FR2471629A1 - Three=dimensional locating system for mobile tool member - assigns position vector for all theoretical locations which is corrected as function of field position - Google Patents

Abstract

The orthogonal axis placement of a sensor or tool is accurately performed without feedback circuits by experimentally measuring the location performance of the mechanism against a theoretical reference location field. Correcting the signals, based on these measurements, are used to position the mechanism on each of its three axes. The movement is controlled by a set of adjustable cams or by electronic control using electronic memories. The errors in the angular position of a vector (V) related to a movable part of a tool which undergoes a translation, and a rotation is determined by evacuating the scalar product of the displacement vector with a tensor. The field of the position vectors is determined by placing either a sphere or a cylinder on a plane surface and contouring them with the extendable part of the tool.

Description

METHOD FOR REPERTING THE POSITION OF A MOVING ORGAne
CHINA OR APPARATUS AND APPLICATIONS TO THE ORDER OF THESE
CHINES OR APPARATUS.

 The present invention relates to a method of locating the position, in space, of a movable member of a machine or apparatus, these machines or apparatus possibly being inachines-tools or other machines having one or a machine or a movable treatment device, industrial robots or tools, three-dimensional measuring machines, measuring or detection devices such as, for example, scanners, radar sonar radars, photo-grammar apparatus, ie machines or apparatus in which any tool, or any effector device or sensor, detector, transmitter, receiver or other is movable in an active voice within which it is desired to combat its position with a degree of accuracy particularly high.

The invention also relates to the application of this method to the control and operation of these machines or apparatus, for example manual, cam or digital program control of a machine tool or a robot or apparatus. such as a scanner, a tintillograph, radar or other, or to display, read or use measurements of a measuring machine or a device
The movable active parts of the machines, such as machine tool tools, measuring machine probes, active devices of the robots or the aforementioned apparatus members are caused to move in the space with a further provision. in bigger. The location in space of these organs is carried out by means of markers which are generally orthonormal three-dimensional markers or sometimes polar markers. These markers correspond most often to a system of slides along the three axes permitting to the organ to reach any point of the useful space.

 Precision requirements in the field of these machines or devices now require the taking into account of systematic faults arising either from manufacturing errors, applied forces or temperature variations and corresponding in particular to the lack of orthogonality. , linearity or alignment of the slides or other parts of the machines and either from manufacturing or operating circumstances.

This consideration is currently done through two distinct approaches
The first, which is that of classical metrology, lies in the measurement of the errors of position and shape of the slides of the machine. These processes are long, motteux and, if they allow to define a degree of precision of the machine allowing its classification, the information obtained is only usable for a good order of it.

 The second approach is to carry out practical tests, for example to machine a part in the case of machine tools or to measure it, in the case of robots or measuring machines, after which a comparison is made. In the case of a machine tool, for example, the actual geometry of the part obtained is compared with the dimensional control instructions, whereas in the case of a measuring machine, the measurement results obtained will be compared with the actual measurements of the machine. the room. These practical tests are very useful for defining the actual performance of the machine in the specific cases studied and possibly making the necessary corrections. They can not, however, be extended to different cases.

 The present invention therefore proposes to provide a method of locating the position in the space of a movable member of such machines or apparatus making it possible to perform the work in space with increased precision in the whole of the useful space of the machine or apparatus. In particular, this method proposes to eliminate almost completely the aforementioned systematic errors.

In addition, the invention proposes to easily determine, without accessories and with the aid of a number of measurements, the corrections implemented in the process,
The subject of the invention is a method of locating the position in the space of the mobile member of a machine such as a machine tool, a robot-tool, a measuring machine in which the position in the espaae of said member is associated with corresponding coordinates relative to a physical coordinate system integral with the machine or the apparatus, characterized in that a field is determined for the useful space of the machine or the apparatus. vectors associated with each theoretical point of said space, said vector corresponding to the geometric displacement connecting the theoretical point to the real point and that the coordinates are corrected according to said field.

 By theoretical point of the space of the machine, we mean the point in which we should theoretically be, if the reference was perfectly Cartesian, the organ (defined by a particular point of the organ, for example the point of a probe) of the machine or device, when the coordinates of this point are displayed on the machine's physical reference mark. By real point is meant the point where actually said body when said coordinates are displayed.

In this way, if O is the common origin of the physical (actually curvilinear) repre- sentation and of the cartesian coordinate system, then said vector U (M) is such that

 In the case of a machine tool, it is advantageous to use, to represent the active member of the machine, a given point of the spindle. The machining point will thus be defined taking into account the known distance between the pre-point.

the spindle and the tip of the tool.

où

The invention also makes it possible to determine and correct the errors of angular positions of the spindle or of another part of a machine or apparatus. Indeed, if one considers a vector V coming from a point M of the organ of the machine, point which moves in the useful space, this vector will undergo successively the following transformations
Translation
U (M), rotationCJet deformation

or

et où Dt Dt est le tenseur transposé de D,
Dans les différentes applications décrites, le champ U > (M) représente les déplacements qu'il faut faire subir au point d'un repère cartésien pour l'appliquer sur le repère, en fait curviligne, parfaitement défini par la machine, par exemple par ses glissières. Il existe là une large indétermination au niveau du choix de ce repère cartésien, tous ces repères se déduisant les uns des autres par une translation et une rotation. On peut, par exemple, choisir le repère cartésien qui cotncide au mieux avec le repère curviligne au sens des moindres carrés. Dans ces conditions, lu (Mil est minirn. D being the deformation tensor of the field (M), that is to say:

and where Dt Dt is the transposed tensor of D,
In the different applications described, the field U> (M) represents the displacements to be subjected to the point of a Cartesian coordinate system to apply it to the reference, in fact curvilinear, perfectly defined by the machine, for example by its slides. There exists a wide indetermination in the choice of this Cartesian reference, all these marks being deduced from each other by a translation and a rotation. One can, for example, choose the Cartesian coordinate system that best coordinates with the least-squares curvilinear coordinate system. Under these conditions, read (Mil is minirn.

 The second geometric transformation is the one that causes the local coordinate system, at the point M, to coincide with the previous reference. This is done by rotating the local coordinate system relative to the previous coordinate system plus a local clean deformation. Finally, the third and last transformation is the local pure deformation, which makes it possible to calculate the deformation dV of a vector V by the relation dV = L.V. When these 3 transformations are successively added, it is easy to express a vector V in curvilinear coordinates in the Cartesian frame previously described.

 The invention also relates to the application of this method to the control and operation of said machines or apparatus.

 In one embodiment of the invention applicable in particular; the driving of a machine tool or a robot, the various points of the space, in which the tool must successively be located, are determined in a manner known per se, said points being each identified in the system Cartesian by the theoretical coordinates, and one adds to said coordinates the projections on the Cartesian system of a correction vector - U (M) the machine then being coamandée, in its physical coordinate system, using the coordinates thus corrected.

 In other words, when it is desired to carry the tool to a determined point corresponding to a determined position M of the spindle, the machine is controlled so as to obtain, in its physical coordinate system, not the coordinates of M, but corrected M coordinates, which will appear on the counters of the machine.

In another embodiment applicable to a three-dimensional measuring machine, the measurement is carried out with the probe forming the active organ of the machine, which is then at the real point M. For the actual coordinates of this machine, point, we add to the vector Or 'the vector U (;; mainly defined
The application of the method to other machines or apparatus such as scanners, scintigraphs, industrial radiography apparatus, ultrasound apparatus, photogrammetry apparatus, radars, sonars is carried out analogously to the above applications, according to whether it is desired to bring the movable member to a specific precise position or whether it is desired to determine a position, in which a phenomenon has been detected.

It goes without saying that the invention is applicable a few times to the physical repeater of the appliance or machine, whether the reference mark is (approximately) orthonormal Cartesian or rn, polar or other
The determination of the field U (M), for a given machine or apparatus, can be carried out by any method or process and in particular by successive approximations by carrying out a large number of measurements using appropriate gauges according to the methods of conventional metrology. .

 However, the invention also proposes to determine this field for a given machine by means of a small number of measurements. This method can be implemented in the following way: the machine's sphere of reference, that is to say the reference sphere of the origins of the mark, is used to uniquely associate the co-ordinates identified on the machine (in fact, the co-ordinate coordinates with the sliders of the machine). machine.

- We use a perfectly flat marble that is available in any way in the useful space of the machine and we feel 3 points of the marble, which defines the position of the plane in the curvilinear mark of the machine.

Moreover, we give ourselves a mathematical module of the displacement field U (M); the experience that we can take, for example, next development of the second degree
Ux (M) = A + Bx = Cy + Dz + Ex + Fy + Gz + Hxy + Ixz + Jyz
Uy (M) = A '+ B'x + C'y + D'z + E'x + F'y + G'z + H'xy +
I'xz + J'yz
Uz (M) = A "+ B" x + C "y + D" z + E "x + F" y + G "z + H" xy +
I "xz J" yz
Of course, the accuracy can be increased by ordering even higher if desired.

- Then proceed to the palp of a number of other points of the plan. For each point to be probed, the position revealed by the counters of the machine is noted. The vector U is the one that extends between the point to be probed and the point that should theoretically correspond. We eff between the vector U and the direction perpendicular to the plane passing through the point palpe, perfectly known direction, where we obtain the scalar ss @ U xa @ Uy b + U zc, where a, b, and c are the projections on the reference of the unit vector perpendicular to the plane. We thus obtain a first equation. It suffices to repeat these operations until a sufficient number of equations are found to solve the system and determine the parameters A, B, C, H ", I", J ".

 In order to cover the space over a wide range, it is preferable to carry out measurements using different planes in the machine's working space, ie by tilting the marble in 3 different positions.

The number of measurements, apart from the three iris probes carried out for each plane position, which is expressed by n, n 'and n "for the three planes must satisfy the following conditions:

<tb> n # <SEP><SEP> 1
####
<tb> n "# <SEP><SEP> 1
<Tb>
In other words, n, nt, n "must be at least equal to 1 and their total must be greater than or equal to the number of mees-defining a plane, in this case p = 3.

 Of course, instead of using fine martens, one could use very accurate cylinders or spears or other shapes and the number of feelers would then be increased to an order of its kind on aces.

 When enough equations have been obtained and the system has been solved to obtain the above perameters, the field U (M) is perfectly well known.

It is remarkable that this determination is carried out without the use of external hiding instruments, simply by using the machine's own storytellers. Only a device as simple as a marble must be used or, if desired, another surface, perfectly perfect geometrical defined
The information thus collected on the field T (M) allows, not only as previously seen, to provide a machine control method, such as a machine tool, a robot, a measuring machine or apparatus, but also to finish criteria of dimensional quality of the machines allowing the compares, One can advantageously use as quality oritere for this purpose three eoer ficients characteristic of the geometrical transformations necessary to pass from the curvilinear mark to the cartesian reference
If we assume an elementary cube that moves in the useful space of the machine, we can define the ze-
Cl = &alpha; + ss + T which translates the defect of orientation of the cube
C2 = which represents the variation of volume and the lack of graduation
C3
S where S represents the lateral surface, this formula expressing the angular defect.

These coefficients are determined in the following way
We have seen that the tensor of the deformations obtained from the knowledge of the field U (M) is equal to # + #.

n and e have three invariants. For A the first and the third are zero and the second &alpha; + ss + @ is formed by the rotational module, it gives Cl, 2 + 2 + &gamma; 2
For # we use the first and the second invariants the first being #V where V is the volume that is to say the diversity
V geometry of the field that gives C2 on the first diagonal.

The second invariant is # &gamma; = 1/2 (#ii #jj - #ij #ji) and the co-C3 P #s is equal to the first invariant of @ minus the double of the second invariant of #.

 Of course, when the field # (M) and the invariants C1, C2, 03 are determined for a machine or a useful apparatus reading different coordinates, for example polar the preceding instruction applies, transposed into a system of theoretical polar coordinates, associated with the physical system, of the same origin.

Other advantages and characteristics of the invention will now be described with reference to nonlimiting examples and with reference to the appended drawing in which:
- Figure 1 is a schematic view of a machine tool with three sets of slides.

 FIGS. 2, 3 and 4 are diagrams showing three positions of a plane marble in the physical coordinate system of the machine.

 Referring to Figure 1 there is shown a machine tool comprising a first set of two parallel rails 1 extending in a horizontal plane and on which slides a bridge-shaped carriage 2 carrying a transverse slide 3 orthogonal to the slides 1. On the slide 3 slides a carriage 4 traversed by a carriage 5 slidable vertically and thus perpendicular to the slides 1 and 3. The end of the carriage 5 carries an active head with a pin 6 in which is mounted a tool 7.The different Slides carry graduations which determines an approximately Cartesian coordinate orthonormal with axes Ox, Oy, Oz. In fact, in modern machines the position of the point of the movable member, for example the central point of the lower end of the spindle 6, the tool being deposited, is located on numerical counters which replace the graduations shown.

 The reference 0, x, y, z, however, is not, because of the defects inherent to the machine, a Cartesian reference in the useful volume of the machine, that is to say the volume likely to be This point is, if we consider the degree of precision required in modern machines, which is of a few hundredths of a millimeter on very long lengths beyond the point considered, in the case of the aforementioned point of pin 6. the meter, a curvilinear mark whose geometry is a priori unknown.

 As a result, when the graduations or the machines of the machine indicate the coordinates x, y, Z d a point Mr where is actually said pin 6, the vector starting from the origin O and defined by its projections X @ yz starting from the origin O and defined by its projecti9ons x, x, y, on a genuinely orthonormal reference point of origin Os n does not end at the point Mr but at a point Mth which is a theoretical point at which the spindle is not found Consequently, to pass from the point Mth to the point Ne it is necessary to traverse a path represented by a vector # (M) whose magnitude and direction depend on said coordinates x, y, z.

Thus, if by way of example it is desired that the spindle go to a point having, in the true Cartesian reference of origin O, the coordinates (in millimeters) X = 220.00 y = 142.35 and z = 360,50 and that at a point having said coor data the projections of the vector U is (0,03, 0,01 and the coordinates by which the machine is to be controlled on its counters will then be X
X = 220.00 - 0.03 = 219.97 y = 142.35 - 0.01 = 142.34 zn 360.50 e 0.01 to 360.49
For manual control of the machine the components of the vector # at the different points of the space can be listed on tables. However, preferably in an electronic control of the machine using a digital system, this field of the vector j can be included in an immediate access memory so that each time the program of the machine orders the spindle to go to a given point, the memory subtracts from the coordinates of the program the corresponding values of the vector t the servo -motors of the machine receiving these corrected instructions.

 In the case of a mechanical type control it is also conceivable to present the vector for example in the form of a set of cams.

Referring to FIGS. 2, 3 and 4,
In these figures, the machine is represented in an extremely schematic manner only by the axes of the real curvilinear mark O xyz.

 To perform the determination of the field # (X) is used as above a perfectly flat marble which is arranged for example in the three positions shown in Figures 2, 3 and 4 where we see the intersections between the marble plane and the reference plans.

 The spindle of the machine has no tools and receives a precisely positioned RENISHAW type probe which, at the moment of contact with the marble, emits a signal giving the order to read the counters of the machine.

 The machine being thus equlpée, one successively palpates three points Ml, M2 and M3 whose coordinates define the equation of the plane in the curviligne mark O xyz. A fourth point M of the plane is then palpated and the xyz coordinates are obtained on the counters of the machine. The calculation quickly shows that the xyz coordinates are incompatible with the presence of the point M in the plane defined by the points M1, M2 and M3 in the O xyz frame. On the contrary, in this reference, these xyz coordinates define a point N situated outside the plane. Since we can not know the exact coordinates of the real point M belonging to the plane in the curvilinear coordinate, it is not possible to know in this way the vee- rator t passing from the point N to the point M. On the other hand we know the distance NP, P being the trace on the plane of the normal to the plane passing through N. This distance is the scalar of the vector by the par the unit vector of the normal NP and we can therefore write t = Ux (M) xa + Uy (X) xb + Uz (M) xc where t is equal to the distance NP, Ux, Uy, and Uz are the proJections of the vector and a, b, c, are the components of the unit vector of the normal NX.

The same kind of operation is performed for other positions of the plane determined by the marble as shown in FIGS. 3 and 4 where Mtl, M'2, M'3 and M "1,
M "2 and M" 3 are in each case 3 points making it possible to write the equation of the plane in the curvilinear coordinate system and at least one additional point is palpated in each plane to obtain other similar equations.

 It is then easy to use modern means of calculation, using the developments of Ux, Uy, Uz for example a development of the second degree, to determine the totality of the coefficients belonging to the development and consequently to define the field of the vectors U (M).

 The field thus determined is then used to carry out the corrections in the way that has been deoritized,

Claims (11)

claims  1 - Method for locating the position in the space of a movable member of a machine or apparatus, particularly machine tool, robot, measuring machine, scanner, scintigraphe, radar, sonar and photogrammetry apparatus, wherein the position in the space is associated with coordinates relative to a physical coordinate system integral with the machine or the apparatus, characterized in that a working field is determined for the working space of the machine or the apparatus. vectors t (X) associated with each theoretical point of space, said vector corresponding to the geometric displacement connecting the theoretical point to the real point, and that the coordinates are corrected according to said field.  2 - Process according to claim 1 characterized in that one determines the errors of angular position of a vector t carried by said movable member and undergoing, by displacement of said member a translation t (M) and a rotation A determining the deformation d? fn .V of the vector where e is the tensor such that

 and where I) 'is the transposed tensor of ti. 3 - Method according to one of claims 1 and 2 characterized in that to determine the field of vectors t? (M) a perfect surface, in particular a plane, a cylinder or a sphere, is positioned in the working space, a number of points of this surface equal to the order of the surface is defined by means of said movable member to define thus the equation of the surface using the coordinates read on the physical reference of the machine or the apparatus, one palpates at least one additional point of the surface whose coordinates, in said mark, do not appear to belong at said surface, determining the distance between this point and the surface defined by its equation thus providing the scalar of the vector? (X) by the unit vector of the normal to the surface passing through this point and the said operation is repeated a number of times sufficient to solve a system of linear equations providing the parameters of a determined order of development of the field t (M).

 4 - Process according to claim 3 characterized in that it provides said perfect surface successively in several positions in the usable space.  5 - Method according to one of claims 3 and 4 for a machine or an apparatus having no feeler characterized in that is mounted on the movable member, at a predetermined point, a probe or a contact probe.  6 - Application of the method according to any one of claims 1 to 5 to the control of a machine or apparatus characterized in that for each point of the useful space reached by the movable member is carried out a correction according to the value of said vector # (M) at this point.  7 - Application according to claim 6, in particular to the control of a machine tool or a robot, characterized in that after having determined the points of the space where the movable member, carrying a tool, must blind brought to correct the coordinates of said points by subtracting them from the vector # (M) and use the corrected coordinates as control instructions for the machine or robot.  8 - Application according to claim 7 char acterized by the fact that it automatically performs said corrections ide of a memory or a set of cams memorizing said field U (M).  9 - Application according to claim 6, in particular to the control of a measuring machine or a measuring device such as radar, sonar, scanner, nineteen, photogrammetry apparatus characterized by the fact that we add to the coordinates from a point of the mobile organ the projections of the vector It (N).  10 - Application according to claim 9, characterized in that it automatically performs said adJono- tion with a memory or a set of cams storing said field U (M)  11 - Application according to any one of revendicaw tions 6 to 10 of the method of claim 2 characterized in that one carries out simultaneously an angular position correction of an elongate member of the movable member for example a tool of Machine tool.