JP2002512898A - Method for calibration of parallel manipulators - Google Patents

Abstract

(57) [Summary] The end of a variable-length rod (actuator 3) or a constant-length rod (8 ') is connected to a movable platform (2) via a joint (5). The rods (3, 8) are connected at their other ends to the platform (1) via joints (4). It is brought into various positions characterized by another number index j by the operation of the actuator (3, 3 ') characterized by the number index i. Parameters that partially and / or indirectly characterize the position and orientation of the mobile platform relative to the stationary platform (1) are measured. The actual joint point coordinates are calculated from a system of equations created according to the number and type of parameters to be measured. Therefore, instead of measuring all parameters that completely characterize the position and orientation of the mobile platform, parameters are measured which can be calculated with little technical effort and which allow the automation of the calibration process.

Description

DETAILED DESCRIPTION OF THE INVENTION

The invention relates to a parallel manipulator, in particular a hexapod machine or a linapod machine (Hexapod-oder Linapod-Maschine).
), A method for calibration.

[0002] A conventional construction type of machine tool has a feeder (carriage, Vorschuebe) which is positioned abfolgende at right angles to one another. These are arranged in a so-called opene kinematische Ketten. In the case of the open kinematic chain, during work material processing (Werkstueckbearbeitung), the first drive moves the second drive, the second drive moves the third drive, and the And then move on. Recently, in the case of this machine type, 1m /
It is disadvantageous that quick motion velocities (Eilgangsgeschwindigkeiten) greater than s and orbital accelerations (acceleration along the path, Bahnbeschleunigungen) greater than 1 g can only be achieved at the same time with high trajectory accuracy and only at considerable expense. It turned out. Therefore, modern blade materials (cutting materials, Schneidwerkstoffe)
Possibility of inadequate can only be used. Because of high-speed processing HS
This is because C (High Speed Cutting) is not possible or at least only limited. Against this background, the following machine tools have recently been developed. The machine tool no longer has a fixed right-angled arrangement of the machine axes and in the case of the machine tool a closed kinematic chain (geschlossene kinemati)
sche Ketten) principle was used. In this arrangement, the axes required for the realization of the movement are no longer placed on top of one another and are no longer carried together. Rather,
A movement (kinematics) is used that achieves the appropriate spatial movement of the platform with respect to a spatially fixed second platform, usually a machine table (machine stage). Well-known representatives of modern machine tools, such as Hexapod and Linapod, are described by Weck, M .; Giesler, M .; Pritschow, G.
By Wurst, K.-H. Schweizer Maschinenmarkt, 45/1997, pp. 28-35. Furthermore, hexapods are known from DE 296 07 680.

In the case of the well-known hexapods, the length of the six actuators (Aktoren), each of which is pivotally connected (by articulation) to the platform, is changed by computer control so that the movable platform is changed. It can be moved in six degrees of freedom with respect to the spatially fixed second platform of the machine table. In contrast, linapods have six fixed length (invariant length) rods. Their ends with joints (links, joints, joints, Gelenke) are each pivotally connected at one end to a movable platform and at the other end are also pivotally movable in a linear guide. is there. The latter are usually referred to herein as actuators for reasons of unified language usage. The actuator then linearly moves the position of the joint attached to the stationary platform. The high working accuracy of this machine is based on the relatively complex software of the computer. However, its advantages can only take effect in the case of high-precision calibration of the machine. For this purpose, the actual coordinates (including assembly and / or manufacturing errors) of the joint points on the platform and attached to the movable platform
Decision is appropriate. However, a direct measurement of the joint center coordinates is
This is only possible with relatively small dimensions of the machine. Because for that,
The corresponding measuring machine must be left at will. However, 30
With the actual size of the machine with a positioning range (Verfahrbereich) greater than 0 mm and more, this is no longer practically feasible.

The problem of calibration will be described in detail with reference to FIGS. In the drawings, FIG. 1 shows a schematic diagram of a known hexapod machine, FIG. 2 shows the coordinate system employed and the corresponding orientation of the vectors, and FIG. 3 shows a schematic diagram of the known linapod machine. FIG. 4 shows the coordinate system employed and the corresponding orientation of the vector. In FIG. 1, an immobile table is shown as a platform 1. Underlying at the upper coordinate system _{B = (x B, y B} , z B) is defined (FIG. 2). Movable platform 2 has platform coordinate system _{P = (x P, y P} , z P) a. The platforms 1, 2 are connected via six actuators 3 so as to be movable with respect to one another in six degrees of freedom, such that the length of the actuators 3 is variable. The actuator 3 is connected at one end to a stationary platform 1 via a joint 4 and at the other end to a movable platform 2 via a joint 5. For tight control of the platform 2, the actuator 3 for the position of the center points 6, 7 of the cardan joints or ball joints 4, 5 on both platforms 1, 2 and for a selectable reference position with the number index j = 0. All lengths l _i0 must be known as strictly as possible. However, in practice, this cannot be achieved even during precision manufacturing and assembly. For that reason, a reference position j =
0 is the starting point. Now, the positions of the joint center points 6, 7 in the fully assembled state of the machine and the length l _i0 of the actuator 3 are determined by taking into account all the factors affecting the coordinates and the length. Index i = 1, ...
The problem arises of determining the next 42 scalar quantities with the six actuators with, 6: the vector in the basic coordinate system B Three coordinates of each of the six joint center points 6 of the stationary platform 1 described by: a total of 18 scalar quantities; a vector in the platform coordinate system P Three coordinates of each of the six joint center points 7 of the movable platform 2 described by: a total of 18 scalar quantities; and the length l _i0 of the six actuators 3 in the reference position, a total of 6 scalar quantities .

FIG. 2 shows a distance vector describing the movement of the platform coordinate system P with respect to the basic coordinate system B. Is shown. Thereby, the length of the i-th actuator during the j-th positioning trial (Positionierversuch) From the Pythagorean theorem to determine, we can easily understand the following (Fig. 2): Where: R _j is a platform fixed platform coordinate system P = (x _P , y _P , z _P ) assigned to the movable platform 2 for each position j
, The space-fixed basic coordinate system B assigned to the other platform 1
A 3 × 3 rotation matrix (Weck, M., et al.) That describes the rotation relative to (x _B , y _B , z _B ) and whose elements (Eintraege) consist of sine and cosine functions of three rotation angles. , Werkzeugmaschinen-Fertigungssysteme, Band 3.2 Automa
tisierung und Steuerungstechnik 2, 4th edition, Düsseldorf, VDI Verlag,
1995, 334) and a vector for each of the actuators 3 with index i Describes the joint point coordinates of the movable platform 2 to be calculated in the platform coordinate system P, Describes the distance between the origin of the basic coordinate system B and the origin of the platform coordinate system P in the basic coordinate system B. A vector for each of the actuators 3 Describes the joint point coordinates to be calculated of the spatially fixed platform 1 in the basic coordinate system B, l _i0 is the length of the actuator 3 at the reference position, and Δl _ij is A given or measured actuator length change, where the rotation matrix R _j and the vector The joint center point 5 of the platform 2 moved by Is further converted to a stationary (position fixed) coordinate system B.

The equation (*) links the actuator length, the position and orientation of the movable platform 2 and the positions of the joint points 6, 7 together. In principle, each defined actuator length is set in the control and three rotations (twist) and distance vectors of the platform It is possible to perform a positioning trial in which is measured directly. The elements of the rotation matrix R _j can be calculated from the three angles of rotation of the platform.
If the hexapod has a corresponding measuring system, the starting point can be that the actual actuator length change Δl _ij corresponds to the desired quantity of control. This means that from each positioning trial j Means that it is known. Is not known.

From equation (*), each actuator (
One scalar equation can be established for i = 1,..., 6). That is, a total of six scalar equations are provided for each positioning trial. Thus, with seven independent trials (positionings), the required 42 independent nonlinear equations for the 42 unknowns can be established. Each of these 42 equations is 7
Can be grouped into a system of six linearly independent equations with two unknowns. 7 unknowns for each actuator i There is one system of equations with seven nonlinear equations for determining: Another formulation of the calibration problem can be found in Merlet J.-P., Les robots paralleles, Hermes, Paris, 1997, p. 95.

[0008] What has been described is also fully effective in a method of calibrating a linapod machine.
The application of the Pythagorean theorem to determine the fixed length of the rod 8 '(FIGS. 3 and 4) has the following mathematical relationship: Lead. that time, Has the same meaning as the corresponding quantity in equation (*) for the painted platform or actuator (FIGS. 3, 4): Describes the spatially fixed direction vector of the linear movement of the joint 4 'attached to the immobile platform 1' by the attached i-th actuator 3 ',
A vector for each of the actuators 3 ' Denote the joint point coordinates attached to the spatially fixed platform 1 'to be calculated with respect to the starting position in the basic coordinate system B, the vector for each of the actuators 3' May be calculated with respect to the reference position in basic coordinate system B, 'describes the joint point coordinates that are attached to, · s _i is i th rod 8 is attached to the actuator' platform 1 space fixed Indicates a fixed length.

FIG. 3 shows a schematic diagram of a linapod machine. Here, the stationary table is shown as platform 1 '. Moreover basic coordinate system _{B = (x B, y B} , z B)
Are defined (FIG. 4). Movable platform 2 'is the platform coordinate system _{P = (x P, y P} , z P) having a. The platforms 1 ', 2' are connected by means of a joint 4 'attached to the stationary platform 1' using an actuator 3 '.
Are moved linearly with respect to each other with six degrees of freedom using six actuators 3 ′. A rod 8 'of fixed length is supported at these joints 4' and by another joint located on the movable platform 2 '. Due to the tight control of the platform 2 ', as in the case of the hexapod, the position of the center points 6', 7 'of the cardan joints or ball joints 4', 5 'on both platforms 1', 2 ', and Actuator 3 'for selectable reference position with number index j = 0
The _total length l _i0 of the movement of the joint 4 ′ (corresponding directly to the length of the respective actuator 3 ′) and the fixed length of the rod 8 ′ attached to the actuator 3 ′ Must be strictly known. That is, in this case, the problem arises of defining the following 60 scalar quantities: each of the six basic joint center points at the starting position (origin position) with respect to the stationary (fixed) table coordinate system B; Three coordinates , A total of 18 scalar quantities. Three respective coordinates of the base joint center point at the reference position with respect to the stationary table coordinate system B , A total of 18 scalar quantities. The starting position and the reference position jointly uniquely determine the position and orientation of the guide.・ Three coordinates of each of the six platform joint center points with respect to the platform coordinate system P , A total of 18 scalar quantities. Six rod lengths s _i , a total of six scalar quantities.

[0010] Thus, with 10 independent trials (positioning), the required 60 independent nonlinear equations for the 60 unknowns can be established. These 60
Can be grouped into a system of six linearly independent equations, each with 10 unknowns. For each actuator i, 10 There is a system of equations with ten nonlinear equations to determine:

[0011] At present, no particular method is known for calibrating the linapod. Because the machine is still in the prototype stage. With the method described above for hexapods, a calibration process for linapods could in principle also be performed. In the case of a hexapod, unavoidable assembly errors directly determine the displacement of the joint points. In contrast, in the case of a linapod, the movement of the (moved) joint point of the table is indirectly determined by the orientation error and the position error of the guide.

The difficulty with the described measurement method lies in the exact determination and very great effort of the position and orientation of the platform. In particular, the measurement of the orientation of a movable platform is technically difficult.

The present invention relates to a parallel manipulator (master / slave operating device, Parallel
It is an object of the invention to configure a method of the kind mentioned at the outset so that the elmanipulator can be calibrated precisely and automatably with little effort.

This object is achieved, according to the invention, in the case of a method of the type mentioned at the beginning, by an arrangement according to the features of claim 1.

[0015] The basic idea of the method is that during the positioning trial, instead of measuring all the parameters that completely characterize the position and orientation of the mobile platform, it is calculated with little technical effort. The parameters that are to be obtained and that allow the automation of the calibration process are to be measured. Because each trial computes less information than the method described above,
Indeed, the result is that the number of tests has to be increased. The disadvantage of having to analyze many measuring points is justified by the better automation possibilities in this method.

Measuring only the distance length as stated in claim 2 is much simpler and more precise in terms of measurement technology. Thus, the following attempt is made such that only the distance between the center point of the movable platform 2 (eg the tool receiver) and the center point of the stationary platform 1 (FIG. 1) is measured during each positioning attempt. Derived from This distance is the vector shown in FIG. Is equivalent to the length of On the other hand, the measuring method also derives from a system of equations (*) describing the relationship between the actuator length and the position of the platform in space.
Distance vector Instead of measuring the rotation angles for R _j and R _j , these six scalar values (three coordinates and three angles) are considered as six additional unknowns per positioning trial. Thus, in one trial, from equation (*), 42 + 6 =
Six scalar equations with 48 unknowns are given.

For each positioning trial in the workspace, the length d _j of the vector from the base coordinate system to the platform coordinate system is determined. The length of the vector gives the distance between the reference point on the machine table and the reference point on the platform (eg, tool receiver) and can be calculated by length measurement. Thereby, an additional equation per positioning trial j: Is given. Thus, the performance of one positioning trial is based on (*) six equations and measuring (based on six actuator length changes Δl _ij ) From equation (**). The first trial consists of a total of 48 unknowns ( as well as 3 coordinates multiplied by 6 actuators for each, 6 actuator lengths l _{i0 at} the starting position, 3 coordinates , And three angles in R _j ). Each different trial yields another seven equations. However And only six other unknowns for R _j . The other values are constant regardless of the trial. Therefore, by performing the position measurement 42 times, 29
A system of equations with four equations and 294 unknowns is provided. It can be solved for the determination of joint coordinates.

The above-described measures applied for calibrating a linapod machine have little difference.
Not shown. In this case, the distance vectorAnd R_jInstead of measuring the rotation angle for the calculation of
One scalar value (3 coordinates and 3 angles) is 6 per positioning trial
Are considered as two additional unknowns. Therefore, in one trial, the equation (*
') Gives six scalar equations with 60 + 6 = 66 unknowns. Work
At the time of each positioning trial in the work space, the platform
Vector length d in form coordinate system_jIs determined. As a result,
An additional equation (**) is provided for each training trial j. In all, the first trial is
66 unknowns (and And3 coordinates multiplied by 6 actuators each, 6 rod lengths s
_i, Three coordinatesAnd R_jYields seven equations with three angles). Each different
Trial yields another seven equations. But they have six other unknowns
Only. Therefore, by performing the position measurement 60 times, the joint coordinate
A system of equations with 420 equations and 420 unknowns that can be solved for the decision
Is given.

The system of equations described above is a quadratic homogeneity equation (Gleichungssyste
me). Such a system of equations can be solved iteratively. A possible solution is an optimization method (Optimierungsverfahren) that minimizes the quadratsum of the error. There is a special least squares method for this. However, general optimization methods can also be selected. For this, the Newton-Gauss method is a promising clue.

Next, the calibration method according to the present invention will be described in detail with reference to FIGS. 5 and 6. In the drawings, FIG. 5 shows a linear scale for performing a distance measurement, and FIG. 6 schematically shows a measurement structure for the determination of the distance between a point assigned to a stationary platform and a movable platform. Shown in

A specially constructed linear scale appears to be a promising clue for the determination of the position of the tool center point. Such a linear scale consists of a two-stage or multi-stage telescoping bein 9. At the ends of the telescopic legs, precision balls (Praezisionskugeln) 10, 11 are attached. The length d of the measuring system can be varied within a predetermined range. To determine the length,
A laser interferometer 12 is incorporated in the telescopic leg 9. As can be seen from FIG.
The stationary platform 1, the hexapod machine table and the movable platform 2 comprise flat plates 13, 14, respectively. Each of these plates has a sphere receptacle for precision spheres 10,11. If the receiving parts of the plates 13, 14 of the linear scale 9 are located as such reference points at the respective origins of the platform coordinate system or of the base coordinate system, the measured length is the distance vector Is equivalent to the size of Since only one distance measurement is required each time, the linear scale 9 should be recorded in each test. Thereby, different spatial positions are aimed at in an automated manner, and the measurement of the distance for each spatial position can be performed automatically.

Further measures can be applied to calculate the above-mentioned 42 unknowns in the case of the hexapod calibration method or 60 unknowns in the case of the linapod calibration method. A compromise is then made between the labor of the measurement (automatability, the number and cost of the required measuring means) and the labor of solving the system of equations.

On the other hand, the actuator length change Δl _ij may additionally be measured, for example, by means of a linear scale present in the machine. In the case of the method described above, the value Δ
The starting point is that l _ij corresponds to the target amount of control. If the constant deviation between the target length and the actual length of the actuator cannot be neglected, the measurement described above increases the accuracy of the measuring method.

In addition, one or more equations may be constructed instead of or in addition to equation (**), such as: a platform 2 movable in at least one spatial coordinate Describes the position of at least one of the optional but point fixedly held during the calibration process, and / or the angle of at least one actuator 3 with respect to at least one platform 1,2 Change, or correspondingly, the angular change of at least one rod 8 'with respect to at least one platform 1', 2 'and / or at least one of the joints 4, 5 to 4', 5 ' It describes the angle of rotation of the joint and a corresponding amount is measured during the positioning trial. The additional information calculated in such a manner makes it possible to reduce the number of positioning trials and to make it easier to solve the corresponding system of equations.

Each quantity may be calculated before the assembly of the hexapod machine or linapod machine on the coordinate measuring machine. For example, the coordinates of the platform joint And / or the actuator length l _i0 can be measured. This further reduces the number of unknowns, thereby reducing the number of essential positioning trials.

In this way, the invention makes it possible to reduce the labor of the calibration process and to automate it.

[Brief description of the drawings]

FIG. 1 is a schematic diagram of a known hexapod machine.

FIG. 2 shows the adopted coordinate system and the corresponding orientation of the vector.

FIG. 3 is a schematic diagram of a known linapod machine.

FIG. 4 shows the adopted coordinate system and the corresponding orientation of the vector.

FIG. 5 shows a linear scale for performing a distance measurement.

FIG. 6 schematically shows a measurement structure for the determination of the distance between the points assigned to the stationary and mobile platforms.

[Procedural Amendment] Submission of translation of Article 34 Amendment of the Patent Cooperation Treaty

[Submission date] April 18, 2000 (2000.4.18)

[Procedure amendment 1]

[Document name to be amended] Statement

[Correction target item name] Claims

[Correction method] Change

[Correction contents]

[Claims]

──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Mailan Andreas, Germany Day 52072 Aachen Lütcherstrasse 116 (72) Inventor Damar Michael, Germany Day 52074 Aachen Kronenberg 19F term (reference) 3C007 AS12 BS24 LT17 LV19 MT04

Claims (5)

[Claims] 1. A variable length rod (actuator 3) or correspondingly constant length rod (8 ') is connected to a movable platform (2; 2') by a joint (5; 5 ') at one end. And they are platform (2;
2 ′) is positioned in space with respect to a machine-fixed immobile platform (1; 1 ′) using a computer-controlled actuator (3; 3 ′), and at the other end the actuator (3) is Joints respectively supported by a joint (4) attached to a stationary platform (1) or correspondingly a rod (8 ') attached to the platform (1') and moved by an actuator (3 '). The method for the calibration of parallel manipulators, in particular hexapods or linapods, supported by (4 '), is mainly based on the fact that the actual coordinates of the joint center, including assembly and / or manufacturing errors, are based on the platform ( 2; 2 ') from the quantities characterizing the actual position and orientation of the Cartesian coordinate system In a method essentially consisting of being issued, it comprises the following method steps: a) by actuation of an actuator (3; 3 ') characterized by a number index i, to a different position characterized by a number index j Transferring the mobile platform (2; 2 '), where j is determined by the number and type of parameters to be measured, b) relative to the immobile platform (1; 1') Measuring parameters that partially characterize the position and orientation of the mobile platform (2; 2 ') and / or c) the mobile platform (2; relative to the stationary platform (1; 1'). 2 ') The parameters that indirectly characterize the position and orientation D) calculating the actual joint point coordinates (coordinates of the center of the joint (4,5; 4 ', 5') from a system of equations formed according to the number and type of parameters to be measured A method comprising the step of: 2. In the measurement, the distance between the points assigned to the respective movable or space-fixed platforms (1, 2; 1 ', 2') is determined, these points being the corresponding calibration points. The calibration method according to claim 1, characterized in that the calibration method is held stationary with respect to the corresponding platform during the process. 3. In the measurement, the position error of at least one point of the movable platform (2; 2 ′), which is, however, fixedly maintained during the calibration process, is at least in one spatial coordinate. The calibration method according to claim 1, wherein the calibration method is determined. 4. At least one platform (1, 2) during the measurement
The angle change of at least one actuator (3) with respect to or at least one rod (8 ') with respect to at least one platform (1', 2 ') is measured, And / or joints (4, 5
4 ', 5'), wherein the rotation angle of at least one of the joints is measured. 5. The coordinate of a joint (4, 5; 4 ′, 5 ′) attached to a platform (1, 2; 1 ′, 2 ′) is directly measured in part. Item 5. The calibration method according to any one of Items 1 to 4.