TW201307800A - Method of calibration of a mathematical model of a coordinate measuring machine for the compensation of dynamic errors due to deformation - Google Patents

Abstract

A method of calibration of a mathematical model for the compensation of errors due to dynamic deformation of a measuring machine equipped with a mobile unit able to move a stylus probe in un measuring volume, wherein the model provides, in response to at least one input quantity correlated with a control signal of said drive means (13), a plurality of output quantities comprising at least one component of the measurement error introduced by the deformation and at least one quantity detected by a laser sensor and correlated with the deformation. In the calibration step, the mobile unit is subjected to a movement cycle constituted by small-amplitude oscillations of variable frequency, following the law of sinusoidal motion, keeping the tip of the probe blocked; during the movement cycle, the input and output quantities are sampled and supplied to an algorithm for model identification.

Description

Calibration method for mathematical model of coordinate measuring machine for compensation of dynamic error due to deformation Field of invention

The present invention is directed to a calibration method for a mathematical model of a coordinate measuring machine that compensates for dynamic errors due to deformation.

Background of the invention

As is well known, coordinate measuring machines generally comprise three carriages that are movable along a coordinate axis of a Cartesian reference system and are capable of moving a measurement sensor within the measurement volume. The machine is capable of providing an output of the coordinates of the workpiece detected by the measurement sensor and is calculated as the positions of the carriages vary along the respective axes.

More specifically, the coordinate measuring machine includes a base structure equipped with a guide member that operates along a first axis, for example, a base of granite or another material or a cylindrical structure, a first carriage Moving along the first axis on the base structure, a second carriage is carried by the first carriage and movable along a second axis perpendicular to the first axis and a third slide The frame is carried by the second carriage end and is movable relative to the latter along a third axis that is perpendicular to the first and second axes. The measurement sensor is carried by the third carriage.

Thus, the first shaft is horizontal; depending on the type of machine, the second shaft can be horizontal and the third shaft can be vertical, and vice versa.

For example, in the case of a bridge or scaffolding machine, the first carriage includes a horizontal cross member that defines the portion on which the second carriage moves The two axles and the third carriage are formed by a vertical movable pillar carried on the second carriage.

However, in the case of a horizontal arm machine, the first carriage includes a vertical post that defines the second axis along which the second carriage moves and the third carriage is supported by the second carriage A horizontally movable horizontal arm is carried.

The movement of the carriage is carried out by using an electric motor to transmit the driving force to the carriages via a suitable motion mechanism or, optionally, the linear electric motor is integrally formed with the carriages themselves.

The acceleration required to perform the measurement cycle in a shorter and shorter time requires a high driving force to cause elastic deformation of the moving parts of the machine due to a dynamic (inertia) effect. This deformation is also important for measurement accuracy due to the lightweight structure of the moving parts.

In order to ensure the accuracy level of the measuring machine, it is necessary to evaluate the measurement error due to the elastic deformation and then compensate.

US 2005/0102118 illustrates the use of a laser to determine and compensate for errors in the coordinate measuring machine that are derived from elastic deformation. A laser emitter and sensor are disposed on one of the movable elements of the coordinate measuring machine and have a reflector on a reference plane. Error determination and compensation is performed by relative movement between the reflector positioned on one side and the emitter and sensor positioned on the other side.

EP-A-2160565 and EP-A-2167912 illustrate a measuring machine in which a laser sensor is coupled to a movable member of the machine and provides values associated with dynamic deformation of the movable unit; The value is by a mathematics Model processing allows calculation and compensation of such measurement errors of the machine due to dynamic deformation.

In the calibration step, the position error along the Y and X axes is directly by mounting a two-dimensional position transducer on the reference plane, excluding deformation of the moving part of the machine and measuring by the two-dimensional position The difference between the position of the head of the measurement detected by the transducer and the position detected by the machine.

At least in bridge machines, positional errors along the Z axis are considered negligible.

Summary of invention

It is an object of the present invention to provide a simpler and less expensive calibration method, in particular to enable the avoidance of the use of additional tools, such as a two-dimensional sensor, and to be able to perform work with the machine in its measurement scheme.

The foregoing object is achieved by the calibration method of claim 1 of the patent application.

Simple illustration

For a better understanding of the present invention, some preferred embodiments will be described by way of non-limiting example and with reference to the accompanying drawings in which: FIG. 1 shows a bridge measuring machine of the present invention; Figure 1 is a front and partial cross-sectional view of the machine; Figure 3 is a perspective and schematic view of a carriage of the machine of Figure 1, in the form of a first dynamic deformation; Figure 4 is the first 3 is a front and a schematic view of the carriage, in a second dynamic deformation form; FIG. 5 is a block diagram of one of the dynamic deformation compensation methods using the calibration method of the present invention; and FIG. 6 is a block diagram of a model for implementing the compensation method Fig. 7 schematically shows a stylus of a measuring machine and a tool; and Figs. 8 and 9 show the tendency of the physical quantity associated with a moving period of the carriage of Fig. 3.

Detailed description of the invention

Figure 1 shows a bridge measuring machine 1 comprising a base 5 equipped with a flat horizontal upper surface 6 or reference plane and a movable unit 7.

The movable unit 7 includes a motor-driven carriage 8 that moves on the base 5 along a first horizontal axis (Y-axis) of the X-Y-Z Cartesian reference system of the measurement volume.

The carriage 8 has a bridge structure and includes two vertical upright portions 8a and 8b and an upper horizontal traverse member 8c extending between the upper ends of the vertical upright portions 8a and 8b.

Located at the bottom, adjacent the longitudinal edge of the base 5, the upright portion 8a includes a motor-driven carriage 9 that slides over the guide 11 parallel to the Y-axis and is accomplished in a well-known manner.

The traverse member 8c carries a carriage 10 that slides on a guide (not shown) along an axis parallel to a second axis (X-axis) of the reference system.

a vertical strut 12 movable along a third axis (Z-axis) of the reference system The mechanism is mounted on the carriage 10. Located at the bottom, the vertical strut 12 carries a measurement sensor 3 (in a known version), including a flange 30 constrained to the post 12 and a probe 31 projecting from the flange 30 and resiliently constrained, In a known manner, the likelihood of a traverse of two axes along its own axis and along the flanges perpendicular to each other and perpendicular to the axis of the probe is low. The end of the probe 31 is a spherical tip 32 that is capable of interacting with the member to be tested.

If the flange 30 is firmly fixed to the post 12, the shaft of the probe 31 is parallel to the Z axis when stationary, and the probe has three degrees of freedom associated with the flange 30. 32 is substantially movable along the X, Y, and Z axes.

Alternatively, the flange 30 can be mounted on the strut 12 by an articulated device or shaft joint having a two-rotation shaft of a known type and not shown.

The carriage 8, the carriage 10 and the struts 12 are provided with respective motors 13, for example, linear motors (only one is visible in Fig. 2), the control of which moves along the respective coordinate axes.

The measuring machine 1 is controlled by a control unit 14 having a power section 14a for supplying the supply currents IY, IX and IZ to the respective electric motors of the carriage 8, the slide 10 and the support 12. The measurement sensor 3 and thus its positioning within the measurement volume are moved along the Y, X and Z axes.

The measuring machine 1 is provided as an output - by means of a software based on a known type of operation - by measuring the position of the carriages along the respective X, Y and Z axes in the measuring volume of the measuring sensor 3 The position is xa, ya, za.

In the above operation, the position of the measuring sensor 3 is affected by the dynamic position errors ex, ey, ez associated with the measured values xa, ya, za, because the measuring sensor 3 is supported. The mechanical structure of the movable unit 7 (mainly the vertical upright portion 8a, the traverse member 8c and the joint region between the upper end portion of the upright portion 8a and the traverse member 8c) is subjected to the movement of the slide 8 and The force of 10 of these electric motors.

The deformation of the movable unit 7 of the measuring machine 1 is illustrated in Figs. 3 and 4.

Figure 3 shows the deformation caused by the carriage 8 moving along the y-axis. This deformation mainly comprises: • bending of the upright portion 8a; • bending of the traverse member 8c; • twisting of the upright portion 8a around the Z axis; and • twisting of the traverse member 8c about the X axis.

Figure 4 instead shows the deformation caused by the carriage 10 moving along the X axis.

This deformation mainly includes: - deformation of the joint between the upright portion 8a and the traverse member 8c; - bending of the traverse member 8c.

- the rotation of the upright portion 8a about the Y axis; and - the translation of the traverse member 8c along the X axis.

A laser sensor 16 is also mounted on the measuring machine 1 to provide information on the dynamic deformation of the movable unit 7 during movement of the slider 8 and the slider 10. (For the sake of deformation, see reference 3 and 4 instructions made).

Referring specifically to Figure 2, the laser sensor 16 is wrapped in the longitudinal chamber 24 of the traverse member 8c, and a target 28 is disposed in the chamber. At the opposite end of the 24th. The emitter 22 emits a laser beam 26 that travels through the chamber 24 in parallel with the X-axis and hits the target 28.

The transmitter 22 is conveniently supported by a vertical bar 20 as strong as possible, extending inside a vertical chamber 19 of the upright portion 8a and having a first lower end 20a rigidly secured to the carriage 9 ( And thus avoiding deformation of the vertical upright portion 8a) and a second upper end portion projecting from the vertical portion 8a into the chamber 24 of the traverse member 8c, wherein the laser emitter 22 device is secured.

The target 28 is comprised of a PSD (which is a position sensing device of the well-known type) that detects the displacement of the laser beam 26 along an incident point of the two axes parallel to the Y and Z axes of the reference system, As the mechanical structure changes, it is related to a reference position corresponding to an undeformed condition.

Detecting the displacements my, mz of the laser beam along the Y and Z axes on the target 28, along with other information, enables tracking back (eg, borrowing the techniques described below) due to the mechanical structure in Y And the dynamic deformation of the Z-axis movement.

In an initial calibration step (block 100, Figure 2), an input-output model M is defined which illustrates the dynamic behavior of the measuring machine 1 (this step is also defined as model identification).

The input-output model M (Fig. 6) is multivariable and has supply currents for the motors as inputs (u) for controlling movement along the respective X and Y axes and as output (y) The complex number includes the position xa, ya of the measuring sensor 3 obtained by the axes of the measuring machine, the position error ex, ey generated by the elasticity of the measuring machine 1 along the X and Y axes, and Sense of lightning The deformation of the measuring machine measured by the detector 16 is my, mz. This ez error can be considered negligible in a bridge machine.

Due to the linear phenomenon for small disturbances, the entire model is decomposed into two models: a first model M1 that receives the input current Iy as a Y-axis motor and provides the position ya along the Y-axis as an output, along the Y and Z axes. The position error ey, ex and the deformation measurement my, mz; and a second model M2, completely equivalent to the model M1, which is received as the current Ix input of the X-axis motor and provided as the output position xa along the X-axis And the position error ey, ex and the deformation along the Y and Z axes measure my, mz.

In fact, when stress is applied along one of the axes, there is a corresponding primary error effect along the same axis and a primary effect along the orthogonal axis (due to the mechanical couplers). All of the errors of the measuring machine are obtained by applying the superposition principle to the error effects provided by the two models (this section will be further explained).

If it is also desired to take into account the error along the Z-axis, then the models M1 and M2 will also have to provide the ez error as an output and it will need to provide a third model M3, equivalent to the models M1 and M2, which are received as The current Iz of the Z-axis motor is input, and the position za as the output along the Z-axis, and the position error ey, ex, ez and the deformation measurements my, mz along the Y and Z axes are provided.

The definition of the first model M1 will be described below with respect to one of the axes (the Y-axis), which is identical for the method of defining the second model M2 with respect to the other axis (X-axis).

As already explained, the model M1 has a current Iy as an input quantity u. The output y is: The position ya along the Y-axis is provided by the measuring machine 1; the deformations my, mz along the Y and Z axes measured by the laser sensor 16; and the two-dimensional position converter 15 The positional errors ey, ex along the Y and Z axes are measured.

The differential equation for the performance model M1 is: x = Ax + Bu + Kε

y = Cx + Du + ε where u is the input to the measurement (current Iy input to the motor), y the output, x the dynamic variable and ε represent the innovative processing method resulting from the identification of the invention. Finally, A, B, C, D, and K are the matrices of the model. Especially u =[ Iy ]

For a definition of this innovative approach, reference is made to the book entitled "System Identification - Theory for Users" by Lennart Ljung, published by Prentice Hall, Upper Saddle River, N.J.1999.

In the calibration step, the measuring machine accepts a series of duty cycles that result in dynamic errors ex, ey (assuming the ez error is negligible), which can be conveniently measured as described below.

A tool 15 (Fig. 7) is attached to the reference plane 6 and is provided with an upper chamber 35, preferably conical, assembled to receive the tip 32 of the sensor 3 without substantially any side The movement is such that the tip 32 is constrained in the chamber 35 in each direction of the X and Y coordinate axes.

If it is also desirable to take into account the ez error, the tip 32 must also be constrained in the direction Z, such as by magnetic attraction. To this end, it is necessary that the tip 32 of the probe 31 is magnetic and that the tool 15 is made of a ferromagnetic material.

As is well known, the measurement by a measuring machine is performed by the point The reading of the measuring machine axes xa, ya, za and the sum of the deflection components (xd, yd, zd) of the probe 31 along the three axes (i.e., the flange center-tip center vector) are defined.

x=xa+xd;y=ya+yd;z=za+zd

If the tip 32 of the sensor 3 is constrained, the dynamic elastic deformation is omitted, the reading of the measuring machine shaft (xa, ya, za) and the deflection of the probe 31 along each of the three axes (xd, The sum of yd, zd) is constant and constant, defined by the coordination of the tip 32 along the axis in the discussion.

If the reference system is selected as the origin at the center of the tip, then xa+xd=0; ya+yd=0; za+zd=0

Due to the elastic deformation of the measuring machine structure, the reading of the measuring machine shaft is actually affected by the positional errors ex, ey, ez and thus the previous mathematical formula becomes: xa+ex+xd=0; Ya+ey+yd=0; za+ez+zd=0 is easily calculated by the error of the reading of the measuring machine axis and the deflection of the probe ex=-(xa+xd); ey=- (ya+yd);ez=-(za+zd)

To perform the calibration of the mold M1, the sensor 3 receives a movement period caused by the movable unit of the measuring machine, which includes, for example, an oscillation of a small amplitude along the direction Y according to the sinusoidal motion law.

To illustrate that the dynamic performance of the measuring machine is a function of the excitation frequency, which is expediently below a minimum of 5 Hz, such as 1 Hz, and expediently greater than a maximum of 50 Hz, for example 120 Hz, Variable frequency between The rate is executed (Figure 8).

Preferably, the movement period begins at the minimum frequency (e.g., 1 Hz); the frequency is gradually increased in a continuous manner until a maximum value (e.g., 120 Hz - Figure 9) is reached.

At low frequencies (e.g., up to 40-50 Hz), when the tip of the probe is constrained, the amplitude of the movement is primarily determined by the relative movement of the probe 31 relative to the flange 30. .

At higher frequencies, the amplitude of this movement must be reduced to operate within the linear range of motor control (Figure 9).

During the calibration step, the input quantity u and the output quantity y are sampled, for example, having a sampling frequency of 500 microseconds, and stored.

The input and output samples are supplied to a recognition algorithm, which is applied to a linear innovation model using a most approximate method, which is characterized by a 5x matrix A, B, C, D, and E identifying the M1 input - The output model, as illustrated by the system of differential equations above (for the definition of the most approximate algorithm reference, the book titled "System Identification - The Theory Used by the User" by Lennart Ljung" by Prentice Hall, Upper Saddle River, NJ 1999 publishing).

Strictly speaking, the model is not fixed for the entire measurement volume of the measuring machine, and a number of complex calibration steps similar to those described above are carried out to cover the entire measuring volume.

The variability of the model associated with the X and Z axes, which is why the measurement volume is expediently divided into complex segments (eg, divided into 9 segments: bottom-left, bottom-center, bottom-right, center-left, ...) where the respective models M1a, M1b, M1c,...M1n has been defined.

A comprehensive model M1comp1 can thus be defined as being close to different models M1a, M1b, M1c, ... M1n in the measured volume.

In particular, it has been found that the matrices A, B, C, D and K of the different models in the measured volume are substantially fixed, while only a portion of the matrix C in the measured volume changes.

The comprehensive model M1comp1 thus comprises the matrices A, B, C, D and K which do not change in the measured volume and a matrix C which has a part of the variable parameters (corresponding to the ex, ey error signals) The columns are based on the coordinates of the X and Z axes and are thus variable in the measured volume: C=C(xa,za). This function C=C(xa,za) is one and X and The Z-axis related nonlinear function is a C matrix of the different models M1a, M1b, M1c, ... M1n interpolated in different segments of the working volume having a b-spline function. (For the definition of the smoothing function, reference is made by M. Broen, C Harris, title "Neurofuzzy Adaptive Modelling and Control", Prentice Hall International (UK) Limited Published in 1994).

After the definition of the comprehensive model M1comp1 representing the calibrated "signature" of the particular measuring machine, step 100 is followed by step 200 in which an estimated filter 1 is designed to begin with the comprehensive model M1comp1.

For this design step, the M1comp1 model is represented in the following form (a similar representation in a different way in the time domain is feasible): x = Ax + Bu + Kε y = C 1 x + D 1 u z = C 2 x + D 2 u where: u = [ Iy ]

Within the output range, the difference between these measurers (represented by the symbol y in the above system) and those who do not need to be measured is only the purpose of the evaluation (indicated by the symbol z in the above system) .

The matrix C1 contains the first three columns of the matrix C and the matrix C2 contains the last two columns of the matrix C. Similarly, matrix D1 contains the first three columns of matrix D and matrix D2 contains the last two columns of matrix D.

Regarding the variability of the measured volume, according to the new representation of the model, only the C2 matrix is effectively a function of the position of the X and Z axes, while all other matrixes are constant: C2 = C2(xa, za)

The estimation filter 1 is based on a previously validated comprehensive model M1comp1 to design an analytical technique with robust filtering (in this regard, reference is made to P. Colaneri, A. Locatelli and JC Jeromel under the title "Control Theory and Design, RH2-RH-inf viewpoint, published by Academic Press, 1997).

An efficient technique that allows the improved estimator to be accurate is to accept the filter to provide a time delay estimate (interpolation). This technique, for example, is described in an article by P. Bolzerem, P. Colaneri and G. De Nicolao entitled "Discrete-Time H-Infinity fixed lag smoothing" IEEE Trans . On Signal Processing, Vol. 52, No. 1, pp. 132-141, 2004.

In other words, in terms of time (t), the estimator provides an assessment of the time-dependent dynamic deformation (t-Delta). Delta is a time delay that is sufficient to jeopardize the efficiency of the measurement machine's immediately available measurements, but is large enough to improve the accuracy of the evaluation. In practice, it has been found that the value of Delta is equal to a few hundredths of a second.

The measured input value u and the output y (measured along the y-axis and the deformation value my, mz), the estimated filter 1 Provide an assessment of the error.

Estimated filter 1 is expressed in these equations: Where y is the vector of the outputs measured by the measuring machine and u is the vector of the inputs, and wherein the matrices  This is the result of the design estimator starting with the matrix A, B, K, C1, D1, according to the robust filtering technique mentioned above.

So, the estimation filter 1 provides a dynamic assessment of this error as an output.

After its definition, a linear type of estimation filter The matrices of 1 are stored and integrated into the measuring machine measurement software for evaluating unknown errors (block 400).

For a model M2 definition (and M3 if necessary) and an estimation filter 2 (and if necessary 3), repeating the above operations, with appropriate corrections associated with the ex error (and (if necessary).

In particular, for the definition of the model M2, the sensor 3 is subjected to small amplitude oscillations in the direction X due to the movable unit of the measuring machine, using a sinusoidal motion law and a variable frequency as explained in relation to the model M1.

From these filters 1 and 2 (and if necessary The results of 3) are added together according to the superposition principle.

The method described above is a non-limiting example of how to use the measurements my,mz analytically to evaluate the dynamic performance of the measuring machine. Essentially, can make Use any other analytical method appropriate for the purpose.

The method described above can be applied to the calibration of a model of a bridge measuring machine equipped with a laser sensor for detecting other types of deformation, or to other types of measuring machines (eg, horizontal arms, brackets, etc.), As explained in the patent application EP-A-2167912, this description is hereby incorporated by reference.

It will be apparent that the advantages obtained by the present invention are obtained by examining the features thereof.

In particular, the calibration of the model for the correction of the dynamic error of the measuring machine is done in a simple and fast manner, the measuring machine is in its measurement preparation state and does not have to rely on a measuring instrument, such as mentioned The two-dimensional sensor described in the previous document.

Finally, it is to be understood that the method of the description may be modified and modified without departing from the scope of the protection as defined by the scope of the application.

In particular, the movement period does not necessarily have to consist of a continuous frequency sweep. Other excitation techniques can be used, using different and aperiodic motion laws, as long as the frequency spectrum represents dynamic usage. For example, the displacement may have a frequency spectrum similar to white noise based on a virtual random pulse.

In addition, the probe can be pivotally transformed, that is, in place of the Cartesian coordinate system, the two rotational degrees of freedom of the flange relative to the two axes perpendicular to its own axis (as shown in Figure 7) ).

1‧‧‧Bridge measuring machine/estimated filter

3‧‧‧Measurement sensor

5‧‧‧Base

6‧‧‧ upper surface

7‧‧‧ movable unit

8‧‧‧Slide

8a, 8b‧‧‧ vertical uprights

8c‧‧‧Upper horizontal cross member

9‧‧‧Slide

10‧‧‧Slide

11‧‧‧ Guides

12‧‧‧ vertical pillar

13‧‧‧Motor

14‧‧‧Control unit

14a‧‧‧Power section

15‧‧‧Two-Dimensional Position Converter/Tool

16‧‧‧Laser sensor

19‧‧‧Vertical chamber

20‧‧‧ vertical bars

20a‧‧‧Lower end

22‧‧‧transmitter

24‧‧‧Longitudinal chamber

26‧‧‧Laser beam

28‧‧‧ Target

30‧‧‧Flange

31‧‧‧ probe

32‧‧‧Spherical tip

35‧‧‧Upper chamber

100‧‧‧Box/step

200‧‧‧ steps

400‧‧‧ squares

Xa, ya, za‧‧‧ position measurement

Xd, yd, zd‧‧‧ bending component

Ex, ey, ez‧‧‧ dynamic position error

My, mz‧‧‧ displacement

U‧‧‧ input

Y‧‧‧ Output

Ya‧‧‧ position

A, B, C, C1, C2, D, D1, D2, K, Â , ‧‧‧matrix

Iy‧‧‧Input current

IX, IY, IZ‧‧‧ supply current

M‧‧‧Input-Output Model

M1‧‧‧ first model

M2‧‧‧ second model

M3‧‧‧ third model

1, 2, 3‧‧‧Filter

Figure 1 shows a bridge measuring machine of the present invention; Figure 2 is a front and partial cross-sectional view of the machine of Figure 1; Figure 3 is a perspective and schematic view of a carriage of the machine of Figure 1, in the form of a first dynamic deformation Figure 4 is a front and schematic view of the carriage of Figure 3 in a second dynamic deformation form; Figure 5 is a compensation method for the dynamic deformation using the calibration method of the present invention. a block diagram; Fig. 6 is a block diagram of a model for implementing the compensation method; Fig. 7 schematically shows a stylus of a measuring machine and a tool; and Figs. 8 and 9 show The tendency of the physical quantity associated with a movement period of the carriage of Fig. 3.

100‧‧‧ calibration procedure

110‧‧‧Measure input and output during the work cycle

120‧‧‧Provide samples to recognition algorithms

130‧‧‧Storage M

200‧‧‧M filter definition

300‧‧‧Use M filter for immediate error definition

400‧‧‧Use error for measurement correction

Claims (9)

A calibration method for a mathematical model of a measuring machine for compensating for errors due to dynamic deformation, comprising: a movable unit for moving a probe probe in a measurement volume, the movable unit comprising at least one component It is movable along a shaft under the driving force of a driving device, the probe comprising a probe having a tip, and a sensor assembled to instantly detect at least the dynamic deformation associated with An amount, wherein the model, after responding to at least one input associated with a control signal of the one of the driving devices, provides a plurality of outputs including at least one component of the measurement error caused by the deformation and At least the amount detected by the sensor, the calibration method includes the steps of: controlling the movable unit to perform a movement period to be capable of generating dynamic deformation; collecting the plurality of inputs and samples of the output during the movement period Storing the samples; and supplying the samples to a recognition algorithm to define the model; characterized by performing the movement cycle to maintain A tip of the probe of the probe is fixed using a law of motion having a range of displacement less than the tip of the probe relative to the positioning flange of the probe, and a frequency spectrum representative of the dynamics of use of the measuring machine situation. The method of claim 1, wherein the method is characterized by The period includes a series of oscillations along at least one axis. The method of claim 2, wherein the oscillations are of a variable frequency. The method of claim 3, characterized in that it comprises the step of varying the frequency of the oscillations in a continuous manner from a minimum to a maximum. The method of claim 4, wherein the minimum value is less than 5 Hz. The method of claim 4 or 5, wherein the maximum value is greater than 50 Hz. The method of any one of claims 3 to 6, wherein the amplitude of the oscillations decreases as the frequency increases, to maintain control of the movable unit along the axis in a linear condition. . A method according to any one of the preceding claims, wherein the sensor is a laser sensor comprising a transmitter fixed to a first portion of a movable member of the movable unit, And a target fixed to a second portion of the movable member, and the amount detected by the sensor is such that the laser beam is undeformed with respect to one of the movable units on the target The displacement of one of the corresponding reference positions of the incident point. The method of claim 8 is characterized in that the step of detecting the displacement of the incident point of the laser beam is performed by a position sensing device (PSD) defining the target.