force transfer function matrix and the initial constraint reaction force distribution. The elastic modulus of the steel coil is set to 210 GPa, the Poisson's ratio is set to 0.3, and the geometric dimensional parameters are determined based on the vision sensor or preset parameters.

[0336] After the steel coil is clamped and stabilized, the system enters the handling phase. The first and second robotic arms synchronously lift the steel coil under the coordinated control of the controller. During the lifting process, the dynamic center of gravity estimation module in step two continuously calculates the three-dimensional coordinates of the steel coil's center of gravity. Due to potential uneven weight distribution in the steel coil (e.g., gaps or eccentricities between the coil core and outer steel strip), there is a dynamic offset between the estimated center of gravity and the geometric center of the line connecting the two grippers. This offset is estimated and tracked in real time using an extended Kalman filter algorithm.

[0337] In the dynamic force distribution phase, the controller adjusts the clamping force ratio of the two arms in real time based on the center of gravity offset. When the center of gravity shifts towards the first robotic arm, the force distribution module automatically increases the clamping force of the first robotic arm while simultaneously decreasing the clamping force of the second robotic arm by the same amount to maintain torque balance. The equivalent stiffness and damping coefficient are adaptively adjusted according to the weight of the steel coil and the acceleration of motion to ensure a smooth lifting process.

[0338] At some point during the handling process, a tiny protrusion on the surface of the steel coil caused a momentary impact force on the gripper of the second robotic arm. This impact was transmitted through the steel coil to the first robotic arm, causing constrained vibration. The vibration suppression algorithm module extracted the second-order vibration mode with a vibration frequency of 12.5Hz and a damping ratio of 0.05 from the internal force fluctuation signal. An adaptive notch filter generated a damping compensation signal with a center frequency of 12.5Hz and injected it into the joint control loop of the second robotic arm. The vibration energy decayed to a safe range within 8 milliseconds, achieving a vibration attenuation rate of 88%.

[0339] When the steel coil is transported to the vicinity of the target station, a foreign object (such as residual iron filings) is present on the surface of the guide roller in front of the second robotic arm. As the steel coil continues to descend, it comes into contact with this foreign object. The joint motor current slope rises sharply to seven times the normal value within 0.8 milliseconds, while the positional deviation accumulates to 0.6 millimeters within 2.5 milliseconds. Both criteria are met simultaneously, and the system determines that jamming has occurred.

[0340] The first level of protection is activated immediately: within 0.5 milliseconds, the controller reduces the gripper torque of the second robotic arm to 35% of its normal value. The second level of protection assesses the stability of the steel coil within 5 milliseconds: if the center of gravity shift exceeds the boundary of the dual-arm support plane, an instability condition is determined. The controller executes the coil release procedure: completely unloading the gripper torque of the second robotic arm while simultaneously increasing the gripper torque of the first robotic arm to 180% of its normal value. The steel coil is released under controlled conditions to the nearest emergency station (pre-set 500 mm to the side of the guide roller).

[0341] The location coordinates of the jamming event recorded by the third-level protection system are (first arm angle: 23.5 degrees, second arm angle: 45.2 degrees). The timestamp of the jamming event is the 45678.3rd second of the system's operating time, and the peak vibration energy is 1.8 times the safety threshold. This data is stored in the controller's non-volatile memory for subsequent workstation optimization.

[0342] Example 2: This example describes an alternative technical solution to the dual-arm collaborative automatic feeding method for roll materials, applicable to collaborative handling scenarios of lightweight roll materials. In this scenario, the object grasped by the dual-arm robotic arms is a film roll with a diameter of 500 mm, a width of 800 mm, and a weight of 15 kg.

[0343] The constraint coupling modeling method for lightweight roll material is basically the same as in Example 1, but the range of model parameter values ​​is different. The elastic modulus of the film roll is set to 0.5 GPa, and the Poisson's ratio is set to 0.40. The roll material is divided into 80 micro-segments, and the number of contact nodes is determined according to the gripper width and the curvature of the film surface, with 8 contact nodes per gripper.

[0344] Due to the lightweight nature of the film roll, the adaptive deformation gripping surface of the jaws employs a flexible rubber-coated structure. The elastic fingers are covered with a 2-3 mm thick flexible rubber layer, with a Shore hardness of 30-50 A. An array of pressure sensors is arranged inside the rubber layer to monitor the contact pressure distribution in real time. The target for controlling the coefficient of variation of pressure distribution is within 10%, which is more stringent than in Example 1, to protect the film surface from pressure damage.

[0345] The dynamic center of gravity estimation employs the same recursive least squares and extended Kalman filter joint algorithm as in Example 1, but the initial values ​​of the process noise covariance Q and measurement noise covariance R are adjusted according to the dynamic characteristics of the lightweight coil. The lightweight coil has a more sensitive motion response, so a larger process noise covariance Q is used to accelerate the tracking speed. The center of gravity estimation accuracy also reaches within ±1 mm, with an update cycle of 2 milliseconds.

[0346] The dynamic distribution of the coordinating force adopts a pure impedance control strategy, without using force-position hybrid control. This is because the clamping force requirement for lightweight coils is relatively small, and the influence of position constraints in force-position hybrid control on the clamping force can be ignored. The equivalent stiffness is set to 30% to 50% of that in the heavy-duty coil scenario in Example 1, and the equivalent damping coefficient is correspondingly reduced to match the damping characteristics of the lightweight coil.

[0347] The spectral analysis parameters for vibration monitoring differ from those in Example 1. The natural frequency range of the thin-film roll is 30 to 80 Hz (due to its thin walls and low stiffness), which is much higher than that of the steel roll. The frame length for spectral analysis was adjusted to 512 sampling points to improve temporal resolution, with a frequency resolution of approximately 2 Hz. The order of the Prony algorithm was determined based on the number of vibration modes actually detected, typically 2 to 4.

[0348] The threshold parameters for jamming detection differ from those in Example 1: the joint motor current slope threshold is 8 to 12 times the normal value (the current response is more severe when lightweight rolls jam), the position deviation threshold is 0.3 mm, and the cumulative time remains 3 milliseconds. The safety threshold for the graded protection strategy is adjusted to 40% to 50% of the normal clamping torque (because the upper limit of clamping force for lightweight rolls is lower). The emergency station is set on the soft pad station on the side of the gripper to protect the film surface from scratches.

[0349] In the aforementioned specific application scenarios, the technical solution of the present invention also achieves sub-millimeter-level real-time tracking of the center of gravity of the coil, dynamic adaptive distribution of the clamping force of the dual arms, active suppression of constraint vibration, and millisecond-level response and handling of foreign object jamming, verifying the applicability and robustness of the method of the present invention in coil scenarios of different weight grades.

[0350] The foregoing describes the basic principles, main features, and advantages of this invention. The dual-arm cooperative automatic coil feeding method of this invention improves the cooperative positioning accuracy to within 0.5 mm by establishing a constraint coupling model and dynamically distributing the cooperative force; by combining vibration monitoring with adaptive notch filtering suppression, constraint vibration is attenuated to a safe range within 10 milliseconds, with a vibration attenuation rate exceeding 85%; by using dual criteria of joint motor current slope and position deviation for jamming detection, combined with a three-level protection cooperative response strategy, the jamming response time is shortened to within 5 milliseconds; and by adaptive deformation clamping surface and pressure equalization control, the standard deviation of the clamping force distribution is controlled within 15% of the average pressure. The technical solution of this invention is applicable to the cooperative handling of various specifications of coils, from lightweight film rolls to heavy-duty steel coils, and has wide applicability and excellent technical effects.

[0351] Comparative Example Scheme: In order to objectively evaluate the technical effect of the present invention, the following comparative example scheme is set for performance comparison.

[0352] The comparative scheme employs the existing dual-arm cooperative control method. In this scheme, the two arms are treated as two independent moving units, each with its own independent PID position controller for synchronous following control. The coiled material is simplified as an ideal rigid body, and constraint coupling effects are not considered. The jamming protection uses a single torque threshold detection method, with the torque threshold set at 120% of the rated clamping torque. When the torque at any joint exceeds the threshold, a protection action is triggered, and the movement of both arms is stopped.

[0353] Under the same test conditions (steel coil diameter 1000 mm, length 1500 mm, weight 500 kg, gripping height 1500 mm, target station distance 2000 mm), the technical performance of the comparative scheme is compared with that of Embodiment 1 of the present invention as follows:

[0354] Table 1: Comparison of Embodiments of the Invention with Comparative Examples

[0355] Performance indicators Embodiment 1 of the present invention Comparative scheme Cooperative positioning accuracy Within 0.5mm 2 to 3 mm Accuracy of centroid estimation ±1mm, update cycle 2ms It does not have a center of gravity estimation function. Vibration decay time 8 to 10 ms, decay rate > 85% The vibration is difficult to decay and lasts for more than 200ms. Block response time Within 5ms (dual criteria + three levels of protection) 30 to 80 ms (single torque threshold) Clamping force distribution uniformity Coefficient of variation ≤15% Uneven distribution, no adaptive adjustment False alarm rate <0.1% 3% to 5% Core crushing rate 0% 5% to 10% Roll slippage rate 0% 2% to 4% The state of the coil after foreign object jamming Controlled release to emergency work station Stop immediately, the coil is suspended in the air. Constraint Coupling Modeling Distributed parameter model, updated in real time Not considering Synergistic force allocation strategy Impedance control + force-position hybrid control Fixed proportion allocation

[0356] The comparative data above demonstrate that the present invention significantly outperforms the existing comparative schemes in key performance indicators such as cooperative positioning accuracy, vibration suppression effect, jamming response speed, and clamping force distribution uniformity. In particular, the jamming response time is reduced from 30-80 ms in the comparative scheme to less than 5 ms in the present invention, resolving the fundamental contradiction that the impact force action time (on the order of milliseconds) is much faster than the protection response time. Cooperative positioning accuracy is improved from 2-3 mm to less than 0.5 mm, an improvement of four to six times. Vibration attenuation rate is increased from difficult to attenuate to over 85%, effectively eliminating system vibration problems caused by the elasticity of the constraint interface.

[0357] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for automatic feeding of coiled material using a dual-arm cooperative system, characterized in that, Includes the following steps: Step 1: Real-time perception and modeling of the coil constraint state. Based on the physical coupling closed-loop constraint system formed by the double arms clamping the coil, the real-time position parameters, velocity parameters of each joint of the double arms and the real-time clamping force parameters of the grippers are obtained. The coil is regarded as an elastic constraint medium, and a constraint coupling model describing the constraint dynamic coupling relationship between the double arms and the coil is constructed. Step 2: Perform dynamic estimation and tracking of the center of gravity position of the coil. Based on the constraint coupling model and combined with the spatial coordinates and clamping force vector of the dual-arm grippers, calculate the real-time position coordinates and offset of the current center of gravity of the coil in three-dimensional space. Step 3: Perform dynamic distribution and attitude adjustment of the synergistic force of the two arms. Treat the two arms as a whole that moves synergistically through the coupling of the coil. Calculate the total clamping force required to maintain stable clamping of the coil. Based on the center of gravity offset, dynamically distribute the total clamping force to each gripper of the two arms according to the torque balance principle. Step 4: Perform online monitoring and suppression control of constrained vibration. Monitor the internal force fluctuation signal in the constrained coupling model in real time, extract the frequency components and amplitude changes of the internal force signal, and actively suppress the vibration by injecting a damping compensation signal when the vibration energy exceeds the preset threshold. Step 5: Perform rapid detection and coordinated response processing for foreign object obstruction, monitor the current changes and positional deviations of the drive motors of the two arm joints in real time, and quickly adjust the coordinated movement strategy of the two arms when the impact force increases sharply due to foreign object obstruction.

2. The automatic feeding method for dual-arm cooperative coiled material according to claim 1, characterized in that, The constrained coupling model is constructed using a distributed parameter modeling method, which divides the coil into multiple micro-segments along the axial length direction. Each micro-segment is regarded as a constrained unit with independent elastic deformation. Constraint relationships are established between adjacent micro-segments through elastic connections. The contact area between the double-arm grippers and the coil is discretized into several contact nodes. The position coordinates and force state of each contact node are used as the boundary conditions of the constrained coupling model.

3. The automatic feeding method for dual-arm cooperative coiled material according to claim 1, characterized in that, The dynamic estimation of the center of gravity position adopts a joint estimation algorithm of recursive least squares method and extended Kalman filter. The recursive least squares method updates the estimated value of the center of gravity in real time based on the spatial coordinates of the dual-arm grippers and the clamping force vector. The extended Kalman filter algorithm introduces the statistical characteristics of system process noise and measurement noise on the basis of recursive least squares method to perform optimal fusion of the estimated value of the center of gravity.

4. The automatic feeding method for dual-arm cooperative coiled material according to claim 1, characterized in that, The dynamic distribution of the synergistic force adopts a fusion strategy of impedance control and force-position hybrid control. Impedance control equates the constraint dynamic relationship between the two arms and the coil to a spring-damped system, and achieves flexible adjustment of the movement trajectory of the two arms by adjusting the equivalent stiffness and damping coefficient. Force-position hybrid control plans the movement path of the two arms according to the spatial constraints of the target workstation, under the premise of meeting the clamping force requirements.

5. The automatic feeding method for dual-arm cooperative coiled material according to claim 1, characterized in that, Vibration monitoring employs an adaptive notch filter for active vibration suppression. The center frequency of the adaptive notch filter is automatically adjusted based on the real-time estimation of the system's natural frequency. The estimation of the natural frequency uses a combination of spectrum analysis and the Prony algorithm to extract the frequency and damping ratio of the dominant vibration mode from the internal force fluctuation signal.

6. The automatic feeding method for dual-arm cooperative coiled material according to claim 5, characterized in that, When multiple vibration modes are detected to coexist, the adaptive notch filter generates a multi-frequency notch combination to simultaneously suppress each vibration component, and the amplitude of the damping compensation signal is adaptively adjusted according to the real-time monitoring results of the vibration energy.

7. The automatic feeding method for dual-arm cooperative coiled material according to claim 1, characterized in that, The foreign object jamming detection uses a dual criterion of joint motor current slope detection and position deviation threshold detection. The joint motor current slope reflects the rate of change of motor output torque. When foreign object jamming occurs, the motor current slope on the jamming side rises sharply to several times the normal value. The position deviation threshold detection monitors the deviation between the actual position of the joint and the target position.

8. The automatic feeding method for dual-arm cooperative coiled material according to claim 1, characterized in that, The coordinated response processing adopts a hierarchical protection strategy. The first level of protection immediately reduces the output torque of the clamping jaws on the jamming side to a safe threshold after detecting the jamming signal, maintaining the basic clamping state of the coil. The second level of protection evaluates the stability of the coil after the execution of the first level of protection. If it is determined that the coil is in an unstable state, the coil release procedure is initiated. The third level of protection records the location and time information of the jamming after the coil is released.

9. The automatic feeding method for dual-arm cooperative coiled material according to claim 1, characterized in that, The gripper is designed with an adaptive deformation gripping surface, which is composed of multiple independent elastic fingers. Each elastic finger has a pressure sensor array on its inner side. The elastic fingers can adaptively deform according to the curvature of the roll surface, so that the gripping force is evenly distributed on the roll surface.

10. The automatic feeding method for dual-arm cooperative coiled material according to claim 9, characterized in that, The pressure sensor array collects the contact pressure of each elastic finger in real time. When the pressure of a certain elastic finger exceeds the average pressure of the adjacent elastic fingers, the control module automatically adjusts the driving current of that elastic finger to achieve pressure balance.

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