Spatial accuracy correction method and apparatus

Abstract

A method that corrects an error in positioning in a positioning mechanism by using a measurable length value measured by a laser interferometer and a measured value for spatial coordinates measured by the positioning mechanism. The method includes a measurement step in which a retroreflector affixed to a displacer is displaced to a plurality of measurement points, and the measured length value and the measured value at each of the measurement points is acquired; and a parameter calculation step in which a correction parameter is calculated based on the measured value, the measured length value, and the coordinates of a rotation center of the tracking-type laser interferometer. A first correction constant is applied to the measured length value for each measurement line, and a second correction constant different from the first correction constant is applied to the coordinates of the rotation center of the interferometer for each measurement line.

Claims

1. A spatial accuracy correction method having a positioning mechanism displacing a displacement body to a predetermined set of spatial coordinates, the positioning mechanism also having a retroreflector mounted to the displacement body, and a laser interferometer having a reference point and measuring a distance from the reference point to the retroreflector, the method performing spatial accuracy correction of the positioning mechanism using a measured length value measured by the laser interferometer and a measured value for spatial coordinates of the retroreflector measured by the positioning mechanism, the method comprising: dividing a plurality of measurement points into a plurality of measurement lines, displacing the displacement body to the plurality of measurement points, and acquiring the measured length value and the measured value at each of the measurement points for each measurement line; and calculating a correction parameter based on the measured value, the measured length value, and the coordinates of the reference point, the calculating the calculating of the parameter comprising: applying a first correction constant to the measured length value for each measurement line; and applying a second correction constant different from the first correction constant to the coordinates of the reference point for each measurement line.

2. A spatial accuracy correction apparatus comprising: a positioning machine that displaces a displacer to a predetermined set of spatial coordinates, the positioning machine comprising a retroreflector mounted to the displacer, the positioning machine being configured to measure a measurable value of the spatial coordinates of the retroreflector; a laser interferometer having a reference point and configured to measure a measurable length value that is a distance from the reference point to the retroreflector; and a controller operably connected to the positioning machine and the laser interferometer, the controller comprising a processor and a memory that stores an instruction, the processor further comprising, as a configuration when the processor executes the instruction stored in the memory: a measurement controller that divides a plurality of measurement points into a plurality of measurement lines, displaces the displacer to the plurality of measurement points, and acquires the measured length value and the measured value at each of the measurement points; and a correction value calculator that performs parameter calculation that calculates a correction parameter based on the measured value, the measured length value, and the coordinates of the reference point, wherein the correction value calculator applies a first correction constant to the measured length value for each measurement line, and applies a second correction constant different from the first correction constant to the coordinates of the reference point for each measurement line to calculate the correction parameter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The present invention is further described in the detailed description which follows, in reference to the noted plurality of drawings by way of non-limiting examples of exemplary embodiments of the present invention, in which like reference numerals represent similar parts throughout the several views of the drawings, and wherein:

(2) FIG. 1 illustrates a schematic configuration of a spatial accuracy correction apparatus according to an embodiment;

(3) FIG. 2 is a flow chart illustrating a spatial accuracy correction method according to the embodiment;

(4) FIG. 3 is a flow chart illustrating a measuring process according to the embodiment; and

(5) FIG. 4 illustrates a schematic configuration of a conventional spatial accuracy correction apparatus.

DETAILED DESCRIPTION OF THE INVENTION

(6) The particulars shown herein are by way of example and for purposes of illustrative discussion of the embodiments of the present invention only and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the present invention. In this regard, no attempt is made to show structural details of the present invention in more detail than is necessary for the fundamental understanding of the present invention, the description taken with the drawings making apparent to those skilled in the art how the forms of the present invention may be embodied in practice.

(7) Hereafter, a spatial accuracy correction apparatus according to an embodiment of the present invention is described. FIG. 1 illustrates a schematic configuration of a spatial accuracy correction apparatus 1 according to the embodiment. The spatial accuracy correction apparatus 1 includes a CMM 10, a tracking-type laser interferometer 20, and a control device (controller) 30. In FIG. 1, the CMM 10 and the tracking-type laser interferometer 20 have the same configuration as the conventional example illustrated in FIG. 4. Specifically, the CMM 10 is equivalent to a positioning mechanism in the present invention, and includes a measurement probe 101, a Z spindle 102 to which the measurement probe 101 is affixed, an X guide 103 holding the Z spindle 102 so as to be capable of displacement in an X direction, and a column 104 to which the X guide 103 is affixed and which is capable of displacement in a Y direction. In addition, the CMM 10 includes a Y displacement mechanism, an X displacement mechanism, a Z displacement mechanism, and various scales, none of which are shown in the drawings. The CMM 10 also positions the measurement probe 101 (displacement body or displacer) by displacing the measurement probe 101 to a position having predetermined spatial coordinates, and measures the spatial coordinates of the positioned measurement probe 101 as a measured or measurable value X.sub.CMM. In the present embodiment, by controlling the Y displacement mechanism, X displacement mechanism, and Z displacement mechanism, the measurement probe 101 and the Z spindle 102 to which the measurement probe 101 is affixed are displaced in XYZ directions, configuring the displacement body of the present invention. Moreover, a retroreflector 105 that reflects laser light from the tracking-type laser interferometer 20 is mounted at a tip position of the measurement probe 101 configuring the displacement body. The measurement probe 101 may also be detached and the retroreflector 105 mounted to a tip position of the Z spindle 102.

(8) The tracking-type laser interferometer 20 is equivalent to a laser interferometer in the present invention, and is installed within a measurement range of the CMM 10 (a table 106 or the like on which a measured or measureable object is placed, for example) or in the vicinity thereof. Although not shown in the drawings, the tracking-type laser interferometer 20 includes, for example, a laser light source that emits laser light, a light separator that separates the laser light into measurement light and reference light, a light receiver receiving interfering light that is a composite of the reference light and laser light reflected by the retroreflector 105 (return light), and a two-axis rotation mechanism that controls an emission direction of the measurement light (laser light). In addition, the tracking-type laser interferometer 20 tracks the retroreflector 105 by controlling the two-axis rotation mechanism, such that an optical axis of the return light reflected by the retroreflector 105 coincides with an optical axis of the emitted light. More specifically, the two-axis rotation mechanism includes a horizontal rotation mechanism that rotates the emission direction of the laser centered around a perpendicular axis that is parallel to a Z axis and sweeps the emission direction of the laser in a horizontal direction, and a Z rotation mechanism that causes rotation centered around a horizontal axis that is orthogonal to the perpendicular axis and sweeps the emission direction of the laser in the Z direction. Also, a point of intersection between the perpendicular axis and the horizontal axis is a rotation center M of the tracking-type laser interferometer 20, and serves as a reference point in the present invention. The tracking-type laser interferometer 20 uses the interference between the reference light and the return light from the retroreflector 105 to measure a distance from the rotation center M of the two-axis rotation mechanism to the retroreflector 105. The distance measured by the tracking-type laser interferometer 20 is designated as a measured length value d.

(9) The control device 30 is connected to both the CMM 10 and the tracking-type laser interferometer 20. Also, the control device 30 controls the CMM 10 and the tracking-type laser interferometer 20, acquires the measured value X.sub.CMM for the position of the retroreflector 105 from the CMM 10 and the measured length value d from the tracking-type laser interferometer 20, respectively, and performs a spatial accuracy correction process of the CMM 10.

(10) Specifically, the control device 30 is configured by, e.g., a computer, and includes, for example, storage configured by a memory or the like and a calculator configured by a CPU (Central Processing Unit), computer processor or the like. Also, as shown in FIG. 1, the calculator retrieves and executes a program stored in the storage, and the controller 30 thereby carries out operations as a measurement controller 31, a measurement result acquirer 32, a correction value calculator 33, and the like.

(11) The measurement controller 31 displaces the retroreflector 105 to a predetermined measurement point X. In the present embodiment, a plurality of measurement points at which measurement is conducted and a measurement order for the measurement points are defined ahead of time. In this example, in the present embodiment, the plurality of measurement points are divided into a plurality of measurement lines that include a predetermined number Ka of measurement points, and the measurement controller 31 measures each of the measurement points belonging to the measurement line in order, then measures the measurement points belonging to the next measurement line in order.

(12) The measurement result acquirer 32 acquires the measurement results for each measurement point. In other words, the measurement result acquirer 32, for example, synchronizes the CMM 10 and the tracking-type laser interferometer 20, and causes the measured value X.sub.CMM and the measured length value d for the measurement point X to be measured simultaneously. The measurement probe 101 may also be stopped at the measurement point X by the measurement controller 31 and the measured value X.sub.CMM and the measured length value d may be measured at substantially the same time.

(13) The correction value calculator 33 calculates a correction parameter Bα based on the measured value X.sub.CMM and the measured length value d acquired by the measurement result acquirer 32. Detailed processes of the measurement controller 31, the measurement result acquirer 32, and the correction value calculator 33 are described below.

(14) Spatial Accuracy Correction Method

(15) Hereafter, a spatial accuracy correction method (spatial accuracy correction process) performed by the spatial accuracy correction apparatus 1 is described in which a correction parameter for correcting the spatial coordinates of the CMM 10 is calculated. In the spatial accuracy correction process according to the present embodiment, the position of the rotation center M of the tracking-type laser interferometer 20 (installation position of the tracking-type laser interferometer 20) and a stylus offset (relative position of the retroreflector 105 with respect to the Z spindle) are modified and the measured values X.sub.CMM and measured length values d for the plurality of measurement points X are acquired, and the correction parameter Bα is calculated. In this example, the present embodiment is described as having a variable that indicates the stylus offset designated n (where n is an integer from 1 to n.sub.max and an initial value is n=1) and a variable that indicates the position of the rotation center M of the tracking-type laser interferometer 20 designated m (where m is an integer from 1 to m.sub.max and an initial value is m=1).

(16) FIG. 2 is a flow chart illustrating a spatial accuracy correction process (spatial accuracy correction method) according to the present embodiment. In the spatial accuracy correction process according to the present embodiment, first, the position of the rotation center M of the tracking-type laser interferometer 20 is set to an m.sup.th installation position (step S1). The stylus offset is set to a position of an n.sup.th offset pattern (step S2). In steps S1 and S2, an operator may, for example, manually modify the mount position of the retroreflector 105 and the installation position of the tracking-type laser interferometer 20, or the mount position of the retroreflector 105 and the installation position of the tracking-type laser interferometer 20 may be modified automatically. For example, a motorized probe that is capable of modifying an orientation of the stylus using electric drive may be used as the measurement probe 101, and the relative position of the retroreflector 105 with respect to the Z spindle 102 may be displaced through control executed by the control device 30. In addition, the tracking-type laser interferometer 20 may be held by a movable arm that is capable of displacing with respect to the XYZ directions, and the installation position of the tracking-type laser interferometer 20 may be set to a predetermined position by controlling the movable arm through control executed by the control device 30. After this, the control device 30 conducts a measurement process (measurement step) of the measured values X.sub.CMM and the measured length values d for the plurality of measurement points X (step S3).

(17) FIG. 3 is a flow chart illustrating a process according to the present embodiment for measuring the measured values X.sub.CMM and the measured length values d for the plurality of measurement points X. In the measuring process of step S3, similar to a conventional spatial accuracy correction process, first presetting is performed in which the position of the rotation center M of the tracking-type laser interferometer 20 and an absolute distance from the rotation center M to the retroreflector 105 are defined (step S11). In step S11, as in the specification of German Patent No. 102007004934 and Umetsu et al. (2005), for example, a multilateration method is used to calculate the coordinates of the rotation center M and the absolute distance from the rotation center M to the retroreflector 105, and presetting is performed such that the measured length value d acquired by the tracking-type laser interferometer 20 equals the absolute distance from the rotation center M to the retroreflector 105.

(18) Next, the control device 30 controls the CMM 10, displaces the retroreflector 105 to the plurality of measurement points X, and conducts a measurement with the CMM 10 and a length measurement with the tracking-type laser interferometer 20 for each of the measurement points X. For these measurements, the control device 30 first sets a variable a that indicates the measurement line to an initial value (a=1) (step S12), then sets a variable A that indicates the measurement point X belonging to each measurement line to an initial value (A=1) (step S13). The variable a is an integer from 1 to a.sub.max, and “measurement line L.sub.a” indicates an a.sup.th measurement line L. Furthermore, the variable A is an integer from 1 to Ka, and a measurement point X.sub.A indicates a measurement point X that is measured A.sup.th on the measurement line. The number Ka of measurement points X included in the measurement line L may be a different value for each measurement line L, or may be the same value for each.

(19) Also, the measurement controller 31 controls the CMM 10 and displaces the retroreflector 105 to a measurement point X.sub.A on a measurement line L.sub.a (step S14). The measurement result acquirer 32 measures the measurement point X.sub.A on the measurement line L.sub.a with the CMM 10 and the tracking-type laser interferometer 20, and acquires the measured value X.sub.CMM measured by the CMM 10 and the measured length value d measured by the tracking-type laser interferometer 20, respectively (step S15). In step S15, the CMM 10 and the tracking-type laser interferometer 20 may be synchronized and the measured value X.sub.CMM and the measured length value d may be acquired simultaneously; the retroreflector 105 may also be stopped at a position corresponding to the measurement point X.sub.A and the measurement by the CMM 10 and the measurement by the tracking-type laser interferometer 20 may be carried out in order.

(20) After this, the measurement controller 31 determines whether the variable A equals Ka (step S16). Specifically, the measurement controller 31 determines whether measurement for all (for Ka) of the measurement points X belonging to the measurement line L.sub.a has ended. When the measurement controller 31 reaches a “no” determination in step S16, 1 is added to the variable A (step S17) and the process returns to step S14. That is, measurement points X at Ka points from A=1 to A=Ka belonging to the measurement line L.sub.a are measured in succession.

(21) Meanwhile, when the measurement controller 31 reaches a “yes” determination in step S16, the measurement controller 31 determines whether the variable a equals a.sub.max (step S18). When the measurement controller 31 reaches a “no” determination in step S18, 1 is added to the variable a (step S19) and the process returns to step S13. Accordingly, in the present embodiment, the measurement lines L.sub.a (from the measurement line L.sub.1 to the measurement line L.sub.amax) are measured in order, and in the measurement of each measurement line L.sub.a, a number Ka of measurement points X belonging to the measurement line L.sub.a are measured in order, from measurement point X.sub.1 to measurement point X.sub.Ka.

(22) Then, when the measurement controller 31 reaches a “yes” determination in step S18, and the measured values X.sub.CMM and measured length values d for all of the measurement points X in all of the measurement lines L have been measured, the measurement process for a case where the stylus offset is an n.sup.th offset pattern and the position of the rotation center M is an m.sup.th position is ended.

(23) After this, the control device 30 determines whether the variable n equals n.sub.max (step S4), and when the control device 30 reaches a “no” determination, 1 is added to the variable n (step S5) and the process returns to step S2. Also, when the control device 30 reaches a “yes” determination in step S4, a determination is made as to whether the variable m equals m.sub.max (step S6), and when a “no” determination is made, 1 is added to the variable m and the variable n is set to the initial value of 1 (step S7) and the process returns to step S1.

(24) Meanwhile, in step S6, when a “yes” determination is reached, the correction value calculator 33 uses the measured value X.sub.CMM and the measured length value d measured by the measuring process of step S3 and calculates the correction parameter Bα of the CMM 10 (step S8: parameter calculation step). In this example, in step S8, the correction value calculator 33 applies (adds) a first correction constant F.sub.da to the measured length value d for each measurement point X, and applies (adds) a second correction constant F.sub.Ma different from the first correction constant F.sub.da to the coordinates of the rotation center M to calculate the correction parameter Bα. In this example, the subscript “a” in the first correction constant F.sub.da and the second correction constant F.sub.Ma is the variable indicating the measurement line. In other words, in the present embodiment, the first correction constant F.sub.da and the second correction constant F.sub.Ma are respectively different constants for each measurement line. For example, with the measurement line L.sub.1, a first correction constant F.sub.d1 is applied to the measured length value d for each measurement point X, and a second correction constant F.sub.M1 is applied to the rotation center M. Meanwhile, with a measurement line L.sub.2, a first correction constant F.sub.d2 is applied to the measured length value d for each measurement point X, and a second correction constant F.sub.M2 is applied to the rotation center M.

(25) The correction value calculator 33 substitutes the first correction constant F.sub.da and the second correction constant F.sub.Ma (f.sub.xma, f.sub.yma, f.sub.zma) applied to each measurement line, the several thousand measured values X.sub.CMM (x.sub.CMM, y.sub.CMM, z.sub.CMM) and measured length values d measured by the measuring process of step S3, and the coordinates (x.sub.m, y.sub.m, z.sub.m) of the rotation center M measured in step S11 into Expression (1) as well as (3), which is given below, and simultaneous equations for several thousand Expressions (1) and (3) are generated, and the correction parameter Bα is calculated by solving the simultaneous equations using the least square method.

(26) $\begin{array}{cc}\left[\mathrm{Formula}2\right]& \\ \delta p\equiv {\left[\begin{array}{ccc}\delta x& \delta y& \delta z\end{array}\right]}^T=\mathrm{HB}\alpha & \left(1\right)\\ \sqrt{\begin{array}{c}{\left\{\left(x_{\mathrm{CMM}}+\delta x\right)-\left(x_m+f_{\mathrm{xma}}\right)\right\}}^2+{\left\{\left(y_{\mathrm{CMM}}+\delta y\right)-\left(y_m+f_{\mathrm{yma}}\right)\right\}}^2+\\ {\left\{\left(z_{\mathrm{CMM}}+\delta z\right)-\left(z_m+f_{\mathrm{zma}}\right)\right\}}^2\end{array}}=\left(d+F_{\mathrm{da}}\right)& \left(3\right)\end{array}$

(27) When Bα is a matrix of correction parameters for the CMM 10 expressed by a B-spline function, B is a matrix of basis functions of B-spline functions, and a is a matrix of coefficients for the basis functions. H is a matrix converting the correction parameter Bα to an error δp of the measured value X.sub.CMM, and is a known matrix configured from a mechanical structure and stylus offset information for the CMM 10 to be corrected. Also, the left and right sides of Expression (3) express, respectively, the measured value X.sub.CMM for the CMM 10 and the distance from the rotation center M to the retroreflector 105, which is expressed by the measured length value d of the tracking-type laser interferometer 20.

(28) The first correction constant F.sub.da and the second correction constant F.sub.Ma are both unknown quantities, and a different correction constant is applied each time the position of the rotation center M of the tracking-type laser interferometer 20 is changed, each time the stylus offset is changed, and also for each measurement line. These correction constants can be found, together with the correction parameter Bα, when solving the simultaneous equations of Expressions (1) and (3). At this time, the correction value calculator 33 also calculates an optimal solution for the first correction constant F.sub.da and the second correction constant F.sub.Ma, simultaneously with the correction parameter Bα. In other words, an amount of offset of the position of the rotation center M generated during measurement at the measurement points X on each measurement line is calculated simultaneously with an error incorporated into the measured length value d due to the offset.

Advantages of Present Embodiment

(29) In the present embodiment, for each measurement line L.sub.a, the correction value calculator 33 applies the first correction constant F.sub.da to the measured length value d, and applies the second correction constant F.sub.Ma to the coordinates of the rotation center M to calculate the correction parameter Bα.

(30) Accordingly, even when the position of the rotation center M of the tracking-type laser interferometer 20 becomes offset due to a temperature drift during measurement of the plurality of measurement points, and an error is incorporated into the measured length value d due to the offset, by correcting an amount of offset in the position of the rotation center M and the error included in the measured length value d for each measurement line L.sub.a, the incorporation of such errors can be inhibited and a highly accurate correction parameter can be calculated.

(31) Moreover, the correction value calculator 33 calculates the first correction constant F.sub.da and the second correction constant F.sub.Ma, simultaneously with calculating the correction parameter Bα. Accordingly, during the measurement of each measurement line, the timing at which offset of the rotation center M occurs and the amount of that offset, as well as the error incorporated into the measured length value d, can be determined.

(32) Modification

(33) Moreover, the present invention is not limited to the above-described embodiment, and includes modifications not deviating from the scope of the present invention. For example, in the embodiment described above, the CMM 10 is given as an example of a positioning mechanism, but the present invention is not limited to this. As noted above, any mechanism that positions a displacement body by displacing the displacement body to a predetermined set of spatial coordinates can be employed as the positioning mechanism. For example, the positioning mechanism may be a machine tool having a processing tool that cuts, polishes, or performs similar work on an object as the displacement body, where the machine tool displaces the processing tool to a predetermined coordinate position. The positioning mechanism may also be a transport robot having a gripping arm that grips an object as the displacement body, where the transport robot transports the gripped object to a predetermined position.

(34) In the embodiment described above, the plurality of measurement points X are divided into a plurality of measurement lines L.sub.a, and in each measurement line L.sub.a, the first correction constant F.sub.da applied to the measured length value d and the second correction constant F.sub.Ma applied to the rotation center M are defined as different constants for each measurement line L.sub.a. However, the present invention is not limited to this. For example, after the presetting in step S11, when correcting a change in position of only the rotation center M that has occurred in a period before measurement of each of the measurement points is begun, the first correction constants F.sub.da applied to each of the totality of measurement lines L.sub.a may be identical, and the second correction constants F.sub.Ma applied to the rotation center M may also be identical.

(35) In the embodiment described above, an example is given in which the number of measurement points X (number Ka of measurement points) belonging to the measurement line L.sub.a is a different value for each measurement line L.sub.a, but the number of measurement points X belonging to each measurement line L.sub.a may be an identical number Ka of measurement points.

(36) A method of defining the measurement points X belonging to the measurement line L.sub.a in the embodiment described above may be any method. For example, measurement points having a distance that is within a predetermined value from a preset reference measurement point may be included in a single measurement line L.sub.a. In other words, the measurement points X that are positioned near to each other may be included in the same measurement line L.sub.a. Also, when the plurality of measurement points are measured in succession, the measurement lines L.sub.a may be divided at the measurement points that can be measured within a predetermined amount of time. Specifically, the plurality of measurement points X that are measured within a predetermined first time t from the beginning of the measurement are the measurement points X belonging to the measurement line L.sub.1, and the measurement points X that are measured within a second time 2t from the first time t are the measurement points X belonging to the measurement line L.sub.2. Also, in such a case, time intervals for the measurement lines L.sub.a are not necessarily constant. For example, the measurement points X that are measured within a first time t.sub.1 from the beginning of the measurement may be designated as the measurement points X belonging to the measurement line L.sub.1, and the measurement points X that are measured from the first time t.sub.1 up to a second time t.sub.2 (t.sub.1≠t.sub.2−t.sub.1) may be designated as the measurement points X belonging to the measurement line L.sub.2.

(37) In the embodiment described above, the tracking-type laser interferometer 20 having the rotation center M as the reference point is given as an example of a laser interferometer, but the present invention may also employ a laser interferometer that does not have a tracking function. However, each time a measurement point X is displaced, the length measurement direction for measuring the distance with the laser interferometer must be modified. Accordingly, in such a case, preferably, a plurality of measurement points are defined on the length measurement direction of the laser interferometer (on a straight line), and once the retroreflector 105 has been displaced to each measurement point the measured value X.sub.CMM and the measured length value d are measured. In addition, the length measurement direction is preferably changed to a plurality of directions, and the plurality of measurement points X are preferably defined for each length measurement direction.

(38) In the embodiment described above, an example is given where the first correction constant F.sub.da is applied to the measured length value d and the second correction constant F.sub.Ma is applied to the rotation center M. However, a correction constant may also be applied to only one of the measured length value d and the rotation center M. For example, when a correction constant is applied to only the measured length value d, in Expression (3) given above, simultaneous equations may be created with f.sub.xma, f.sub.yma, and f.sub.zma set to 0 to find the correction parameter Bα.

(39) The present disclosure can be used for spatial accuracy correction of a positioning mechanism or machine, such as a coordinate measuring machine (CMM), machine tool, robot, or the like that positions a displacement body by displacing the displacement body to a predetermined coordinate position.

(40) It is noted that the foregoing examples have been provided merely for the purpose of explanation and are in no way to be construed as limiting of the present invention. While the present invention has been described with reference to exemplary embodiments, it is understood that the words which have been used herein are words of description and illustration, rather than words of limitation. Changes may be made, within the purview of the appended claims, as presently stated and as amended, without departing from the scope and spirit of the present invention in its aspects. Although the present invention has been described herein with reference to particular structures, materials and embodiments, the present invention is not intended to be limited to the particulars disclosed herein; rather, the present invention extends to all functionally equivalent structures, methods and uses, such as are within the scope of the appended claims.

(41) The present invention is not limited to the above described embodiments, and various variations and modifications may be possible without departing from the scope of the present invention.