A robot linear shaft motion compensation method, device, equipment and medium

Abstract

This application belongs to the field of robot automated assembly technology, and discloses a method, device, equipment, and medium for motion compensation of a robot linear axis. The method includes: acquiring endpoint information of the robot's linear axis and position vectors of three target balls; obtaining pose error based on the position vectors and endpoint information of each target ball; performing B-spline fitting on the pose error to obtain a compensation function; acquiring sampling data of each target ball when the robot moves in multiple approach directions; obtaining the robot's approach direction error curve based on the sampling data of each target ball; and obtaining posture motion compensation based on the approach direction error curve and the compensation function. This application can compensate for systematic errors in linear axis deformation and systematic errors in motion anisotropy, thereby improving the robot's motion accuracy.

Description

Technical Field

[0001] This application relates to the field of robot automated assembly technology, and in particular to a method, device, equipment and medium for motion compensation of a robot linear axis. Background Technology

[0002] In industrial grinding and welding, the use of robots with linear axes is very common in ultra-large machining tasks. The positioning error of the linear axis is a major factor affecting the absolute accuracy of the robot tool's center point, and this error is amplified by the cascading configuration. Especially for robot paths with high precision requirements, these deviations can lead to instability or severe deviations along the robot path. Therefore, it is necessary to use certain compensation methods to identify the deformation of the linear axis and compensate for motion errors. The traditional method for using linear axis guides is as follows: 1. Coarse positioning of the axis: The linear axis is placed on the floor using pre-set user-defined positioning points. 2. Leveling of the axis: During the initial setup of the axis, the mounting points are manually leveled with the aid of a theodolite or laser tracker to ensure linearity in both vertical and horizontal directions. 3. Welding and assembly process: After initial leveling, the axis is permanently connected to the floor using screw joints with locking systems and / or welding techniques.

[0003] Traditional assembly strategies identify the external parameters of the guide rails, but often fail to consider the flexible deformation of the linear axis and the anisotropic errors during robot movement. In real-world scenarios, the deformation of the linear axis is usually strongly correlated with errors, and typically manifests as a systematic error strongly correlated with stroke. Ignoring deformation errors introduces additional systematic errors that contradict the ideal model, leading to a decrease in the robot's absolute accuracy. Summary of the Invention

[0004] This application provides a method, apparatus, device, and medium for motion compensation of a robot linear axis, which can compensate for systematic errors in linear axis deformation and systematic errors in motion anisotropy, thereby improving the motion accuracy of the robot.

[0005] In a first aspect, embodiments of this application provide a motion compensation method for a robot's linear axis, including:

[0006] Obtain the endpoint information of the robot's linear axis and the position vectors of the three target balls;

[0007] The pose error is obtained based on the position vector and endpoint information of each target ball;

[0008] The pose error is fitted with a B-spline to obtain the compensation function;

[0009] Acquire sampling data of each target ball as the robot moves in multiple approach directions;

[0010] The robot's approach direction error curve is obtained based on the sampling data of each target ball;

[0011] Attitude motion compensation is obtained based on the approach direction error curve and compensation function.

[0012] Furthermore, the endpoint information and the position vectors of each target ball are obtained through laser tracker measurements.

[0013] Furthermore, the pose error obtained above based on the position vectors and endpoint information of each target ball includes:

[0014] Establish an orthogonal right-handed coordinate system based on the position vectors of each target ball;

[0015] The position vector of the target ball, which is parallel to the ground and perpendicular to the linear axis, is taken as the target position vector;

[0016] The base position is obtained based on the target position vector and the orthogonal right-handed coordinate system;

[0017] Construct the ideal location based on endpoint information;

[0018] The pose error is obtained based on the base position and the ideal position.

[0019] Furthermore, the pose error obtained above based on the base position and the ideal position includes:

[0020] Calculate the positional error between the base position and the ideal position;

[0021] The position error is parameterized to obtain the pose error.

[0022] Furthermore, the above-mentioned B-spline fitting of the pose error yields a compensation function, including:

[0023] The pose error is subjected to discrete Fourier transform and low-pass filtering to obtain the measurement point information;

[0024] The compensation function is obtained by performing B-spline fitting on the measurement point information.

[0025] Furthermore, the multiple approach directions include multiple positive approach directions and multiple negative approach directions;

[0026] The angular difference between the near-positive direction and the direction from the linear axis to the target position conforms to the preset positive direction rule;

[0027] The angle difference between the near-negative direction and the direction from the linear axis to the target position conforms to the preset negative direction rule.

[0028] Furthermore, the sampling data for each target ball includes positive sampling data corresponding to each near-positive direction and negative sampling data corresponding to each near-negative direction.

[0029] Furthermore, the robot's approach direction error curve, obtained from the sampling data of each target ball, includes:

[0030] The mean of each positive sampling data corresponding to the same positive position is calculated using a Gaussian error model;

[0031] The positive error curve is obtained based on each positive position and its corresponding mean value;

[0032] The mean of each negative sampled data corresponding to the same negative position is calculated using the Gaussian error model;

[0033] The negative error curve is obtained based on each negative position and its corresponding mean value;

[0034] The positive and negative error curves are used as the approach direction error curves.

[0035] Furthermore, the sampling frequency corresponding to the sampling data of each target ball is equal to the cutoff frequency when performing low-pass filtering on the pose error.

[0036] Secondly, embodiments of this application provide a motion compensation device for a robot linear axis, comprising:

[0037] The acquisition module is used to acquire the endpoint information of the robot's linear axis and the position vectors of the three target balls;

[0038] The error module is used to obtain the pose error based on the position vector and endpoint information of each target ball;

[0039] The fitting module is used to perform B-spline fitting on the pose error to obtain the compensation function.

[0040] The sampling module is used to acquire sampling data of each target ball when the robot moves in multiple approach directions;

[0041] The curve module is used to obtain the robot's approach direction error curve based on the sampling data of each target ball;

[0042] The supplementary module is used to obtain attitude motion compensation based on the approach direction error curve and the compensation function.

[0043] Thirdly, embodiments of this application provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs the steps of a motion compensation method for a robot linear axis as described in any of the above embodiments.

[0044] Fourthly, embodiments of this application provide a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a motion compensation method for a robot linear axis as described in any of the above embodiments.

[0045] In summary, compared with the prior art, the beneficial effects of the technical solution provided in this application include at least the following:

[0046] This application provides a motion compensation method for a robot linear axis. The method obtains the pose error by using the position vectors of three target balls on the robot and the endpoint information of the linear axis, thereby acquiring the linear axis deformation error. It also obtains the approach direction error curve by collecting sampling data from each target ball when the robot moves in the approach direction, thus acquiring the motion anisotropy error. Finally, the method determines the attitude motion compensation based on the pose error compensation function and the approach direction curve. This method can compensate for the systematic errors of linear axis deformation and motion anisotropy, thereby improving the robot's motion accuracy. Attached Figure Description

[0047] Figure 1 A flowchart illustrating a motion compensation method for a robot linear axis, provided as an exemplary embodiment of this application.

[0048] Figure 2 A structural diagram of a measured robot motion system provided for an exemplary embodiment of this application.

[0049] Figure 3 This is a schematic diagram of the approach direction error curve provided for an exemplary embodiment of this application.

[0050] Figure 4 This is a structural diagram of a motion compensation device for a robot linear axis, provided as an exemplary embodiment of this application. Detailed Implementation

[0051] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0052] Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0053] Please see Figure 1 This application provides a motion compensation method for a robot linear axis, including:

[0054] Step S1: Obtain the endpoint information of the robot's linear axis and the position vectors of the three target balls.

[0055] The endpoint information and the position vectors of each target ball are obtained through laser tracking. For example... Figure 2 As shown, the installed laser tracker is aimed at the linear axis, and after the linear axis comes to a complete stop, it sequentially measures the three target balls on the robot.

[0056] The target ball must be installed in a way that ensures it is always within the measurement range of the laser tracker, the robot maintains its working posture (ensuring that the load on the linear axis, including mass and inertia, is consistent with the actual working conditions), and the target ball is not obstructed.

[0057] Step S2: The pose error is obtained based on the position vector and endpoint information of each target ball.

[0058] Step S3: Perform B-spline fitting on the pose error to obtain the compensation function.

[0059] Step S4: Obtain sampling data of each target ball when the robot moves in multiple approach directions.

[0060] Step S5: Obtain the robot's approach direction error curve based on the sampling data of each target ball.

[0061] Step S6: Obtain attitude motion compensation based on the approach direction error curve and compensation function.

[0062] Specifically, the attitude motion compensation is calculated using the following formula:

[0063]

[0064] Among them, T com T represents attitude motion compensation at the end point. robot T represents the pose transformation of the robot from the base to the end effector, which can be considered as the trajectory planned by the user; plan T represents the position that the robot's end effector plans to reach, as specified by the planner. ―1 (sign(Direction)Δe) represents the approach direction error curve; T ―1 (p(s) d ) represents the expected degree of freedom of the robot chassis in the current plan, obtained from the compensation function.

[0065] The above embodiment provides a motion compensation method for a robot linear axis. It obtains the pose error by using the position vectors of three target balls on the robot and the endpoint information of the linear axis, thereby acquiring the linear axis deformation error. It also obtains the approach direction error curve by collecting sampling data from each target ball when the robot moves in the approach direction, thus acquiring the motion anisotropy error. Finally, it determines the attitude motion compensation based on the pose error compensation function and the approach direction curve. This method can compensate for the systematic errors of linear axis deformation and motion anisotropy, thereby improving the robot's motion accuracy.

[0066] In some embodiments, the above-mentioned method of obtaining pose error based on the position vector and endpoint information of each target ball includes:

[0067] Step S21: Establish an orthogonal right-handed coordinate system based on the position vectors of each target ball.

[0068] Specifically, let the position vectors of the three target balls be respectively... R P1, R P2, R P3:

[0069]

[0070] Step S22: The position vector of the target ball that is parallel to the ground and perpendicular to the linear axis is taken as the target position vector.

[0071] Step S23: Obtain the basic position based on the target position vector and the orthogonal right-handed coordinate system.

[0072] Specifically, with Figure 2 For example, using the position vector of target ball number 1 as the target position vector, the basic position is obtained. This represents the robot's base coordinate system along the linear axis, with the scale s as the independent variable:

[0073]

[0074] Where R is (e x e y e z The symbol for this matrix represents the attitude matrix in space; That is the position vector of target ball number 1; t is the position of base.

[0075] Step S24: Construct the ideal location based on the endpoint information.

[0076] Specifically, motion along a linear axis is described by establishing a linear degree of freedom; a linear position scale in space is described using a scale s from 0 to 1. The ideal position of the linear axis is represented by p(s). d :

[0077]

[0078] The endpoint information of the linear axis includes p0, p... M(0) and p M(max) ; where p M(0) and p M(max) These are the position coordinates of the two endpoints of the linear axis. Subtracting the two position coordinates gives the result. Then it is... Normalization and linear interpolation are performed; in the above formula, s0 refers to the scale from the orthogonal right-handed coordinate system to the starting point of the linear axis, s max ―s0 refers to the length of the measured linear axis. This represents a complete interpolation process, moving from the starting point to the ending point; the ideal position can be considered as the distance from the initial point p0 to p1. M(0) to p M(max) The process of linear interpolation in the direction of [the target].

[0079] Step S25: Obtain the pose error based on the base position and the ideal position.

[0080] Specifically, the pose error obtained from the base position and the ideal position includes:

[0081] Step S251: Calculate the position error between the base position and the ideal position.

[0082]

[0083] Where T is a homogeneous transformation matrix of spatial pose; p(s) d It actually describes the process of spatial position changing with s, where p represents the combination of the errors of the three translation components plus the errors of the three Euler angles. The base position is obtained from actual measurements and is also represented by an index 's'. The pose error corresponding to two positions with the same 's' is calculated and parameterized to obtain the pose error Δe. Spline fitting is performed on Δe, and the result is used to compensate for the end effector motion.

[0084] Step S252: Parameterize the position error to obtain the pose error.

[0085] Specifically, parameterization means that for every measured coordinate in space, it must be converted into a six-dimensional data point:

[0086] Δe=(t x ,t y ,t z ,α,β,γ) T =(t T ,θ T )

[0087] Where θ represents (t) x ,t y ,t z ,α,β,γ) T The last three parameters in the equation represent the attitude error.

[0088] In some embodiments, the above-mentioned B-spline fitting of the pose error to obtain the compensation function includes:

[0089] Step S31: Perform Discrete Fourier Transform and low-pass filtering on the pose error to obtain the measurement point information.

[0090] Specifically, to derive an appropriate number of data points to describe the shaft's deformation error, the Discrete Fourier Transform (DFT) is used to determine the spectrum along the shaft. The data is analyzed in the frequency domain, and filtering methods to eliminate high-frequency components are used to remove the influence of high-frequency random positioning and measurement noise. The minimum number of measurement data points along the shaft can be estimated using the spectrum. Excessive data can cause jitter and noise information from the machine tool's movement to be fitted into the control quantity, affecting the fitting effect.

[0091] Step S32: Perform B-spline fitting on the measurement point information to obtain the compensation function.

[0092] Specifically, a B-spine curve is used to fit the filtered measurement point information. The reason for choosing a B-spline is that this spline curve possesses high-order smoothness, and as an incremental motion, it will not introduce additional joint vibrations during the movement. Furthermore, the spline curve is only affected near the considered measurement points, thus limiting the impact to a localized area.

[0093] Let P represent the filtered measurement point information (Δe1, Δe2, ..., Δe). n ):

[0094]

[0095]

[0096]

[0097] In the above formula, t represents the sampling points of the spline; see the basis functions for B-splines for details. After fitting, a continuous compensation function Δe(t) is obtained. The Δe above is discrete, but the fitted Δe(t) is continuous, and all splines can be used for fitting.

[0098] In some embodiments, the plurality of approach directions include a plurality of positive approach directions and a plurality of negative approach directions.

[0099] The angle difference between the near-positive direction and the direction from the linear axis to the target position conforms to the preset positive direction rule.

[0100] The angle difference between the near-negative direction and the direction from the linear axis to the target position conforms to the preset negative direction rule.

[0101] The target position is the correct position the robot needs to reach. Both the preset positive and negative rules can be angle ranges. The sampling data for each target ball includes positive sampling data corresponding to each positive approach direction and negative sampling data corresponding to each negative approach direction. The robot's approach direction error curve, obtained from the sampling data of each target ball, includes:

[0102] The mean of each positive sampling data corresponding to the same positive position is calculated using a Gaussian error model.

[0103] The positive error curve is obtained based on each positive position and its corresponding mean value.

[0104] The mean of each negative sampled data corresponding to the same negative position is calculated using a Gaussian error model.

[0105] The negative error curve is obtained based on each negative position and its corresponding mean value.

[0106] The positive and negative error curves are used as the approach direction error curves.

[0107] Specifically, taking a target ball representing the x-direction as an example, a single sampling (moving from the left side of the linear axis in a positive direction to the right side, or vice versa) yields a set of sampling points. Multiple samplings will result in multiple sampling points at the same location. The Gaussian error model for each sampling point is calculated, yielding a mean and a variance. The mean is taken as the measurement value at that location. See [link to relevant documentation]. Figure 3 The points obtained from movement in both the positive and negative x-direction are related to the direction of movement. Therefore, the measured values ​​at each position for the two different approach directions are fitted separately to obtain error curves for the two directions. For the three target balls, the positive error curves include the positive x-error curve, the positive y-error curve, and the positive z-error curve (i.e.,... Figure 3 The curves to the right of the origin of the three coordinate systems (the negative error curves are further divided into negative x-error curves, negative y-error curves, and negative z-error curves) Figure 3 (The curve to the left of the origin of the three coordinate systems).

[0108] In the formula of step S6, (Direction) represents the positive and negative directions of the error curve, and Δe is obtained by sampling the compensation function.

[0109] The sampling frequency corresponding to the sampling data of each target ball is equal to the cutoff frequency when performing low-pass filtering on the pose error.

[0110] Before performing error calculation and compensation, the robot can be made to move at a constant speed, and different sampling frequencies can be taken to check the data recovery effect until the main components of the low-frequency signal are preserved, thereby determining the cutoff frequency and sampling frequency.

[0111] Please see Figure 4 Another embodiment of this application provides a motion compensation device for a robot linear axis, comprising:

[0112] The acquisition module 101 is used to acquire the endpoint information of the linear axis where the robot is located and the position vectors of the three target balls.

[0113] Error module 102 is used to obtain pose error based on the position vector and endpoint information of each target ball.

[0114] The fitting module 103 is used to perform B-spline fitting on the pose error to obtain the compensation function.

[0115] The sampling module 104 is used to acquire sampling data of each target ball when the robot moves in multiple approach directions.

[0116] Curve module 105 is used to obtain the robot's approach direction error curve based on the sampling data of each target ball.

[0117] Supplementary module 106 is used to obtain attitude motion compensation based on the approach direction error curve and the compensation function.

[0118] The specific limitations of the motion compensation device for a robot linear axis provided in this embodiment can be found in the embodiment of the motion compensation method for a robot linear axis described above, and will not be repeated here. Each module in the above-described motion compensation device for a robot linear axis can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0119] This application provides a computer device that may include a processor, memory, network interface, and database connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface communicates with external terminals via a network connection. When the computer program is executed by the processor, it causes the processor to perform the steps of a motion compensation method for a robot linear axis as described in any of the above embodiments.

[0120] The working process, working details, and technical effects of the computer device provided in this embodiment can be found in the embodiment of a motion compensation method for a robot linear axis described above, and will not be repeated here.

[0121] This application provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the steps of a motion compensation method for a robot linear axis as described in any of the above embodiments. The computer-readable storage medium refers to a data storage medium, which may include, but is not limited to, floppy disks, optical disks, hard disks, flash memory, USB flash drives, and / or memory sticks. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The working process, details, and technical effects of the computer-readable storage medium provided in this embodiment can be found in the embodiments of a motion compensation method for a robot linear axis described above, and will not be repeated here.

[0122] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM).

[0123] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0124] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for motion compensation of a robot's linear axis, characterized in that, include: Obtain the endpoint information of the robot's linear axis and the position vectors of the three target balls; The pose error is obtained based on the position vector of each target ball and the endpoint information; The pose error is fitted with a B-spline to obtain a compensation function; Acquire sampling data of each target ball as the robot moves in multiple approach directions; The plurality of approach directions include a plurality of positive approach directions and a plurality of negative approach directions; the angle difference between the positive approach direction and the direction from the straight axis to the target position conforms to a preset positive rule; the angle difference between the negative approach direction and the direction from the straight axis to the target position conforms to a preset negative rule; the sampling data of each target ball includes positive sampling data corresponding to each positive approach direction and negative sampling data corresponding to each negative approach direction; The approach direction error curve of the robot is obtained based on the sampling data of each target ball; specifically, the mean of each positive sampling data corresponding to the same positive position is calculated using a Gaussian error model; a positive error curve is obtained based on each positive position and its corresponding mean; the mean of each negative sampling data corresponding to the same negative position is calculated using a Gaussian error model; a negative error curve is obtained based on each negative position and its corresponding mean; the positive error curve and the negative error curve are used as the approach direction error curve; Attitude motion compensation is obtained based on the approach direction error curve and the compensation function.

2. The motion compensation method for a robot linear axis according to claim 1, characterized in that, The endpoint information and the position vectors of each target ball are obtained by measuring with a laser tracker.

3. The motion compensation method for a robot linear axis according to claim 1, characterized in that, The method of obtaining the pose error based on the position vectors of each target ball and the endpoint information includes: Establish an orthogonal right-handed coordinate system based on the position vectors of each target ball; The position vector of the target ball, which is parallel to the ground and perpendicular to the linear axis, is taken as the target position vector; The basic position is obtained based on the target position vector and the orthogonal right-handed coordinate system; Construct the ideal location based on the endpoint information; The pose error is obtained based on the base position and the ideal position.

4. The motion compensation method for a robot linear axis according to claim 3, characterized in that, The step of obtaining the pose error based on the base position and the ideal position includes: Calculate the positional error between the base position and the ideal position; The position error is parameterized to obtain the pose error.

5. The motion compensation method for a robot linear axis according to claim 4, characterized in that, The step of performing B-spline fitting on the pose error to obtain the compensation function includes: The pose error is subjected to discrete Fourier transform and low-pass filtering to obtain the measurement point information; The compensation function is obtained by performing B-spline fitting on the measurement point information.

6. The motion compensation method for a robot linear axis according to claim 5, characterized in that, The sampling frequency corresponding to the sampling data of each target ball is equal to the cutoff frequency when the pose error is low-pass filtered.

7. A motion compensation device for a robot linear axis, characterized in that, include: The acquisition module is used to acquire the endpoint information of the robot's linear axis and the position vectors of the three target balls; An error module is used to obtain the pose error based on the position vector of each target ball and the endpoint information; The fitting module is used to perform B-spline fitting on the pose error to obtain a compensation function; The sampling module is used to acquire sampling data of each target ball when the robot moves in multiple approach directions; The plurality of approach directions include a plurality of positive approach directions and a plurality of negative approach directions; the angle difference between the positive approach direction and the direction from the straight axis to the target position conforms to a preset positive rule; the angle difference between the negative approach direction and the direction from the straight axis to the target position conforms to a preset negative rule; the sampling data of each target ball includes positive sampling data corresponding to each positive approach direction and negative sampling data corresponding to each negative approach direction; The curve module is used to obtain the approach direction error curve of the robot based on the sampled data of each target ball; specifically, it calculates the mean of each positive sampled data corresponding to the same positive position using a Gaussian error model; obtains a positive error curve based on each positive position and its corresponding mean; it calculates the mean of each negative sampled data corresponding to the same negative position using a Gaussian error model; obtains a negative error curve based on each negative position and its corresponding mean; and uses the positive error curve and the negative error curve as the approach direction error curve. The supplementary module is used to obtain attitude motion compensation based on the approach direction error curve and the compensation function.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the motion compensation method for the linear axis of the robot as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the motion compensation method for the linear axis of the robot as described in any one of claims 1 to 6.

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