A dual-robot collaborative circular trajectory processing method

Abstract

The present invention discloses a dual-robot collaborative circular trajectory processing method, which belongs to the field of robot collaborative processing. It comprises: decomposing the target circular trajectory by orthogonal axes to generate two periodic single-axis motion sequences along the X-axis and Y-axis directions respectively; then, the two robots respectively execute their own axial motion sequences, and complete the synthetic execution of the target circular trajectory through spatial collaboration; then, using a measuring device to collect radial error data during the trajectory execution process; extracting the non-orthogonal error between the coordinate systems based on the error data, and performing error compensation and updating on the trajectory generation program. The present invention realizes the orthogonal axis decoupling control of the circular trajectory, which can improve the flexibility and controllability of trajectory generation; supports closed-loop feedback and automatic compensation of trajectory errors, significantly reducing roundness errors; effectively controls dimensional drift during the processing process, improves dimensional consistency and repeatability; does not need to rely on complex high-end external measurement systems, and the system deployment cost is low and the versatility is strong.

Description

Technical Field

[0001] The present invention belongs to the field of robot collaborative processing, and in particular relates to a dual-robot collaborative circular trajectory processing method. Background Art

[0002] As industrial manufacturing evolves towards high-precision machining of large, complex structural parts, traditional CNC machine tools, constrained by processing space and system rigidity, face layout limitations and insufficient trajectory accuracy when machining large annular or circular parts. Industrial robots, due to their flexibility and low cost, are gradually being introduced into machining scenarios. Systems that utilize multiple robots working collaboratively can effectively expand the machining range and meet the requirements of special-shaped and oversized workpieces.

[0003] Current research on robot machining trajectory compensation focuses on single-robot scenarios, such as improving trajectory accuracy through end-point error modeling, joint space compensation, and sensor feedback control. However, these methods are difficult to directly apply to dual-robot collaborative path generation and compensation control.

[0004] However, multi-robot systems inherently suffer from structural redundancy, complex collaborative control, and significant coordinate system coupling errors. Path control and error suppression are key constraints on system accuracy. This is especially true when machining circular or annular contours, where inter-robot synchronization errors, path deviations, and coordinate non-orthogonality become more prominent. These issues include:

[0005] 1) Path synchronization deviation: There are slight differences between the two robots in parameters such as trajectory starting point, speed, acceleration, etc., which can easily lead to asynchronous processing paths or interpolation mismatch;

[0006] 2) Coordinate system error coupling: If the coordinate reference points of the two robots are not accurately aligned, topographic errors such as "path eccentricity" or "elliptical distortion" will occur during the execution of the circular trajectory;

[0007] 3) Compensation path transmission obstacles: Dual robots usually use independent controllers (such as FANUC RJ systems), and the standard circular path compensation program is difficult to directly and synchronously update;

[0008] 4) Dynamic response difference: Differences in the load or stiffness structure of the two robots will lead to trajectory response deviation and cutting vibration coupling;

[0009] 5) Error source tracing is complex: Processing errors often include trajectory errors, geometric coupling errors, sensor delay errors, etc., and a complete closed loop must be formed from measurement-compensation-verification.

[0010] Furthermore, while some literature has attempted to utilize laser trackers, photogrammetry, or vision positioning systems for path monitoring and error feedback compensation of multi-robot end-effectors, these methods generally suffer from expensive equipment, complex installation and debugging, and large space requirements, making them difficult to deploy and apply in typical industrial environments. Furthermore, structural coupling issues exist between multi-robot systems, such as separate control logic, inconsistent coordinate systems, and asymmetric mechanical responses. This makes it difficult to effectively adapt compensation strategies based on extensions of single-arm control theory. Existing methods generally fail to implement a closed-loop process—pre-processing—error identification—program compensation—result verification—and lack a universal compensation mechanism for complex collaborative paths, such as circular trajectories. Therefore, there is an urgent need to develop a low-cost, structurally universal, closed-loop compensation method for dual-robot circular trajectory errors to improve the system's machining accuracy and engineering adaptability. Summary of the Invention

[0011] The present invention aims to solve the problems of synchronization error, path deviation and roundness error and dimensional deviation caused by non-orthogonality of coordinate system in the collaborative processing of circular trajectories by dual robots, and establish a closed-loop control method combining trajectory decomposition, error modeling and automatic compensation to improve the stability and processing quality of the multi-robot system in circular path processing.

[0012] To achieve the above object, the present invention provides a dual-robot collaborative circular trajectory machining method, comprising:

[0013] Decompose the target circular trajectory into orthogonal axes respectively to obtain periodic single-axis motion sequences in two orthogonal axis directions;

[0014] The two robots are respectively subjected to the periodic single-axis motion sequence in the orthogonal axis direction to collaboratively complete the processing of the target circular trajectory, and radial error data of the robots during the execution of the target circular trajectory motion is obtained using a measuring device;

[0015] extracting coordinate system error parameters according to the radial error data;

[0016] Compensating the target circular trajectory according to the coordinate system error parameters to generate compensated path points;

[0017] The compensated path points are converted into a robot controller instruction format, and a machining program is generated and uploaded to the robot system.

[0018] Preferably, the process of performing orthogonal axis decomposition on the target circular trajectory includes:

[0019] Decomposing the target circular trajectory into a sine-law motion sequence along the X-axis and a cosine-law motion sequence along the Y-axis, and converting the result into two periodic single-axis motion sequences of sine and cosine laws;

[0020] The periodic single-axis motion sequence of the sine and cosine laws is executed by two robots arranged perpendicular to each other to execute the trajectory points in the X-axis and Y-axis directions respectively.

[0021] Preferably, the process of obtaining radial error data of the robot during the target circular trajectory motion using a measuring device includes:

[0022] Non-cutting circular path execution tests were performed using a ballbar in multiple planes, capturing real-time radial error data and path deviation values.

[0023] Preferably, the process of extracting coordinate system error parameters according to the radial error data includes:

[0024] Based on the radial error data, coordinate system error parameters are extracted through polar coordinate fitting and error decomposition model.

[0025] Preferably, the coordinate system error parameters include non-orthogonality error, backlash, straightness error, periodic error and axis runout error.

[0026] Preferably, based on the radial error data, the process of extracting coordinate system error parameters through polar coordinate fitting and error decomposition model includes:

[0027] Use a ballbar to measure at specific locations and analyze the circular trajectory error at 45° or 135°, thereby calculating the existing perpendicularity error.

[0028] According to the radial error data, the angular error is calculated; the calculation formula of the angular error is:

[0029] ;

[0030] The angle error is converted into a vertical error value, and the conversion formula is:

[0031] ;

[0032] Where δ is the maximum deviation measured in the diameter direction, R is the radius of the circular trajectory, and sa is the angular error value in arc seconds.

[0033] Preferably, the target circular trajectory is compensated according to the coordinate system error parameter to generate the compensated path points, which includes:

[0034] According to the angular error value of the non-orthogonal error and combined with the circular trajectory geometric model, the original trajectory points are corrected to obtain the compensated coordinate path points.

[0035] Preferably, the compensation formula is expressed as:

[0036] ;

[0037] ;

[0038] ;

[0039] Among them, X i and Y i is the coordinate path point after compensation, x0 and y0 are the original trajectory points, R is the radius of the circular trajectory, is the angle of the trajectory point, s is the vertical error value after the angle error value is converted, sa is the angle error value, and R is the radius of the circular trajectory.

[0040] Preferably, under actual machining conditions, comparative cutting experiments are conducted on the workpiece before and after compensation, and key indicators of the workpiece are quantitatively analyzed in combination with measuring equipment.

[0041] Preferably, the key indicators include roundness error, dimensional stability and surface roughness.

[0042] Compared with the prior art, the present invention has the following advantages and technical effects:

[0043] Significantly reduces roundness error: The typical roundness deviation range is 85-138µm before compensation, and stabilizes to 34-55µm after compensation, with roundness improved by more than 60%.

[0044] Improve dimensional consistency: The dimensional fluctuation of the workpiece after processing is controlled within ±0.3-0.35mm, meeting the requirements of most medium-precision industrial components.

[0045] Improve path consistency: Achieve good path compensation effects in multiple spatial planes and multiple measurement radii, with stable and consistent error distribution and spatial versatility.

[0046] Low system deployment cost: It does not rely on high-end laser measurement systems, but is based on universal ballbar measurement and independent compensation procedures, making it easy to integrate and promote.

[0047] Support for multi-robot expansion: The proposed compensation strategy and trajectory decomposition method can be extended to multi-arm collaborative systems, multi-plane path compensation and complex contour control tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0049] Figure 1 A schematic diagram of a cylindrical part milling application according to an embodiment of the present invention;

[0050] Figure 2 This is a schematic diagram of an expanded application of laser cutting according to an embodiment of the present invention;

[0051] Figure 3 A schematic diagram of trajectory measurement and error modeling according to an embodiment of the present invention;

[0052] Among them, 1. Robot A; 2. Connection tool flange; 3. Path execution interface; 4. Robot B; 5. B end effector flange; 6. Control cable and end feedback element; 7. Laser processing nozzle and guide rail fixture; 8. End motion controller; 9. Laser generation control cabinet; 10. Ballbar measuring rod and mounting suction cup. DETAILED DESCRIPTION

[0053] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0054] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0055] This embodiment provides a dual-robot collaborative circular trajectory processing method, including:

[0056] Decompose the target circular trajectory into orthogonal axes respectively to obtain periodic single-axis motion sequences in two orthogonal axis directions;

[0057] The two robots are respectively subjected to periodic single-axis motion sequences in the directions of orthogonal axes to collaboratively complete the machining of the target circular trajectory, and the radial error data of the robots during the execution of the target circular trajectory motion is obtained using a measuring device;

[0058] Extract coordinate system error parameters based on radial error data;

[0059] According to the coordinate system error parameters, the target circular trajectory is compensated to generate the compensated path points;

[0060] The compensated path points are converted into the robot controller instruction format, and the machining program is generated and uploaded to the robot system.

[0061] Furthermore, the process of performing orthogonal axis decomposition on the target circular trajectory includes:

[0062] The target circular trajectory is decomposed into a sine motion sequence along the X-axis and a cosine motion sequence along the Y-axis by performing orthogonal axis decomposition, and two periodic single-axis motion sequences of sine and cosine laws are obtained.

[0063] The periodic single-axis motion sequence of sine and cosine laws is executed by two robots arranged perpendicular to each other to execute the trajectory points in the X-axis and Y-axis directions respectively.

[0064] Furthermore, the process of obtaining radial error data of the robot during the target circular trajectory motion using the measuring device includes:

[0065] Non-cutting circular path execution tests were performed using a ballbar in multiple planes, capturing real-time radial error data and path deviation values.

[0066] Furthermore, based on the radial error data, the process of extracting the coordinate system error parameters includes:

[0067] Based on the radial error data, the coordinate system error parameters are extracted through polar coordinate fitting and error decomposition model.

[0068] Furthermore, the coordinate system error parameters include non-orthogonality error, backlash, straightness error, periodic error and axis runout error.

[0069] Furthermore, based on the radial error data, the process of extracting the coordinate system error parameters through polar coordinate fitting and error decomposition model includes:

[0070] Conduct circular trajectory tests at target locations and analyze ballbar measurement results. Specifically, use the ballbar to measure at selected locations and analyze circular trajectory errors at 45° or 135° to maximize the impact of non-orthogonality between the two axes.

[0071] According to ISO230-4 standard, the radial error data at both ends of the circular trajectory are used to calculate the angular error; the calculation formula for the angular error is:

[0072] ;

[0073] Convert the angle error to the angle error value (arc seconds). The conversion formula is:

[0074] ;

[0075] Where δ is the maximum deviation measured in the diameter direction, R is the radius of the circular trajectory, and sa is the perpendicularity error value in arc seconds.

[0076] Furthermore, the target circular trajectory is compensated according to the coordinate system error parameters, and the process of generating the compensated path points includes:

[0077] According to the angular error value of the non-orthogonal error and combined with the circular trajectory geometric model, the original trajectory points are corrected to obtain the compensated coordinate path points.

[0078] Furthermore, a non-orthogonal error compensation term is introduced to perform offset correction on the X-direction trajectory points so that the overall path can be restored to orthogonality. Specifically, the radius of the ideal circular trajectory is set to R, and the angle position is θ i ,In the actual path of collaborative control, the coordinate systems of the two robots may have a non-orthogonal error δ, where sa is the deflection angle between the X and Y axes (in arcsec);

[0079] The error is obtained by fitting the ballbar trajectory and converted to a unit dimensionless offset according to the following formula:

[0080] ;

[0081] The coordinates of the trajectory points after compensation can be expressed as:

[0082] ;

[0083] ;

[0084] Among them, X i and Y i is the coordinate path point after compensation, x0 and y0 are the original trajectory points, R is the radius of the circular trajectory, is the angle of the trajectory point, s is the vertical error value after the angle error value is converted, sa is the angle error value, and R is the radius of the circular trajectory. It reflects the projection offset of the Y-axis error in the X-axis. After correcting the original trajectory, it can significantly improve the problems of path ellipticalization and roundness reduction caused by non-orthogonal coordinates, and effectively improve the path geometric accuracy and processing consistency.

[0085] Furthermore, converting the compensated path points into a robot controller instruction format includes:

[0086] The compensated path points are converted into standard robot controller instruction format (such as FANUC TP instruction), and the circular trajectory machining program is automatically generated and uploaded to the dual robot system.

[0087] Furthermore, under actual machining conditions, comparative cutting experiments were conducted on the workpiece before and after compensation, and key indicators of the workpiece were quantitatively analyzed using measuring equipment.

[0088] Furthermore, key indicators include roundness error, dimensional stability and surface roughness.

[0089] More specifically, under actual processing conditions, comparative cutting experiments were conducted on aluminum alloy workpieces before and after compensation, and key indicators such as the workpiece's roundness error, dimensional stability, and surface roughness were quantitatively analyzed using a three-coordinate measuring machine (CMM).

[0090] Take a typical dual industrial robot collaborative platform as an example:

[0091] like Figure 1 The cylindrical part milling application shown includes: robot A 1; connecting tool flange 2; path execution interface 3 (linked fixture); robot B 4; B end effector flange 5; control cable and end feedback element 6.

[0092] Figure 1 Demonstrating the configuration of a dual-robot system for simultaneous milling of the outer contour of a cylindrical component while gripping and driving it. The two robots independently execute orthogonal motions, driving the tool through a linked fixture to achieve high-precision circular machining.

[0093] like Figure 2 The laser cutting application expansion shown includes: robot A 1; laser processing nozzle and guide rail fixture 7; robot B 4; end motion controller 8; laser generation control cabinet 9;

[0094] Figure 2 This example demonstrates the application of the method of this embodiment to the laser arc cutting of large sheet metal or composite panels. Two robots achieve a highly circular cutting path using the collaborative drive of the end-user laser nozzles.

[0095] like Figure 3 The trajectory measurement and error modeling shown includes: robot A 1; ballbar measuring rod and mounting suction cup 10; robot B 4;

[0096] Figure 3 This demonstrates how to use a ballbar measurement system to collect radial errors while a robot executes a circular trajectory. The test results are then fed into a compensation model to extract squareness error parameters and enable subsequent program corrections.

[0097] Take a typical dual collaborative milling platform as an example:

[0098] System structure: Robot A 1 controls the X-axis linear trajectory, and robot B 4 controls the Y-axis trajectory. The two robots together construct a circular path in the XY plane.

[0099] Non-machining verification phase: Execute 50, 100, and 150mm radius paths, use a ballbar to measure trajectory errors, and establish an error parameter model;

[0100] Path correction and automatic program generation: perform trajectory compensation based on the extracted vertical angle error and generate FANUCTP program;

[0101] Processing verification stage: The actual milling task was completed under the guidance of the compensation program. The measurement results showed that the roundness and dimensional accuracy were significantly better than the original program, and the Ra value also decreased.

[0102] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A dual-robot collaborative circular trajectory processing method, characterized in that: include: Decompose the target circular trajectory into orthogonal axes respectively to obtain periodic single-axis motion sequences in two orthogonal axis directions; The two robots are respectively subjected to the periodic single-axis motion sequence in the orthogonal axis direction to collaboratively complete the processing of the target circular trajectory, and radial error data of the robots during the execution of the target circular trajectory motion is obtained using a measuring device; extracting coordinate system error parameters according to the radial error data; Compensating the target circular trajectory according to the coordinate system error parameters to generate compensated path points; The compensated path points are converted into a robot controller instruction format, and a machining program is generated and uploaded to the robot system.

2. The method according to claim 1, characterized in that The process of performing orthogonal axis decomposition on the target circular trajectory includes: Decomposing the target circular trajectory into a sine-law motion sequence along the X-axis and a cosine-law motion sequence along the Y-axis, and converting the result into two periodic single-axis motion sequences of sine and cosine laws; The periodic single-axis motion sequence of the sine and cosine laws is executed by two robots arranged perpendicular to each other to execute the trajectory points in the X-axis and Y-axis directions respectively.

3. The method according to claim 1, characterized in that The process of obtaining radial error data of the robot while executing the target circular trajectory motion using the measuring device includes: Non-cutting circular path execution tests were performed using a ballbar in multiple planes, capturing real-time radial error data and path deviation values.

4. The method according to claim 1, wherein The process of extracting coordinate system error parameters based on the radial error data includes: Based on the radial error data, coordinate system error parameters are extracted through polar coordinate fitting and error decomposition model.

5. The method according to claim 4, characterized in that The coordinate system error parameters include non-orthogonality error, backlash, straightness error, periodic error and axis runout error.

6. The method according to claim 4, characterized in that Based on the radial error data, the process of extracting coordinate system error parameters through polar coordinate fitting and error decomposition model includes: Perform circular trajectory analysis at 45° or 135° to maximize the impact of non-orthogonality between the two axes; According to the radial error data, the angular error is calculated; the calculation formula of the angular error is: ； The angle error is converted into an angle error value, and the conversion formula is: ； Where δ is the maximum deviation measured in the diameter direction, R is the radius of the circular trajectory, and sa is the angular error value in arc seconds.

7. The method according to claim 1, characterized in that The process of compensating the target circular trajectory according to the coordinate system error parameter to generate compensated path points includes: According to the angular error value of the non-orthogonal error and combined with the circular trajectory geometric model, the original trajectory points are corrected to obtain the compensated coordinate path points.

8. The method according to claim 7, characterized in that The compensation formula is: ； ； ； Among them, X i and Y i is the coordinate path point after compensation, x0 and y0 are the original trajectory points, R is the radius of the circular trajectory, is the angle of the trajectory point, s is the vertical error value after the angle error value is converted, sa is the angle error value, and R is the radius of the circular trajectory.

9. The method according to claim 1, characterized in that The method further comprises: Under actual machining conditions, comparative cutting experiments are carried out on the workpiece before and after compensation, and the key indicators of the workpiece are quantitatively analyzed using measuring equipment.

10. The method according to claim 9, characterized in that The key indicators include roundness error, dimensional stability and surface roughness.

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