A control method of a multi-station robot for washing machine shell stamping

Abstract

The present application relates to the technical field of machine intelligence, in particular to a control method of a multi-station manipulator for stamping of a washing machine shell, which constructs a synchronization error matrix to determine an error transmission station sequence and a disturbance source station by using a station cooperative calibration experiment; in the working process of the station manipulator, the end load error coefficient of each station is determined, and the cumulative error weight of each station is determined in combination with the sequence number difference of each station and the disturbance source station in the error transmission station sequence; based on the cumulative error weight and the real-time position error of the manipulator of the disturbance source station, and in combination with the synchronization error matrix, the cumulative error amount of each station is determined; finally, according to the real-time position error and the cumulative error amount of the manipulator of each station, the error compensation value of each station is determined and compensation control is performed. The present application improves the accuracy of manipulator error compensation by determining the cumulative error amount of each station.

Description

Technical Field

[0001] This invention relates to the field of machine intelligence technology, specifically to a control method for a multi-station robotic arm used in stamping washing machine casings. Background Technology

[0002] In the stamping process of washing machine shells, multi-station robotic arms are driven by servo motors to achieve rapid positioning and transfer. Combined with a PLC control system, the movements of the press and the robotic arm are coordinated. For example, a lateral translation structure and auxiliary lifting design are used to adapt to the continuous stamping requirements of multi-station washing machine shells. These robotic arms can simultaneously complete loading, stamping, unloading, and inter-station transfer, significantly reducing manual intervention and improving production efficiency.

[0003] In existing multi-station robotic arms for stamping washing machine casings, insufficient precision and real-time performance of multi-motor coordinated motion control have become critical issues. Because the stamping process requires the robotic arm to switch rapidly between multiple stations, the translational and lifting movements driven by servo motors must be strictly synchronized with the stroke of the press slide. However, traditional control methods are prone to accumulating errors when dynamically adjusting the motion trajectories of each axis, leading to workpiece positioning deviations or mold interference. In particular, the complex temporal coupling relationships between multiple stations cause a decrease in system stability when handling sudden disturbances, affecting the reliability of continuous production. While the derivative gain of traditional PID controllers can be used to compensate for accumulated errors, it only focuses on the instantaneous rate of change of the current error and cannot effectively predict or compensate for such dynamic superposition errors across stations. Furthermore, its predictive effect is limited to the local trend of a single station, resulting in poor compensation and consequently, poor control precision in multi-station robotic arms. Summary of the Invention

[0004] To address the aforementioned technical problem of poor control accuracy in multi-station robotic arms, the present invention aims to provide a control method for a multi-station robotic arm used in stamping washing machine outer shells. The specific technical solution adopted is as follows:

[0005] In a first aspect, the present invention provides a control method for a multi-station robotic arm used in stamping the outer casing of a washing machine, comprising the following steps:

[0006] Using a workstation collaborative calibration experiment, a synchronization error matrix is ​​constructed, where each element in the synchronization error matrix represents the asymmetric dynamic coupling strength of one workstation to another.

[0007] Based on the synchronization error matrix, the error transmission station sequence and the interference source station are determined. The error transmission station sequence is used to reflect the error transmission direction when different stations work together.

[0008] During the operation of the robot arm at the workstation, the end-effector load error coefficient of each workstation is determined based on the relevant information of the robot arm end at different workstations.

[0009] The cumulative error weight of each station is determined based on the difference in the sequence number of each station and the interference source station in the error transmission station sequence, and the difference in the end load error coefficient between each station and the interference source station.

[0010] Based on the real-time position error of the robot arm at the interference source station, and the difference between the asymmetric dynamic coupling strength of each station to the interference source station and the asymmetric dynamic coupling strength of the interference source station to each station in the synchronization error matrix, the initial cumulative error of each station is determined.

[0011] The initial cumulative error is multiplied by the cumulative error weight of each workstation to obtain the cumulative error of each workstation.

[0012] Based on the real-time position error of the robot at each workstation and the cumulative error, an error compensation value is determined for each workstation, and compensation control is performed on the robot at each workstation based on the error compensation value.

[0013] In conjunction with the first aspect mentioned above, among some possible implementation methods, a synchronization error matrix is ​​constructed using workstation collaborative calibration experiments, including:

[0014] In the workstation collaborative calibration experiment, step acceleration excitation was applied to different workstations to obtain the basic coupling coefficient between workstation i and workstation j under different step acceleration excitations.

[0015] Based on the variation of the basic coupling coefficient under adjacent step acceleration excitation, and combined with the angle between the force transmission direction of the robot at station i and the motion axis of the robot at station j, the structural arm length between station i and station j, the equivalent mass of the robot at station i and the step acceleration excitation, the asymmetric dynamic coupling coefficient of station i to station j is determined.

[0016] Based on the asymmetric dynamic coupling coefficient and the distribution positions of different workstations, the asymmetric dynamic coupling strength between the p-th workstation and the q-th workstation is determined as the element in the p-th row and q-th column of the synchronization error matrix.

[0017] In conjunction with the first aspect mentioned above, among some possible implementation methods, the basic coupling coefficient between station i and station j under different step acceleration excitations is obtained, including:

[0018] Based on the positional deviation between workstation i and workstation j, the structural arm length between workstation i and workstation j, and the positional error of each joint of the robot arm at workstation i, the basic coupling coefficient between workstation i and workstation j under static conditions is determined.

[0019] In the workstation collaborative calibration experiment, step acceleration excitation was continuously applied to workstation i to obtain the basic coupling coefficient between workstation i and workstation j under different step acceleration excitations.

[0020] In conjunction with the first aspect mentioned above, among some possible implementation methods, the asymmetric dynamic coupling coefficient between station i and station j is determined, including:

[0021] Determine the change in the basic coupling coefficient under adjacent step acceleration excitations, and perform linear fitting on the change to obtain a fitted straight line;

[0022] Determine the slope of the fitted line to obtain the slope of the change in the basic coupling coefficient;

[0023] Based on the slope of the change of the basic coupling coefficient, and combined with the angle between the force transmission direction of the robot at station i and the motion axis of the robot at station j, the structural arm length between station i and station j, the equivalent mass of the robot at station i, and the acceleration value of the step acceleration excitation, the asymmetric dynamic coupling coefficient of station i to station j is determined.

[0024] In conjunction with the first aspect mentioned above, in some possible implementations, the asymmetric dynamic coupling strength between the p-th workstation and the q-th workstation is determined as the element in the p-th row and q-th column of the synchronization error matrix, including:

[0025] All workstations are sorted according to the order from upstream to downstream of the production line to obtain the serial number of each workstation.

[0026] The basic elements at each position on the main diagonal of the synchronization error matrix are set to the first value, and the basic elements at other positions in the synchronization error matrix excluding the main diagonal are set to the second value, wherein the first value is greater than the second value.

[0027] The asymmetric dynamic coupling coefficient of the p-th workstation to the q-th workstation is determined by adding the basic element of the p-th row and q-th column of the synchronization error matrix, which is then used as the asymmetric dynamic coupling strength of the p-th row and q-th column of the synchronization error matrix, thus obtaining the synchronization error matrix.

[0028] In conjunction with the first aspect mentioned above, the error propagation station sequence is determined in several possible implementation methods, including:

[0029] The sum of the absolute values ​​of the upper right triangular elements in the synchronization error matrix is ​​used to obtain the forward propagation strength, and the sum of the absolute values ​​of the lower left triangular elements in the synchronization error matrix is ​​used to obtain the reverse propagation strength.

[0030] The ratio of the forward transmission intensity to the reverse transmission intensity is determined to obtain a first ratio.

[0031] If the first ratio is greater than the upper threshold, all workstations are sorted in the order from upstream to downstream of the production line to obtain the error propagation workstation sequence. If the first ratio is less than the lower threshold, all workstations are sorted in the order from downstream to upstream of the production line to obtain the error propagation workstation sequence.

[0032] Otherwise, the sum of all column elements in the synchronization error matrix for each workstation is determined to obtain the comprehensive interference intensity of each workstation, and all workstations are sorted in ascending order of comprehensive interference intensity to obtain the error transmission workstation sequence.

[0033] In conjunction with the first aspect mentioned above, the interference source workstations are identified in several possible implementation methods, including:

[0034] The sum of all row elements in the synchronization error matrix for each workstation is determined to obtain the overall interference intensity for each workstation.

[0035] Determine the maximum value among all workstations' overall interference intensity, and identify the workstation corresponding to the maximum value as the interference source workstation.

[0036] In conjunction with the first aspect above, in some possible implementations, the relevant information of the robotic arm end effector includes at least: the speed and distance in each motion direction obtained by disassembling the tasks performed by the robotic arm at different workstations; the motor current data of the robotic arm at different workstations during task execution; the mass of the motion axis of the robotic arm at different workstations and the distance from the center of mass of the robotic arm to the end effector; and the contact force data between the robotic arm and the workpiece at different workstations; determining the end effector load error coefficient for each workstation, including:

[0037] The ratio of speed to distance in the current motion direction is determined by breaking down the task performed by the robot arm at each workstation, thus obtaining the second ratio.

[0038] The ratio of the increase in motor current to the fluctuation in motor current is determined when the robot arm at each workstation is currently performing a task, thus obtaining the third ratio.

[0039] By combining the second and third ratios, the end-load inertia of each station is determined;

[0040] The moment of inertia of each station is determined based on the mass of the motion axis of the robot and the distance from the center of mass of the robot to its end effector.

[0041] The load inertia ratio of each station is determined based on the ratio of the end load inertia to the load inertia.

[0042] The contact force error for each station is calculated based on the difference between the current contact force and the expected contact force in the contact force data between the robot and the workpiece at each station.

[0043] By combining the load inertia ratio and contact force error, the end load error coefficient of each station is determined.

[0044] In conjunction with the first aspect mentioned above, the cumulative error weight for each workstation is determined in several possible implementation methods, including:

[0045] The difference between the sequence number of each workstation and the interference source workstation in the error transmission workstation sequence is negatively correlated and mapped to obtain the sequence number difference mapping value.

[0046] The ratio of the end load error coefficient of each workstation to that of the interference source workstation is determined to obtain the fourth ratio.

[0047] By combining the sequence number difference mapping value and the fourth ratio value, the cumulative error weight of each workstation is obtained.

[0048] In conjunction with the first aspect mentioned above, the initial cumulative error for each workstation is determined in several possible implementation methods, including:

[0049] The ratio of the asymmetric dynamic coupling strength of each station to the interference source station in the synchronization error matrix to the asymmetric dynamic coupling strength of the interference source station to each station is determined to obtain the fifth ratio.

[0050] The initial cumulative error of each station is obtained by integrating the product of the real-time position error of the robot arm at the interference source station and the fifth ratio over time.

[0051] Secondly, the present invention also provides a control system for a multi-station robotic arm used for stamping the outer casing of a washing machine, including a memory and a processor. The memory is used to store executable computer program code, and the processor is used to call and run the executable computer program code from the memory, causing the system to perform the methods in the first aspect or any possible implementation thereof.

[0052] Thirdly, the present invention also provides a computer program product comprising: computer program code, which, when run on a computer, causes the computer to perform the method described in the first aspect or any possible implementation thereof.

[0053] Fourthly, the present invention also provides a computer-readable storage medium storing computer program code that, when executed on a computer, causes the computer to perform the method described in the first aspect or any possible implementation thereof.

[0054] This invention has the following beneficial effects: First, by conducting pre-conducting station collaboration calibration experiments, a synchronization error matrix is ​​constructed. Each element in the synchronization error matrix represents the asymmetric dynamic coupling strength between one station and another, reflecting the error transmission strength between the two stations. Based on the distribution of the asymmetric dynamic coupling strength in the synchronization error matrix, an error transmission station sequence reflecting the error transmission direction during collaborative work of different stations is determined, as well as interference source stations that may cause error interference to other stations. Second, during the normal operation of the multi-station robot, based on the relevant information of the robot's end effector at different stations, the end-effector load error coefficient of each station is determined. This end-effector load error coefficient reflects the error caused by the end-effector load at each station. Furthermore, based on the distance of error transmission between each station and the interference source station in the error transmission station sequence and the difference between the end-effector load error coefficients of each station and the interference source station, the cumulative error weight of each station is determined. This weight is used to correct the cumulative error caused by the error transmission of the interference source station at each station, thereby ultimately determining the cumulative error of each station. Finally, based on the real-time position error and cumulative error of the robot at each workstation, the error compensation value for each workstation is determined, and robot compensation control is performed. This invention effectively improves the accuracy of robot error compensation by accurately determining the cumulative error at each workstation, thereby improving the control accuracy of multi-workstation robots. Attached Figure Description

[0055] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart illustrating the steps of a control method for a multi-station robotic arm used in stamping a washing machine casing, according to an embodiment of the present invention.

[0057] Figure 2 This is a flowchart illustrating the steps of constructing the synchronization error matrix according to an embodiment of the present invention;

[0058] Figure 3 This is a flowchart illustrating the steps for determining the interference source workstation according to an embodiment of the present invention.

[0059] Figure 4 This is a flowchart illustrating the steps for determining the end-load error coefficient of each workstation according to an embodiment of the present invention.

[0060] Figure 5 This is a flowchart illustrating the steps for determining the cumulative error weight for each workstation according to an embodiment of the present invention.

[0061] Figure 6 This is a flowchart illustrating the steps for determining the cumulative error at each workstation according to an embodiment of the present invention.

[0062] Figure 7 This is a schematic diagram of the control system of a multi-station robotic arm for stamping the outer shell of a washing machine, according to an embodiment of the present invention. Detailed Implementation

[0063] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific embodiments and in conjunction with the accompanying drawings.

[0064] Embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. While some embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the invention. It should be understood that the accompanying drawings and embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the invention.

[0065] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0066] The term "comprising" and its variations as used herein are open-ended inclusions, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the description below.

[0067] It should be noted that the concepts of "first" and "second" mentioned in this invention are only used to distinguish different devices, modules or units, and are not used to limit the order of functions performed by these devices, modules or units or their interdependencies.

[0068] Although operations or steps are described in a specific order in the accompanying drawings in the embodiments of the present invention, this should not be construed as requiring these operations or steps to be performed in the specific order or serial order shown, or requiring all of the shown operations or steps to be performed to obtain the desired result. In the embodiments of the present invention, these operations or steps may be performed serially; they may be performed in parallel; or a portion of these operations or steps may be performed.

[0069] Furthermore, it is understood that the data involved in the technical solutions of this invention (including but not limited to the data itself, the acquisition or use of the data) shall comply with the requirements of relevant laws, regulations and related provisions. Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains, and all parameters or indicators in the formulas involved in this invention are normalized values ​​that have eliminated the influence of dimensions.

[0070] To address the issue of poor control accuracy in existing multi-station robotic arms, this invention provides a control method for a multi-station robotic arm used in washing machine casing stamping. This method first utilizes a station collaborative calibration experiment to obtain the asymmetric dynamic coupling strength between different stations to construct a synchronization error matrix. Based on this synchronization error matrix, it identifies the interference source station and the error propagation station sequence characterizing the error propagation relationship between stations. Then, it analyzes the errors caused by differences in end-load, calculates the end-load error coefficient for each station, and determines the cumulative error weight for each station. Based on this cumulative error weight, it corrects the initial cumulative error caused by the error propagation from the interference source station for each station, obtaining the cumulative error for each station. Finally, based on the position errors and cumulative error of each motion axis of the robotic arm at each station, it determines the error compensation value for each station. Based on this error compensation value, it performs compensatory control on the robotic arm at each station. Compared to traditional PID controllers that only focus on instantaneous changes and use fixed differential gain to control accumulated errors, the method provided in this invention analyzes the causal relationship and hierarchical relationship of accumulated errors between multiple workstations. This makes error compensation for robotic arms in complex multi-workstation collaborative scenarios more accurate, effectively improving the control precision of multi-workstation robotic arms, and thus improving the precision of the stamping process for washing machine shells.

[0071] The following will describe in detail, with reference to the accompanying drawings, a control method for a multi-station robotic arm used in stamping the outer shell of a washing machine according to an embodiment of the present invention.

[0072] Figure 1 This diagram illustrates the basic flow chart of a control method for a multi-station robotic arm used in stamping a washing machine casing, as provided in an embodiment of the present invention. Figure 1 As shown, the method specifically includes the following steps:

[0073] Step S100: Construct a synchronization error matrix using a workstation collaborative calibration experiment. Each element in the synchronization error matrix represents the asymmetric dynamic coupling strength between one workstation and another.

[0074] Specifically, for multi-station stamping platforms, taking a cantilevered multi-station stamping platform as an example, the multi-station robotic arms include: loading robotic arms, stamping auxiliary robotic arms, and unloading robotic arms. Tracking and positioning of the multi-station robotic arms is performed to determine the tracking and positioning information for each station. This information reflects the movement and position of the robotic arms at different stations. For example, optical encoders are integrated and installed on the motion axes (i.e., links) of the robotic arms to monitor the X / Y / Z axis movement positions and obtain position coordinate data. High-speed industrial cameras (1000fps) are deployed between stations to perform visual positioning in conjunction with vision algorithms, which is used for mutual verification with the position coordinate data measured by the optical encoders. Simultaneously, a six-dimensional force sensor is integrated into the end effector of the robotic arm to detect the contact force data between it and the workpiece. Real-time motion position data of the robotic arms is collected, and Kalman filtering is used to eliminate noise. Multi-sensor data is then fused to generate estimates of the motion state of each axis's position, velocity, and force.

[0075] Based on the tracking and positioning information of each workstation, a synchronization error matrix is ​​constructed through multi-workstation collaborative calibration experiments to reflect the dynamic differences when multiple workstations work together. The construction of the synchronization error matrix needs to reflect the asymmetry of dynamic coupling between workstations. For example, the error propagation weights of the loading workstation (workstation 1) and the stamping workstation (workstation 2) are different due to their different motion characteristics.

[0076] Furthermore, in one possible implementation, such as Figure 2 As shown, in step S100 above, a synchronization error matrix is ​​constructed using a workstation collaborative calibration experiment, including:

[0077] Step S101: In the workstation collaborative calibration experiment, step acceleration excitation is applied to different workstations to obtain the basic coupling coefficient between workstation i and workstation j under different step acceleration excitations.

[0078] Specifically, each station's robotic arm has several joints. Based on the tracking and positioning information of each station, and according to the deviation between the actual position of each joint on the robotic arm and the target trajectory, a tracking error vector is defined for each station. Taking the r-th station as an example, the tracking error vector e r =[e 1, e2,…,e n ,…,e N ] T Among them, e n Let N represent the tracking error of the nth joint on the robot arm at the rth station. This tracking error is equal to the difference between the expected joint angle position and the actual joint angle position of the nth joint. N represents the total number of joints on the robot arm at the rth station.

[0079] Based on the tracking error vector of each workstation, static calibration is performed using impact tests to obtain the basic coupling coefficient between different workstations under different step acceleration excitations. This means obtaining the relative error between adjacent workstations through experimental calibration. Further, in a possible implementation, obtaining the basic coupling coefficient between workstation i and workstation j under different step acceleration excitations in step S101 includes: determining the basic coupling coefficient between workstation i and workstation j under static conditions based on the positional deviation between workstation i and workstation j, the structural arm length between workstation i and workstation j, and the positional errors of each joint of the manipulator at workstation i; and applying a step acceleration excitation to workstation j in a workstation collaborative calibration experiment to obtain the basic coupling coefficient between workstation i and workstation j under different step acceleration excitations.

[0080] Specifically, static calibration is performed using impact testing: the robot arm at each station moves independently. Taking the movement of any station i as an example, the positional deviation between any two stations i and j is measured. This positional error refers to the difference between the actual distance between the two stations i and j and the set distance (the positional deviation can be positive or negative; a positive value indicates that the actual distance between the two stations has increased, and vice versa). Therefore, based on the positional deviation between station i and j, the structural arm length between station i and j, and the positional error of each joint of the robot arm at station i, the basic coupling coefficient between station i and j under static conditions is calculated using the following formula:

[0081]

[0082] In the formula: f i,j Δx represents the basic coupling coefficient between workstation i and workstation j under static conditions. i,j L represents the positional deviation between workstation i and workstation j; i,j Indicates the length of the structural arm between workstation i and workstation j; ||e i ‖ represents the Euclidean norm of the tracking error of all joints at station i. The denominator is multiplied by the two values ​​to eliminate the influence of differences in mechanical structure dimensions.

[0083] Using the above method, the basic coupling coefficient between different workstations under static conditions can be determined through experimental calibration, which can be used to reflect the relative error between different workstations.

[0084] Then, a step acceleration excitation is applied to the impact test. Taking station i as an example, a step acceleration (amplitude 5 m / s²) is applied to station i. 2 (Duration 50ms) to obtain the basic coupling coefficient between station i and station j under continuous step acceleration excitation.

[0085] Step S102: Based on the changes in the basic coupling coefficient under adjacent step acceleration excitation, and combined with the angle between the force transmission direction of the robot at station i and the motion axis of the robot at station j, the structural arm length between station i and station j, and the equivalent mass of the robot at station i and the step acceleration excitation, determine the asymmetric dynamic coupling coefficient of station i to station j.

[0086] Specifically, for workstations i and j, based on the changes in the basic coupling coefficients of workstations i and j under adjacent step acceleration excitations, and combined with the angle between the force transmission direction of the manipulator at workstation i and the motion axis of the manipulator at workstation j, the structural arm length between workstations i and j, the equivalent mass of the manipulator at workstation i, and the step acceleration excitation, the asymmetric dynamic coupling coefficient of workstation i to workstation j can be determined. The asymmetric dynamic coupling coefficient between the two workstations reflects the difference in error propagation intensity between workstations. For example, due to the directionality of inertial force transmission, the influence coefficient γ of the high acceleration at stamping workstation 2 on the adjacent workstation 3... 23 It may be greater than the inverse asymmetric dynamic coupling coefficient γ. 32 This indicates that the error at the workstation has a stronger impact on the downstream workstations.

[0087] Furthermore, in one possible implementation, determining the asymmetric dynamic coupling coefficient between workstation i and workstation j in step S102 includes: determining the change in the basic coupling coefficient under adjacent step acceleration excitation; performing linear fitting on the change to obtain a fitted line; determining the slope of the fitted line to obtain the slope of the change in the basic coupling coefficient; and determining the asymmetric dynamic coupling coefficient between workstation i and workstation j based on the slope of the change in the basic coupling coefficient, combined with the angle between the force transmission direction of the manipulator of workstation i and the motion axis of the manipulator of workstation j, the structural arm length between workstation i and workstation j, the equivalent mass of the manipulator of workstation i, and the acceleration value of the step acceleration excitation.

[0088] Specifically, for station i, the change Δf of the basic coupling coefficient between station i and station j under continuous step acceleration excitation is obtained. i,j The method of least binary values ​​is used to analyze the change Δf. i,j A fitting process is performed to obtain the slope value of the change, and this slope value is used as the slope of the basic coupling coefficient change.

[0089] Then, based on the slope of the basic coupling coefficient change, and combined with the angle between the force transmission direction of the robot at station i and the motion axis of the robot at station j, the structural arm length between station i and station j, the equivalent mass of the robot at station i, and the acceleration value of the step acceleration excitation, the asymmetric dynamic coupling coefficient of station i to station j is calculated using the following formula:

[0090]

[0091] In the formula: γ i,j θ represents the asymmetric dynamic coupling coefficient between workstation i and workstation j; i,j This represents the angle between the force transmission direction of the robot arm at workstation i and the motion axis of the robot arm at workstation j (this angle is a real-time variable). The motion axis refers to the direction of the coordinate axis along which the robot arm moves in three-dimensional space. For example, the robot arm can extend and retract (moving along the x-axis), move left and right (moving along the y-axis), and move up and down (moving along the z-axis); L ij This represents the structural arm length between workstation i and workstation j, that is, the distance between the cantilever arms connected to the robotic arms at all workstations between workstation i and workstation j; m i a represents the equivalent mass (actual mass) of the robot arm at workstation i; j represents the acceleration value of the step acceleration excitation applied to station i; k represents the slope of the change in the basic coupling coefficient corresponding to station i and station j.

[0092] Following the same method described above, based on the rate of change of the basic coupling coefficient under static calibration under continuous step acceleration excitation and the mass inertia of the workstation robot, the asymmetric dynamic coupling coefficient between any two workstations can be obtained. This asymmetric dynamic coupling coefficient reflects the difference in error propagation intensity between the two corresponding workstations.

[0093] Step S103: Based on the asymmetric dynamic coupling coefficient and the distribution positions of different workstations, determine the asymmetric dynamic coupling strength between the p-th workstation and the q-th workstation as the element in the p-th row and q-th column of the synchronization error matrix.

[0094] Specifically, the synchronization error matrix is ​​determined based on the asymmetric dynamic coupling coefficients between different workstations and their distribution locations. The differences in the motion trajectories of the robotic arms at different workstations lead to asymmetric coupling weights in the synchronization error matrix. For example, the error propagation coefficients between the rapid translational motion of the robotic arm at the loading workstation and the high-frequency reciprocating motion at the stamping workstation should show significant differences in the matrix.

[0095] Furthermore, in step S103 above, determining the asymmetric dynamic coupling strength between the p-th workstation and the q-th workstation as the element in the p-th row and q-th column of the synchronization error matrix includes: sorting all workstations according to the order of the production line from upstream to downstream to obtain the serial number of each workstation; setting the basic element at each position on the main diagonal of the synchronization error matrix as the first value, and setting the basic element at other positions in the synchronization error matrix except for the main diagonal as the second value, wherein the first value is greater than the second value; determining the sum of the asymmetric dynamic coupling coefficient between the p-th workstation and the q-th workstation and the basic element in the p-th row and q-th column of the synchronization error matrix as the asymmetric dynamic coupling strength in the p-th row and q-th column of the synchronization error matrix, thereby obtaining the synchronization error matrix.

[0096] Specifically, the size of the synchronization error matrix is ​​set according to the total number of workstations; this matrix is ​​a square matrix with a size equal to the total number of workstations. All workstations are sorted from upstream to downstream of the production line to obtain their serial numbers. The fundamental element at each position on the main diagonal (the diagonal from the upper left to the lower right) of the synchronization error matrix is ​​set to 2, derived from the diagonal terms of the Laplace matrix, representing the dominant contribution of the workstation's own tracking error to synchronization. If the element in the p-th row and q-th column of the synchronization error matrix is ​​on the matrix diagonal, then 2 + γ is added. p,q This represents the asymmetric dynamic coupling strength between the p-th workstation and the q-th workstation, and is used as the element value of the p-th row and q-th column of the synchronization error matrix. For example, the high acceleration of the stamping workstation (the 2nd workstation) will increase its coupling coefficient with the loading workstation (the 1st workstation), thus amplifying its own diagonal weight. Simultaneously, the basic element at each position outside the main diagonal of the synchronization error matrix is ​​set to -1, representing the negative feedback effect of adjacent workstation errors in traditional collaborative control, forcing the errors between workstations to tend towards consistency. If the element in the p-th row and q-th column of the synchronization error matrix is ​​not on the diagonal, then -1 to γ ​​is used. p,q The term represents the asymmetric dynamic coupling strength between the p-th workstation and the q-th workstation, and is used as the element value of the p-th row and q-th column in the synchronization error matrix. For example, if the rapid movement of the first workstation causes additional interference to the second workstation, the coupling term becomes more negative, enhancing the suppression effect. Thus, the synchronization error matrix can be determined, reflecting the complex coupling relationship between the robotic arms at each workstation during coordination.

[0097] Following the above method, a synchronization error matrix for a multi-station robotic arm can be constructed by utilizing station collaborative calibration experiments.

[0098] Step S200: Based on the synchronization error matrix, determine the error transmission station sequence and the interference source station. The error transmission station sequence is used to reflect the error transmission direction when different stations work together.

[0099] Specifically, a sudden disturbance at one workstation, such as an external force impact, can rapidly spread to other workstations. By analyzing the asymmetric dynamic coupling strengths in the synchronization error matrix, the specific direction of this spread can be determined. Therefore, by extracting the row, column, and diagonal features of this error synchronization matrix, the error propagation relationship during multi-workstation collaboration can be obtained, including the error propagation direction, the magnitude of the impact, and the workstation where the interference source is located.

[0100] Furthermore, in one possible implementation, such as Figure 3 As shown, determining the error propagation station sequence in step S200 above includes:

[0101] Step S201: Determine the sum of the absolute values ​​of the upper right triangular elements in the synchronization error matrix to obtain the forward propagation strength, and determine the sum of the absolute values ​​of the lower left triangular elements in the synchronization error matrix to obtain the reverse propagation strength.

[0102] Specifically, the diagonal elements in the synchronization error matrix reflect the direction of error propagation. If the forward propagation intensity (from the upper left corner to the lower right corner) is much greater than the reverse propagation intensity, it indicates that the error propagates more significantly from upstream (such as the loading station) to downstream (such as the unloading station) along the production line. For example, the high acceleration of the stamping station results in a strong inertial force interference on the downstream station, forming an "error propagation chain".

[0103] Therefore, the sum of the absolute values ​​of the upper right triangular elements in the synchronization error matrix is ​​calculated to obtain the forward transmission strength, which reflects the cumulative interference from the upstream workstation to the downstream workstation. Simultaneously, the sum of the absolute values ​​of the lower left triangular elements in the synchronization error matrix is ​​calculated to obtain the reverse transmission strength, which reflects the feedback interference from the downstream workstation to the upstream workstation.

[0104] Step S202: Determine the ratio of forward transmission intensity to reverse transmission intensity to obtain the first ratio.

[0105] Step S203: If the first ratio is greater than the upper threshold, then sort all workstations in the order from upstream to downstream of the production line to obtain the error propagation workstation sequence. If the first ratio is less than the lower threshold, then sort all workstations in the order from downstream to upstream of the production line to obtain the error propagation workstation sequence.

[0106] Specifically, the ratio of forward propagation intensity to reverse propagation intensity is calculated and recorded as the first ratio. When the first ratio is greater than the upper threshold, in one specific implementation, the upper threshold is set to 1.5. This indicates that the error propagates forward along the production line station sequence, i.e., station 1, station 2, station 3, etc. Therefore, all stations are sorted according to the production line from upstream to downstream to obtain the error propagation station sequence. When the first ratio is less than the lower threshold, in one specific implementation, the lower threshold is set to 0.8. This indicates that the error propagates backward, and all stations are sorted according to the production line from downstream to upstream to obtain the error propagation station sequence.

[0107] Step S204: Otherwise, determine the sum of all column elements in the synchronization error matrix for each workstation to obtain the comprehensive interference intensity of each workstation, and sort all workstations in ascending order of comprehensive interference intensity to obtain the error transmission workstation sequence.

[0108] Specifically, when the first ratio is greater than the upper threshold or less than the lower threshold, the error propagation direction is considered linear. Conversely, when the first ratio is between the upper and lower thresholds, it indicates that the error propagation is non-linear. In this case, the error propagation workstation sequence is obtained by sorting the workstations according to the column elements, i.e., according to the comprehensive interference level of each workstation from other workstations. The specific implementation process includes: determining the sum of all elements in each column of the synchronization error matrix, and using this sum as the comprehensive interference intensity of the workstation corresponding to that column. This comprehensive interference intensity reflects the comprehensive interference intensity of the corresponding workstation affected by all other workstations. Thus, the comprehensive interference intensity of each workstation can be obtained. If the sum of the column elements of the q-th workstation in the synchronization error matrix (i.e., the sum of all elements in the q-th column of the synchronization error matrix) is lower than the average sum of the elements in all columns (the sum of the elements in each column divided by the number of columns), that is, the comprehensive interference intensity of the q-th workstation is lower than the comprehensive interference intensity of other workstations, it means that the q-th workstation is most affected by external errors. All workstations are sorted in ascending order of overall interference intensity to obtain the error propagation workstation sequence.

[0109] By analyzing the column and diagonal features of the synchronization error matrix in the above manner, the error transmission station sequence can be accurately determined.

[0110] Furthermore, in one possible implementation, such as Figure 3 As shown, the step S200 above, which identifies the interference source station, includes:

[0111] Step S205: Determine the sum of all row elements in the synchronization error matrix for each workstation to obtain the comprehensive interference intensity of each workstation.

[0112] Specifically, the sum of all elements in each row of the synchronization error matrix is ​​determined, and this sum is taken as the comprehensive interference intensity of the corresponding workstation. This comprehensive interference intensity reflects the overall influence of the corresponding workstation on all other workstations. Thus, the comprehensive interference intensity of each workstation can be obtained.

[0113] If the sum of the column elements of the p-th workstation in the synchronization error matrix (i.e., the sum of all elements in the p-th row of the synchronization error matrix) is significantly higher than that of other workstations, it indicates that the p-th workstation is a "critical source of interference" for multi-workstation collaboration. For example, due to high-frequency impact vibration, the dynamic error of the stamping workstation will be transmitted to adjacent workstations through the mechanical structure.

[0114] Step S206: Determine the maximum value among all workstations in terms of overall interference intensity, and identify the workstation corresponding to the maximum value as the interference source workstation.

[0115] Specifically, determine the maximum value among all workstations' overall interference intensity, and identify the workstation corresponding to this maximum value as the interference source workstation. This allows you to determine the interference source workstation.

[0116] Step S300: During the operation of the robot arm at the workstation, determine the end-load error coefficient of each workstation based on the relevant information of the robot arm end at different workstations.

[0117] Specifically, for multi-station stamping platforms, vibration and temperature sensors are installed in key components such as the press crankshaft, die guide pillars, and robot joints. These sensors collect real-time vibration and temperature data from the press and robot. A pre-set safe operating threshold is established. If the robot's prolonged operation causes the real-time vibration or temperature values ​​to exceed the safe operating threshold, the machine is stopped directly without error compensation; otherwise, it continues to operate normally.

[0118] During normal operation of a multi-station stamping platform, differences in the end-effector loads (such as the weight of the stamping die and the workpiece clamping force) at different stations lead to inconsistencies in the end-effector inertia during multi-station collaboration. For example, the end-effector inertia of the robot at the unloading station undergoes significant abrupt changes due to the need for rapid workpiece release. This inconsistency in end-effector inertia disrupts the torque balance of multi-axis collaborative control, resulting in the accumulation of trajectory tracking errors. Therefore, error compensation is necessary during the operation of multi-station robots to improve their control accuracy.

[0119] To perform error compensation, it is first necessary to obtain relevant information about the robot end effector at different workstations. This information includes: the speed and distance of each motion direction obtained by breaking down the robot's task at each workstation; the motor current data of the robot at each workstation during task execution; the mass of the robot's motion axes and the distance from the robot's center of mass to the end effector at each workstation; and the contact force data between the robot and the workpiece at each workstation. Specifically, the task performed by the robot at each workstation is broken down to obtain the speed and distance of each motion direction. The motor current is collected using a current sensor to obtain the motor current data of the robot at each workstation during task execution. The total mass of each motion axis of the robot at each workstation (i.e., the mass of the robot's components other than the end effector) and the distance from the robot's center of mass to the end effector are pre-acquired. The contact force between the robot and the workpiece is collected using a six-dimensional force sensor integrated into the robot's end effector at each workstation to obtain the contact force data between the robot and the workpiece at each workstation.

[0120] Furthermore, in one possible implementation, such as Figure 4 As shown, based on the relevant information of the robot end effector at different workstations, the determination of the end effector load error coefficient for each workstation in step S300 above includes:

[0121] Step S301: Determine the ratio of speed to distance in the current motion direction obtained by disassembling the task performed by the robot arm at each workstation, and obtain the second ratio.

[0122] Specifically, the task to be performed by the robotic arm at each workstation is broken down, and the velocity v and distance L in the current motion direction are obtained. o The ratio of the two ratios is used to obtain the second ratio. The closer the end effector of the robot is to the workpiece, the greater its movement speed, which will inevitably generate additional inertial force, and the larger this ratio will be.

[0123] Step S302: Determine the ratio of the increase in motor current to the fluctuation in motor current data when the robot arm is currently performing a task at each workstation, and obtain the third ratio.

[0124] Specifically, for the end effector of a robotic arm, the positional error caused by the load inevitably leads to additional inertial force and friction. Friction at the working interface is mostly caused by fixed errors and generally results in horizontal movement. However, inertial force is a dynamic error transmitted from the cantilever, mostly resulting in non-horizontal movement and more easily interfering with other workstations. If the load inertia of the robotic arm's end effector suddenly increases, the motor current increases significantly under the same acceleration, i.e., the increase in motor current ΔI is larger. In one specific implementation, this increase in motor current ΔI can be obtained by calculating the difference between the last current value and the first current value in the motor current data during the current action of the robotic arm, and using this difference as the exponent of an exponential function with the natural constant e as the base. When additional friction occurs, the fluctuation of the motor current increases, i.e., the motor current fluctuation σ... c Increase. In one specific implementation, the motor current fluctuation σ c This can be obtained by calculating the variance of all current values ​​in the motor current data during the execution of the robot arm's actions at the workstation. The calculation includes the increase in motor current ΔI and the fluctuation in motor current σ. c ratio This ratio This is denoted as the third ratio. The larger the third ratio, the greater the degree to which the error is dominated by inertia. Therefore, this third ratio is also called the inertia dominance coefficient.

[0125] Step S303: Combine the second ratio and the third ratio to determine the end load inertia of each station.

[0126] Specifically, the second and third ratios are combined to determine the end-effector load inertia for each workstation. The larger the values ​​of the second and third ratios, the more likely the end-effector of the robot at that workstation is experiencing a sudden increase in load inertia due to external inertial forces, and the larger the corresponding end-effector load inertia value. In one specific implementation, the product of the second and third ratios is calculated, and this product is used as the end-effector load inertia.

[0127] Step S304: Determine the moment of inertia of each station based on the mass of the motion axis of the robot and the distance from the center of mass of the robot to its end effector.

[0128] Specifically, for each robot at each workstation, its moment of inertia is determined. The greater the mass of the robot's motion axis and the greater the distance from its center of mass to its end effector, the greater its moment of inertia. In one implementation, the product of the robot's motion axis mass and the distance from its center of mass to its end effector is calculated, and this product is used as the moment of inertia for the corresponding workstation.

[0129] Step S305: Determine the load inertia ratio of each station based on the ratio of the end load inertia to the load inertia of each station.

[0130] Specifically, the load inertia ratio for each station is determined based on the ratio of the end-load inertia to the load inertia. A high load inertia ratio indicates that the end-load inertia at that station has already covered the normal rotational inertia of the robot itself, which can easily lead to lag in the acceleration response controlled by the motor, and the acceleration dominated by inertial force will generate more uncontrollable position errors. In one specific implementation, a standard normalization function is used to normalize the end-load inertia and the load inertia ratio for each station, and the ratio of the end-load inertia and the load inertia ratio after normalization is taken as the load inertia ratio.

[0131] Step S306: Based on the difference between the current contact force and the expected contact force in the contact force data between the robot and the workpiece at each station, calculate the contact force error for each station.

[0132] Specifically, for each robot at each workstation, the difference between the current contact force value and the expected contact force in the contact force data between the robot and the workpiece is calculated, and this difference is used as the contact force error. It should be understood that under inertial load conditions, the contact force between the robot and the workpiece will only increase.

[0133] Step S307: Combine the load inertia ratio and contact force error to determine the end load error coefficient for each station.

[0134] Specifically, if the contact force error is large, and the load inertia ratio is high, then it is determined that the end contact force error is mainly caused by inertia, which is likely to transmit errors to other workstations. In one specific implementation, the product of the load inertia ratio and the contact force error for each workstation is determined, and this product is used as the contact force error.

[0135] The above analysis of the errors caused by the differences in end-effector loads of the robotic arms at each workstation allows for the accurate determination of the end-effector load error coefficient for each workstation.

[0136] Step S400: Determine the cumulative error weight of each station based on the difference in the sequence number of each station and the interference source station in the error transmission station sequence, and the difference in the end load error coefficient between each station and the interference source station.

[0137] Specifically, based on the error propagation station sequence, for each station, the cumulative error weight is determined according to the difference in sequence number between the station and the interference source station in the error propagation station sequence, and the end-load error coefficient between each station and the interference source station. The smaller the difference in sequence number between the station and the interference source station in the error propagation station sequence, the faster the error propagation and the greater the impact; therefore, the weight for cumulative error correction should be greater. Simultaneously, the smaller the difference in the end-load error coefficient between the station and the interference source station, the more the end-load of the interference source station has affected the station; therefore, the cumulative error correction weight should also be greater.

[0138] Furthermore, in one possible implementation, such as Figure 5 As shown, the step S400 above, which determines the cumulative error weight for each workstation, includes:

[0139] Step S401: Perform negative correlation mapping on the difference between the serial number of each workstation and the interference source workstation in the error transmission workstation sequence to obtain the serial number difference mapping value.

[0140] Step S402: Determine the ratio of the end load error coefficient of each workstation to that of the interference source workstation to obtain the fourth ratio.

[0141] Step S403: Combine the sequence number difference mapping value and the fourth ratio value to obtain the cumulative error weight of each workstation.

[0142] Specifically, based on the sequence number difference mapping value and the fourth ratio, the cumulative error weight for each workstation is calculated as follows:

[0143]

[0144] Where: β p s represents the cumulative error weight of the p-th workstation; max Indicates the sequence number of the interference source station in the error propagation station sequence; s p z represents the index of the p-th workstation in the error propagation workstation sequence; p z represents the end-load error coefficient of the p-th workstation; max represents the end-load error coefficient of the interference source station; e represents the natural constant.

[0145] In the above formula, the smaller the absolute value of the difference between the p-th workstation and the interference source workstation in the error propagation workstation sequence, the faster the error propagation and the greater the impact; conversely, the larger the absolute value of the difference in the sequence numbers, the smaller the cumulative impact of errors between workstations. To avoid the problem of having too few multi-workstation robots, the difference in the sequence numbers is squared and amplified, and an exponential function is used to perform a negative correlation mapping to obtain the sequence number difference mapping value. The larger the square of the difference, the greater the difference mapping value for that sequence number. The smaller the value of , the smaller the weight that needs to be corrected for the cumulative error. The fourth ratio represents the ratio of the end load error coefficient of the p-th workstation to the end load error coefficient of the interference source workstation. The closer the numerator is to the denominator, the more the end load of the interference source workstation has affected the p-th workstation, and therefore the greater the cumulative error correction weight.

[0146] Step S500: Based on the real-time position error of the robot arm at the interference source station, and the difference between the asymmetric dynamic coupling strength of each station to the interference source station and the asymmetric dynamic coupling strength of the interference source station to each station in the synchronization error matrix, determine the initial cumulative error of each station.

[0147] Specifically, for each workstation, based on the real-time position error of the robot arm at the interference source workstation, and combined with the difference between the asymmetric dynamic coupling strength of each workstation to the interference source workstation and the asymmetric dynamic coupling strength of the interference source workstation to each workstation in the synchronization error matrix, the cumulative error of each workstation can be determined. This cumulative error refers to the cumulative transmission error generated by the interference source workstation to each workstation.

[0148] Furthermore, in one possible implementation, such as Figure 6 As shown, the determination of the initial cumulative error for each workstation in step S500 above includes:

[0149] Step S501: Determine the ratio of the asymmetric dynamic coupling strength of each workstation to the interference source workstation and the asymmetric dynamic coupling strength of the interference source workstation to each workstation in the synchronization error matrix, and obtain the fifth ratio.

[0150] Step S502: Integrate the product of the real-time position error of the robot arm at the interference source station and the fifth ratio over time to obtain the initial cumulative error for each station.

[0151] Specifically, for each workstation, the initial cumulative error is determined using the following formula:

[0152]

[0153] In the formula: ΔW p This represents the initial cumulative error at the p-th workstation; This represents the real-time position error of the robot arm at the interference source station, which is the cumulative value of the real-time position errors of each motion axis of the robot arm. Specifically, it is the end-effector error, formed by the sequential accumulation of the real-time position errors of each motion axis at the interference source station until the error reaches the end point. This end-effector error is the real-time position error of each motion axis. ε p,max ε represents the asymmetric dynamic coupling strength between the p-th workstation and the interference source workstation in the synchronization error matrix; max,pThe value represents the asymmetric dynamic coupling strength between the interference source station and the p-th station in the synchronization error matrix; t represents time.

[0154] In the above formula, the asymmetric dynamic coupling strength ε between the p-th workstation and the interference source workstation in the synchronization error matrix is ​​represented by... p,max The fifth ratio of the asymmetric dynamic coupling strength between the interference source station and the p-th station, multiplied by the real-time position error of the manipulator at the interference source station. The propagation error generated by the interference source station to the p-th station is obtained. This represents the integral term of the transmission error over time, from which the initial cumulative error can be obtained. This initial cumulative error refers to the accumulation of the error at the p-th workstation caused by the interference source workstation in the time sequence.

[0155] Step S600: Use the cumulative error weight of each station to perform a weighted multiplication of the initial cumulative error amount to finally obtain the cumulative error amount of each station.

[0156] Specifically, for each workstation, the initial cumulative error of the workstation is multiplied by the cumulative error weight of that workstation, and the product is taken as the final cumulative error of that workstation.

[0157] Step S700: Determine the error compensation value for each station based on the real-time position error and cumulative error of the robot arm at each station, and perform compensation control on the robot arm at each station based on the error compensation value.

[0158] Specifically, for each workstation, the error compensation value for that workstation can be obtained by combining the real-time position error of the robot arm with the cumulative error of that workstation. The corresponding calculation formula is as follows:

[0159]

[0160] In the formula: W p This represents the error compensation value for the p-th workstation; e represents the real-time position error of the p-th workstation; m This represents the real-time position error of the m-th motion axis of the robot at the p-th station, which is a numerical value; unm represents the total number of motion axes of the robot at the p-th station, which in a specific implementation is 3; ΔW′ p This represents the cumulative error at the p-th workstation.

[0161] Following the above method, the error compensation value for each workstation can be determined. This error compensation value includes the real-time position error. The error consists of two parts: the initial cumulative error and the cumulative error. The cumulative error is obtained by adjusting the initial cumulative error using the cumulative error weight. If a workstation does not generate a large error due to load inertia and is far from the interference source workstation, it is considered that the initial cumulative error of that workstation does not need much correction. Conversely, if the workstation generates a large error due to load inertia and is close to the interference source workstation, the initial cumulative error accumulated over time needs to be increased using the cumulative error weight.

[0162] The error compensation value determined above for each workstation is input into the PID controller, and motor control commands are automatically generated to perform compensation control of the robot arm at that workstation. Since this compensation control process is existing technology, it will not be described in detail here.

[0163] Based on the same inventive concept, embodiments of the present invention also provide a control system for a multi-station robotic arm used for stamping washing machine casings, such as... Figure 7 As shown, the control system includes: a memory 701, a processor 702, and computer program code 703 stored in the memory 701 and running on the processor 702. When the processor 702 executes the computer program code 703, the system can execute any of the control methods for a multi-station robot for stamping a washing machine casing described above.

[0164] In this embodiment of the invention, the system can be divided into functional modules according to the above method example. For example, each module can correspond to a separate functional module, or two or more functions can be integrated into one processing module. The integrated module can be implemented in hardware. It should be noted that the module division in this embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods.

[0165] Based on the same inventive concept, embodiments of the present invention also provide a computer program product, which includes: computer program code, which, when run on a computer, causes the computer to execute any of the control methods for a multi-station robotic arm for stamping a washing machine casing described above.

[0166] Based on the same inventive concept, embodiments of the present invention also provide a computer-readable storage medium storing computer program code, which, when executed on a computer, causes the computer to perform any of the control methods for a multi-station robotic arm used for stamping washing machine casings described above.

[0167] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A control method for a multi-station robotic arm used in stamping the outer casing of a washing machine, characterized in that, Includes the following steps: Using a workstation collaborative calibration experiment, a synchronization error matrix is ​​constructed, where each element of the synchronization error matrix represents the asymmetric dynamic coupling strength of one workstation to another. Based on the synchronization error matrix, the error transmission station sequence and the interference source station are determined. The error transmission station sequence is used to reflect the error transmission direction when different stations work together. During the operation of the robot arm at the workstation, the end-effector load error coefficient of each workstation is determined based on the relevant information of the robot arm end at different workstations. The cumulative error weight of each station is determined based on the difference in the sequence number of each station and the interference source station in the error transmission station sequence, and the difference in the end load error coefficient between each station and the interference source station. Based on the real-time position error of the robot arm at the interference source station, and the difference between the asymmetric dynamic coupling strength of each station to the interference source station and the asymmetric dynamic coupling strength of the interference source station to each station in the synchronization error matrix, the initial cumulative error of each station is determined. The initial cumulative error is multiplied by the cumulative error weight of each workstation to obtain the cumulative error of each workstation. Based on the real-time position error of the robot at each workstation and the cumulative error, an error compensation value is determined for each workstation, and the robot at each workstation is compensated and controlled based on the error compensation value. Using a workstation collaborative calibration experiment, a synchronization error matrix was constructed, including: In the workstation collaborative calibration experiment, step acceleration excitation was applied to different workstations to obtain the basic coupling coefficient between workstation i and workstation j under different step acceleration excitations. Based on the variation of the basic coupling coefficient under adjacent step acceleration excitation, and combined with the angle between the force transmission direction of the robot at station i and the motion axis of the robot at station j, the structural arm length between station i and station j, the equivalent mass of the robot at station i and the step acceleration excitation, the asymmetric dynamic coupling coefficient of station i to station j is determined. Based on the asymmetric dynamic coupling coefficient and the distribution positions of different workstations, the asymmetric dynamic coupling strength between the p-th workstation and the q-th workstation is determined as the element in the p-th row and q-th column of the synchronization error matrix; The asymmetric dynamic coupling strength between the p-th workstation and the q-th workstation is determined as the element in the p-th row and q-th column of the synchronization error matrix, including: All workstations are sorted according to the order from upstream to downstream of the production line to obtain the serial number of each workstation. The basic elements at each position on the main diagonal of the synchronization error matrix are set to the first value, and the basic elements at other positions in the synchronization error matrix excluding the main diagonal are set to the second value, wherein the first value is greater than the second value. The asymmetric dynamic coupling coefficient of the p-th workstation to the q-th workstation is determined by adding the basic element of the p-th row and q-th column of the synchronization error matrix, which is then used as the asymmetric dynamic coupling strength of the p-th row and q-th column of the synchronization error matrix, thus obtaining the synchronization error matrix.

2. The control method for a multi-station robotic arm used in stamping a washing machine casing according to claim 1, characterized in that, Obtain the basic coupling coefficient between station i and station j under different step acceleration excitations, including: Based on the positional deviation between workstation i and workstation j, the structural arm length between workstation i and workstation j, and the positional error of each joint of the robot arm at workstation i, the basic coupling coefficient between workstation i and workstation j under static conditions is determined. In the workstation collaborative calibration experiment, step acceleration excitation was continuously applied to workstation i to obtain the basic coupling coefficient between workstation i and workstation j under different step acceleration excitations.

3. The control method for a multi-station robotic arm used in stamping a washing machine casing according to claim 1, characterized in that, Determine the asymmetric dynamic coupling coefficient between station i and station j, including: Determine the change in the basic coupling coefficient under adjacent step acceleration excitations, and perform linear fitting on the change to obtain a fitted straight line; Determine the slope of the fitted line to obtain the slope of the change in the basic coupling coefficient; Based on the slope of the change of the basic coupling coefficient, and combined with the angle between the force transmission direction of the robot at station i and the motion axis of the robot at station j, the structural arm length between station i and station j, the equivalent mass of the robot at station i, and the acceleration value of the step acceleration excitation, the asymmetric dynamic coupling coefficient of station i to station j is determined.

4. The control method for a multi-station robotic arm used in stamping a washing machine casing according to claim 1, characterized in that, Determine the error propagation station sequence, including: The sum of the absolute values ​​of the upper right triangular elements in the synchronization error matrix is ​​used to obtain the forward propagation strength, and the sum of the absolute values ​​of the lower left triangular elements in the synchronization error matrix is ​​used to obtain the reverse propagation strength. The ratio of the forward transmission intensity to the reverse transmission intensity is determined to obtain a first ratio. If the first ratio is greater than the upper threshold, all workstations are sorted in the order from upstream to downstream of the production line to obtain the error propagation workstation sequence. If the first ratio is less than the lower threshold, all workstations are sorted in the order from downstream to upstream of the production line to obtain the error propagation workstation sequence. Otherwise, the sum of all column elements in the synchronization error matrix for each workstation is determined to obtain the comprehensive interference intensity of each workstation, and all workstations are sorted in ascending order of comprehensive interference intensity to obtain the error transmission workstation sequence.

5. The control method for a multi-station robotic arm used for stamping a washing machine casing according to claim 1, characterized in that, Identify the workstations that are the sources of interference, including: The sum of all row elements in the synchronization error matrix for each workstation is determined to obtain the overall interference intensity for each workstation. Determine the maximum value among all workstations' overall interference intensity, and identify the workstation corresponding to the maximum value as the interference source workstation.

6. The control method for a multi-station robotic arm used for stamping a washing machine casing according to claim 1, characterized in that, The relevant information of the robotic arm end effector includes at least: the speed and distance in each motion direction obtained by disassembling the tasks performed by the robotic arm at different workstations; the motor current data of the robotic arm at different workstations during task execution; the mass of the motion axis of the robotic arm at different workstations and the distance from the center of mass of the robotic arm to the end effector; and the contact force data between the robotic arm and the workpiece at different workstations; and the determination of the end effector load error coefficient for each workstation, including: The ratio of speed to distance in the current motion direction is determined by breaking down the task performed by the robot arm at each workstation, thus obtaining the second ratio. The ratio of the increase in motor current to the fluctuation in motor current is determined when the robot arm at each workstation is currently performing a task, thus obtaining the third ratio. By combining the second and third ratios, the end-load inertia of each station is determined; The moment of inertia of each station is determined based on the mass of the motion axis of the robot and the distance from the center of mass of the robot to its end effector. The load inertia ratio of each station is determined based on the ratio of the end load inertia to the load inertia. The contact force error for each station is calculated based on the difference between the current contact force and the expected contact force in the contact force data between the robot and the workpiece at each station. By combining the load inertia ratio and contact force error, the end load error coefficient of each station is determined.

7. The control method for a multi-station robotic arm used for stamping a washing machine casing according to claim 1, characterized in that, Determine the cumulative error weight for each workstation, including: The difference between the sequence number of each workstation and the interference source workstation in the error transmission workstation sequence is negatively correlated and mapped to obtain the sequence number difference mapping value. The ratio of the end load error coefficient of each workstation to that of the interference source workstation is determined to obtain the fourth ratio. By combining the sequence number difference mapping value and the fourth ratio value, the cumulative error weight of each workstation is obtained.

8. The control method for a multi-station robotic arm used in stamping a washing machine casing according to claim 1, characterized in that, Determine the initial cumulative error for each workstation, including: The ratio of the asymmetric dynamic coupling strength of each station to the interference source station in the synchronization error matrix to the asymmetric dynamic coupling strength of the interference source station to each station is determined to obtain the fifth ratio. The initial cumulative error of each station is obtained by integrating the product of the real-time position error of the robot arm at the interference source station and the fifth ratio over time.

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