Device and method for testing repeatability of planar position of robot

By designing a test device including a robot body, a calibration target and a plane tester, it solves the problem that customers find it difficult to accurately verify the repeatability performance parameters of XY plane position of SCARA robot at low cost, and achieves low-cost and accurate testing, reducing the testing cost and improving the accuracy.

CN115446874BActive Publication Date: 2025-06-13INSPUR SUZHOU INTELLIGENT TECH CO LTD
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Patent Information

Application Number
CN202211161626.1
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-09-22
Publication Date
2025-06-13
Estimated Expiration
2042-09-22

AI Technical Summary

Technical Problem

It is difficult for customers to verify the XY plane position repeatability performance parameters of SCARA robots at low cost but accurately.

Method used

A device for repeatability testing of plane position of robots is designed, including robot body, calibration target and plane tester. By extruding the distance measuring bearing plate in the pre-pressure stroke, driving the movement of the transmission mechanism and the position recording device, the distance value of the robot in the XY plane is measured, and the position of the point to be measured is calculated by the processor.

Benefits of technology

Low-cost, accurate robot plane position repeatability testing is achieved, reducing testing costs for customers and enterprises, improving testing accuracy, and making testing tools modular and lightweight.

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Abstract

The present invention provides a device and method for testing the repeatability of a robot's planar position. The device includes a robot body, a calibration target installed on the robot body, and a planar tester; the robot body is used to squeeze a ranging bearing plate on the planar tester within a preloading stroke after power-on, and the ranging bearing plate is used to drive a transmission mechanism to move under the action of the squeezing force; the transmission mechanism then drives the robot body of the position recording device to move; the position recording device is used to feedback the moving distance to a processor; the processor calculates the position of the point to be measured according to a second value; the planar tester includes an X-axis rangefinder and a Y-axis rangefinder. Based on a device for testing the repeatability of a robot's planar position, a method for testing the repeatability of a robot's planar position is also provided. This application uses a low-cost structure to meet high-cost testing requirements, reduces the testing costs of customers and enterprises, and makes the testing tools modular and lightweight.
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Description

Technical Field

[0001] The present invention belongs to the technical field of robot testing, and particularly relates to a device and method for testing the repeatability of the planar position of a robot. Background Art

[0002] SCARA (Selective Compliance Assembly Robot Arm) is a special type of industrial robot with a cylindrical coordinate type. It is a robot arm applied to operations such as loading and unloading in the workshop, screwing assembly, gluing, welding, spraying, etc. It consists of 3 rotating joints and an up-and-down moving lead screw, and is most suitable for planar positioning.

[0003] With the rapid development of the automation industry in recent years, more and more industrial robots, a new product, have been used in automated equipment. Among them, the proportion of SCARA robots in the industrial robot market has been increasing year by year. As an important performance parameter for measuring a SCARA robot, the repeatability of the XY planar position, more and more customers require robot manufacturers to attach a test report of this performance parameter when the SCARA robot leaves the factory. However, when the robot reaches the customer side, how the customer can verify the authenticity of this parameter at low cost but accurately has become a difficult problem. For some customers with low precision requirements, they directly hang a ballpoint pen at the end of the robot flange, and then let the robot drive the ballpoint pen to make point-to-point movements on white paper all the time. After running a certain number of times, they use the naked eye to observe whether it meets their needs. This method is simple to operate, but the accuracy cannot be guaranteed. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention proposes a device and method for testing the repeatability of the planar position of a robot, which is used to reduce the test cost and make the test tool modular and lightweight.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A device for testing the repeatability of the planar position of a robot, comprising: a robot body, a calibration target 2 and a planar tester mounted on the robot body;

[0007] After the robot body is powered on, it squeezes the ranging bearing plate on the planar tester within the preloading stroke. The ranging bearing plate is used to drive the transmission mechanism to move under the action of the squeezing force; the transmission mechanism then drives the position recording device to move; the position recording device 11 is used to feedback the moving distance to the processor; the processor calculates the position of the point to be measured according to the second value;

[0008] The planar tester includes an X-axis rangefinder and a Y-axis rangefinder; the X-axis rangefinder is used to measure the distance value of the robot body in the X direction within the plane; the Y-axis rangefinder is used to measure the distance value of the robot body in the Y-axis direction.

[0009] Further, the device further includes a robot mounting base;

[0010] The robot body is mounted on the robot mounting base.

[0011] Further, the device further includes a test platform; the robot mounting base is mounted on the test platform

[0012] Further, the calibration target is mounted on the flange of the robot.

[0013] Further, the calibration target adopts a square calibration target.

[0014] Further, the transmission mechanism includes a rack and a gear; the rack is vertically connected to the surface of the ranging support plate;

[0015] The robot body drives the ranging support plate to move backward by squeezing the ranging support plate within the preloading stroke, and the ranging support plate is used to drive the rack to move backward under the action of the squeezing force. The backward movement of the rack then drives the gear to move; the gear then drives the position recording device to move.

[0016] Further, the device further includes a self-resetting spring;

[0017] The self-resetting spring is vertically connected to the plane of the ranging support plate; and the self-resetting spring is parallel to the rack.

[0018] The present invention also proposes a method for testing the repeatability of the planar position of a robot, which is based on a device for testing the repeatability of the planar position of a robot, and is characterized by including the following steps:

[0019] Initialize the robot body, set the preloading stroke of the calibration target from the planar tester; and set the initial distance value of the current planar tester at the initial position to 0;

[0020] Within the preloading stroke, the robot body squeezes the ranging support plate, and the ranging support plate drives the transmission mechanism to move under the action of the squeezing force, and the transmission mechanism then drives the position recording device to move; the position recording device feeds back the second numerical value of the movement to the processor; the processor calculates the position of the point to be measured according to the second numerical value and repeats the loop test for a preset number of times.

[0021] Further, the method further includes representing the degree of consistency of the actual arrival positions of the XY plane of the robot body in response to the same command position from the same direction after repeating n times through the repeatability index RP.

[0022] Furthermore, the calculation process of the repeatability index RP includes:

[0023] When the robot body is being tested, the position coordinates actually reached at the j-th time are (X j , Y j ); when the robot body is being tested, the coordinates of the center of the circle fitted by the actually reached positions in the XY plane are (X 0 , Y 0 ), and the radius of the fitted circle is L 0 ; therefore, the distance between the position coordinates actually reached by the robot body at the j-th time and the coordinates of the center of the fitted circle (X 0 , Y 0 ) is L j : n is the number of tests; therefore:

[0024]

[0025] Assume that the standard deviation of the actually reached positions of the robot body in n tests is S n , then

[0026]

[0027] So RP = L 0 + 3S n ; therefore, the repeatability index RP can be calculated by testing the position coordinates (X j , Y j ) actually reached at the j-th time.

[0028] The effects provided in the invention content are only the effects of the embodiments, rather than all the effects of the invention. One of the technical solutions in the above technical solutions has the following advantages or beneficial effects:

[0029] The present invention provides a device and method for testing the repeatability of a robot's planar position. The device includes a robot body, a calibration target mounted on the robot body, and a planar tester; after the robot body is powered on, it squeezes a ranging support plate on the planar tester within the preloading stroke, and the ranging support plate drives the transmission mechanism to move under the action of the squeezing force; the transmission mechanism then drives the robot body of the position recording device to move; the position recording device is used to feedback the moving distance to the processor; the processor calculates the position of the point to be measured according to the second value; the planar tester includes an X-axis rangefinder and a Y-axis rangefinder; the X-axis rangefinder is used to measure the distance value of the robot body in the X direction within the plane; the Y-axis rangefinder is used to measure the distance value of the robot body in the Y-axis direction. Based on a device for testing the repeatability of a robot's planar position, a method for testing the repeatability of a robot's planar position is also provided, and the test results are represented by repeatability test indicators. This application uses a low-cost structure to solve high-cost test requirements, reduces the test costs of customers and enterprises, and makes the test tools modular and lightweight.

[0030] This application converts the repeatability test of the robot's planar position into the position coordinates actually reached at the jth time, and the scheme is easy to implement and improves the test accuracy. Description of the Drawings

[0031] As Figure 1 is a schematic diagram for calculating the repeatability index RP in Embodiment 1 of the present invention;

[0032] As Figure 2 is a three-dimensional structure schematic diagram of a device for testing the repeatability of a robot's planar position in Embodiment 1 of the present invention;

[0033] As Figure 3 is a top view of the structure of a device for testing the repeatability of a robot's planar position in Embodiment 1 of the present invention;

[0034] As Figure 4 is a three-dimensional structure schematic diagram of the planar tester in a device for testing the repeatability of a robot's planar position in Embodiment 1 of the present invention;

[0035] As Figure 5 is a flowchart of a method for testing the repeatability of a robot's planar position in Embodiment 1 of the present invention;

[0036] 1 - Robot mounting base; 2 - Square calibration target; 3 - X-axis rangefinder; 4 - Y-axis rangefinder; 5 - Test platform; 7 - Ranging support plate; 8 - Self-resetting spring; 9 - Rack; 10 - Gear; 11 - Encoder. Detailed Embodiments

[0037] To clearly illustrate the technical features of this solution, the present invention will be described in detail below through specific embodiments and in conjunction with its accompanying drawings. The following disclosure provides many different embodiments or examples for implementing different structures of the present invention. To simplify the disclosure of the present invention, the components and settings of specific examples are described below. In addition, the present invention may repeat reference numerals and / or letters in different examples. This repetition is for the purpose of simplification and clarity, and does not itself indicate the relationship between the various embodiments and / or settings discussed. It should be noted that the components illustrated in the drawings are not necessarily drawn to scale. The present invention omits the description of well-known components and processing technologies and processes to avoid unnecessarily limiting the present invention.

[0038] Embodiment 1

[0039] Embodiment 1 of the present invention proposes a device for testing the repeatability of a robot's planar position. First, it is necessary to clearly define: The repeatability of the XY planar position of a SCARA robot refers to the degree of consistency of the actual arrival positions after repeating the response to the same command position n times from the same direction in the XY plane where the robot works. Here, it is simply referred to as RP. According to industry-related standards, n takes a value of 30 times.

[0040] As Figure 1 is a reference schematic diagram for calculating the repeatability index RP in Embodiment 1 of the present invention; when the robot body is being tested, the position coordinates actually reached at the j-th time are (X j , Y j ); when the robot body is being tested, the coordinates of the center of the fitting circle of the actually reached position in the XY plane are (X 0 , Y 0 ), and the radius of the fitting circle is L 0 ; therefore, the distance between the position coordinates actually reached by the robot body at the j-th time and the center coordinates of the fitting circle (X 0 , Y 0 ) is L j : n is the number of tests;

[0041] Therefore:

[0042] Assume that the standard deviation of the fitting circle of the actually reached positions of the robot body in n tests is S n , then

[0043]

[0044] Therefore, RP = L 0 + 3S n ; thus, it is possible to test the position coordinates (X j , Y j ) actually reached at the j-th time

[0045] Based on the above principle, the present application uses a device for testing the repeatability of a robot's planar position to test (X j , Y j ), as Figure 2 is a three-dimensional schematic diagram of the structure of a device for testing the repeatability of a robot's planar position in Embodiment 1 of the present invention; as Figure 3 is a top view of the structure of a device for testing the repeatability of a robot's planar position in Embodiment 1 of the present invention;

[0046] The device includes: a robot body, a calibration target installed on the robot body, and a planar tester;

[0047] After the robot body is powered on, it squeezes the distance measuring bearing plate on the planar tester within the preloading stroke. The distance measuring bearing plate is used to drive the transmission mechanism to move under the action of the squeezing force; the transmission mechanism then drives the position recording device to move; the position recording device is used to feed back the moving distance to the processor; the processor calculates the position of the point to be measured according to the second value;

[0048] The planar tester includes an X-axis distance measuring instrument and a Y-axis distance measuring instrument; the X-axis distance measuring instrument is used to measure the distance value of the robot body in the X direction within the plane; the Y-axis distance measuring instrument is used to measure the distance value of the robot body in the Y-axis direction.

[0049] After the robot body is powered on, the calibration target 2 sets a preloading stroke for the planar tester; and the planar tester records the current position and sets the current distance value as the first value; the first value is generally set to 0, and the preloading stroke is set to 10 mm. The scope of protection of the present application is not limited to the data listed in Embodiment 1, and those skilled in the art can set it according to the actual situation.

[0050] The device further includes a test platform 5 and a robot mounting base 1;

[0051] The robot mounting base 1 is set on the test platform 5; the robot body is mounted on the robot mounting base 1. The calibration target 2 is mounted on the flange on the robot. After the installation is completed, let the robot to be tested be powered on and run for 8 hours first. After the time is up, move the SCARA robot to be tested to the point to be measured.

[0052] As Figure 4 is a three-dimensional schematic diagram of the structure of the planar tester in a device for testing the repeatability of a robot's planar position in Embodiment 1 of the present invention; the planar tester includes an X-axis distance measuring instrument 3 and a Y-axis distance measuring instrument 4;

[0053] The X-axis distance measuring instrument 3 is used to measure the distance value of the robot body in the X direction within the plane; the Y-axis distance measuring instrument is used to measure the distance value of the robot body in the Y-axis direction.

[0054] The calibration target 2 uses a square calibration target 2.

[0055] The transmission mechanism includes a rack 9 and a gear 10; the rack 9 is vertically connected to the surface of the distance measuring bearing plate 7;

[0056] When the robot body is being tested, after the robot body presses against the distance measuring bearing plate 7 within the preloading stroke, the distance measuring bearing plate 7 will drive the rack 9 to move backward under the action of force, and the backward movement of the rack 9 will drive the gear 10 to move; the gear 10 then drives the position recording device 11 to move. In this application, the transmission mechanism can also adopt a chain transmission mechanism. The scope of protection of this application is not limited to the transmission mechanism listed in Embodiment 1 of this application. In this application, the position recording device 11 adopts an encoder. The controller of this application calculates the position of the point to be measured according to the motion data of the encoder.

[0057] The device further includes a self-resetting spring 8;

[0058] The self-resetting spring 8 is vertically connected to the plane of the distance measuring bearing plate 7; and the self-resetting spring 8 is parallel to the rack 9; after the test is completed, the distance measuring bearing plate will be self-reset by the self-resetting spring.

[0059] The device for testing the repeatability of the robot's planar position proposed in Embodiment 1 of this application uses a low-cost structure to meet the high-cost testing requirements, reduces the testing costs of customers and enterprises, and makes the testing tool modular and lightweight.

[0060] Embodiment 1 of this application converts the test of the repeatability of the robot's planar position into the position coordinates actually reached at the jth time, and the scheme is easy to implement and improves the accuracy of the test.

[0061] Embodiment 2

[0062] Based on the device for testing the repeatability of the robot's planar position proposed in Embodiment 1 of the present invention, Embodiment 2 of the present invention also proposes a method for testing the repeatability of the robot's planar position. As Figure 5 This is the flowchart of a method for testing the repeatability of the robot's planar position in Embodiment 2 of the present invention;

[0063] In step S500, initialize the robot body, set the preloading stroke of the calibration target from the planar tester; and set the initial distance value of the current planar tester at the initial position to 0;

[0064] In step S510, within the preloading stroke, squeeze the distance measuring bearing plate through the robot body, and the distance measuring bearing plate drives the transmission mechanism to move under the action of the squeezing force, and the transmission mechanism then drives the position recording device to move; the position recording device feeds back the second numerical value of the movement to the processor;

[0065] In step S520, the processor calculates the position of the point to be measured according to the second numerical value and repeats the loop test for a preset number of times.

[0066] The method further includes representing the test result by a repeatability index RP. The calculation process of the repeatability index RP includes:

[0067] When the robot body is being tested, the position coordinates actually reached at the j-th time are (X j , Y j ); when the robot body is being tested, the coordinates of the center of the fitting circle of the actually reached position in the XY plane are (X 0 , Y 0 ), and the radius of the fitting circle is L 0 ; therefore, the distance between the position coordinates actually reached by the robot body at the j-th time and the coordinates of the center of the fitting circle (X 0 , Y 0 ) is L j : n is the number of tests;

[0068] Therefore:

[0069] Assume that the standard deviation of the fitting circle of the actually reached positions of the robot body in n tests is S n , then

[0070]

[0071] Therefore, RP = L 0 + 3S n ; thus, the repeatability index RP can be calculated by testing the position coordinates (X j , Y j ) actually reached at the j-th time.

[0072] This method is implemented based on a device for testing the repeatability of the planar position of a robot disclosed in Embodiment 1. The device specifically includes: a robot body, a calibration target installed on the robot body, and a planar tester;

[0073] After the robot body is powered on, it squeezes the ranging bearing plate on the planar tester within the preloading stroke. The ranging bearing plate is used to drive the transmission mechanism to move under the action of the squeezing force; the transmission mechanism then drives the position recording device to move; the position recording device is used to feed back the moving distance to the processor; the processor calculates the position of the point to be measured according to the second value;

[0074] The planar tester includes an X-axis rangefinder and a Y-axis rangefinder; the X-axis rangefinder is used to measure the distance value of the robot body in the X direction within the plane; the Y-axis rangefinder is used to measure the distance value of the robot body in the Y-axis direction.

[0075] After the robot body is powered on, the calibration target 2 sets a preloading stroke for the planar tester; and the planar tester records the current position and sets the current distance value to the first value; the first value is generally set to 0, and the preloading stroke is set to 10 mm. The scope of protection of this application is not limited to the data listed in Embodiment 1, and those skilled in the art can set it according to the actual situation.

[0076] The device further includes a test platform 5 and a robot mounting base 1;

[0077] The robot mounting base 1 is arranged on the test platform 5; the robot body is mounted on the robot mounting base 1. The calibration target 2 is mounted on the flange of the robot. After the installation is completed, let the robot to be tested run for 8 hours after power-on. After the time is up, move the SCARA robot to be tested to the point to be tested.

[0078] Such as Figure 4 It is a schematic three-dimensional structure diagram of the planar tester in the device for testing the repeatability of the planar position of a robot according to Embodiment 1 of the present invention; the planar tester includes an X-axis distance measuring instrument 3 and a Y-axis distance measuring instrument 4;

[0079] The X-axis distance measuring instrument 3 is used to measure the distance value of the robot body in the X direction in the plane; the Y-axis distance measuring instrument is used to measure the distance value of the robot body in the Y-axis direction.

[0080] The calibration target 2 adopts a square calibration target 2.

[0081] The transmission mechanism includes a rack 9 and a gear 10; the rack 9 is vertically connected to the surface of the distance measuring bearing plate 7;

[0082] When the robot body is being tested, after the robot body presses on the distance measuring bearing plate 7 within the preloading stroke, the distance measuring bearing plate 7 will drive the rack 9 to move backward under the action of force, and the backward movement of the rack 9 will drive the gear 10 to move; the gear 10 then drives the position recording device 11 to move. In this application, the transmission mechanism can also adopt a chain transmission mechanism. The scope of protection of this application is not limited to the transmission mechanism listed in Embodiment 1 of this application. In this application, the position recording device 11 adopts an encoder. The controller of this application calculates the position of the point to be tested according to the motion data of the encoder.

[0083] The device further includes a self-resetting spring 8;

[0084] The self-resetting spring 8 is vertically connected to the plane of the distance measuring bearing plate 7; and the self-resetting spring 8 is parallel to the rack 9; after the test is completed, the distance measuring bearing plate will be self-reset by the self-resetting spring.

[0085] The method for testing the repeatability of the planar position of a robot proposed in Embodiment 2 of the present application utilizes the device for testing the repeatability of the planar position of a robot disclosed in Embodiment 1, adopts a low-cost structure to solve the high-cost testing requirements, reduces the testing costs of customers and enterprises, and makes the testing tool modular and lightweight.

[0086] The method for testing the repeatability of the planar position of a robot proposed in Embodiment 2 of the present application converts the testing of the repeatability of the planar position of the robot into testing the position coordinates actually reached at the j-th time. The scheme is easy to implement and improves the testing accuracy.

[0087] For the description of the relevant parts in the method for testing the repeatability of the planar position of a robot provided in the embodiments of the present application, reference can be made to the detailed description of the corresponding parts in the device for testing the repeatability of the planar position of a robot provided in Embodiment 1 of the present application, which will not be elaborated here.

[0088] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes the inherent elements thereof. Without further limitation, the element defined by the statement "including a..." does not exclude the existence of additional identical elements in the process, method, article or device including the said element. In addition, the parts of the above technical solutions provided in the embodiments of the present application that are consistent with the corresponding technical solutions in the prior art in terms of implementation principles are not described in detail to avoid excessive elaboration.

[0089] Although the specific implementation manners of the present invention have been described above in conjunction with the accompanying drawings, they are not limitations on the protection scope of the present invention. For those skilled in the art, other different forms of modifications or deformations can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. Based on the technical solutions of the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts are still within the protection scope of the present invention.

Claims

1. A device for testing the repeatability of a robot's planar position, characterized in that, it includes: a robot body, a calibration target (2) installed on the robot body, and a planar tester; After the robot body is powered on, it squeezes the ranging bearing plate (7) on the planar tester within the preloading stroke. The ranging bearing plate (7) drives the transmission mechanism to move under the action of the squeezing force; the transmission mechanism then drives the position recording device (11) to move; the position recording device (11) feeds back the second numerical value of the movement to the processor; the processor calculates the position of the point to be measured according to the second numerical value; After the robot body is powered on, the calibration target (2) sets the preloading stroke for the planar tester. The planar tester records the current position and sets the current distance value as the first numerical value; The planar tester includes an X-axis rangefinder (3) and a Y-axis rangefinder (4); the X-axis rangefinder (3) is used to measure the distance value of the robot body in the X direction within the plane; the Y-axis rangefinder (4) is used to measure the distance value of the robot body in the Y-axis direction.

2. The device for testing the repeatability of a robot's planar position according to claim 1, characterized in that, the device further includes a robot mounting base (1); the robot body is installed on the robot mounting base (1).

3. The device for testing the repeatability of a robot's planar position according to claim 2, characterized in that, the device further includes a test platform (5); the robot mounting base (1) is installed on the test platform (5).

4. The device for testing the repeatability of a robot's planar position according to claim 1, characterized in that, the calibration target (2) is installed on the flange of the robot.

5. The device for testing the repeatability of a robot's planar position according to claim 1, characterized in that, the calibration target (2) adopts a square calibration target (2).

6. The device for testing the repeatability of a robot's planar position according to claim 1, characterized in that, the transmission mechanism includes a rack (9) and a gear (10); the rack (9) is vertically connected to the surface of the ranging bearing plate (7); The robot body squeezes the ranging bearing plate (7) within the preloading stroke. The ranging bearing plate (7) drives the rack (9) to move backward under the action of the squeezing force. The backward movement of the rack (9) drives the gear (10) to move; the gear (10) then drives the position recording device (11) to move.

7. The device for testing the repeatability of a robot's planar position according to claim 6, characterized in that, the device further includes a self-resetting spring (8); the self-resetting spring (8) is vertically connected to the plane of the ranging bearing plate (7); and the self-resetting spring (8) is parallel to the rack (9).

8. A method for testing the repeatability of a robot's planar position, which is based on the device for testing the repeatability of a robot's planar position according to any one of claims 1 to 7, characterized in that, it includes the following steps: Initialize the robot body, and set the preloading stroke of the calibration target distance plane tester; and set the initial distance value of the current plane tester at the initial position to 0; Within the preloading stroke, the robot body is used to squeeze the ranging bearing plate. Under the action of the squeezing force, the ranging bearing plate drives the transmission mechanism to move, and the transmission mechanism then drives the position recording device to move; the position recording device feeds back the second value of the movement to the processor; the processor calculates the position of the point to be measured according to the second value, and repeats the loop test for a preset number of times; The method further includes using the repeatability index RP to represent the degree of consistency of the actual arrival positions of the XY plane of the robot body in response to the same command position from the same direction after repeating n times; The calculation process of the repeatability index RP includes: When the robot body is being tested, the position coordinates actually reached at the j-th time are (X j , Y j ); when the robot body is being tested, the coordinates of the center of the circle fitted by the actually reached position in the XY plane are (X 0 , Y 0 ), and the radius of the fitted circle is L 0 ; therefore, the distance between the position coordinates actually reached by the robot body at the j-th time and the coordinates of the center of the fitted circle (X 0 , Y 0 ) is L j : n is the number of test times; Therefore: Assume that the standard deviation of the fitting circle of the actual arrival positions of the robot body in n tests is S n , then Therefore, RP = L 0 + 3S n ; Thus, the repeatability index RP can be calculated by testing the position coordinates (X j , Y j ) actually reached at the j-th time.

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