DE19818635C2 - Procedure for calibrating a parallel manipulator - Google Patents

Description

The invention relates to a method for calibrating a parallel manipulators, especially a Hexapod or Linapod Ma machine, according to the preamble of claim 1.

Conventional designs of machine tools have other successive feeds at right angles to each other on. These are in so-called open kinematic chains ordered, in which a first drive a second drive, the a third drive and so on with the workpiece processing must move. As a disadvantage with this type of machine It has recently emerged that rapid traverse speeds of more than 1 m / s and path accelerations of more than 1 g with high trajectory accuracy only with a significant increase wall are accessible. Thus the possibilities become more modern Cutting materials used inadequately because of a high Speed processing HSC (High Speed Cutting) from the factory pieces or at least only to a limited extent. Before this Background, machine tools have been developed lately, which is not a rigid right-angled arrangement of the machine axes have more, but in those of the principle of closed kinematic chains were used. At this Build the arrangement needed to realize the movement Axes no longer on each other and no longer carry each other opposite. Rather, kinematics are used that have a ge suitable spatial movement of a platform over a fixed one  second platform, usually the machine table. Well-known representatives of the new machine tools, such as the Hexapod and Linapod are from Weck, M .; Giesler, M .; Prit schow, G .; Wurst, K.-H. in "New machine kinematics for the High-speed machining ", Swiss machine market, Vol. 45/1997, pp. 28-35. A hexapod is on known from DE 296 07 680 U1.

In the known Hexapod, a movable platform can be used a fixed second platform of the machine table in six Degrees of freedom are moved by length six each articulated to the platforms of actuators connected to the platforms controls is changed. The Linapod, on the other hand, has six bars constant length, the hinged ends of each because articulated at one end on the movable platform and others renends, again articulated, movable in a linear guide is. The latter is usually standardized here for reasons of th linguistic usage are also referred to as an actuator, wel then assigned the position of the immobile platform neten joint moves linearly relative to this. The high ar The accuracy of these machines is based on a comparative complex software of the computer, but only with one high-precision calibration of the machines, their advantages for tra can come. This is the determination of the actual Coordinates containing assembly and / or manufacturing errors, the rack-side and that assigned to the movable platform Articulation points useful. The direct measurement of Koordina However, the joint centers are only of relatively small dimensions Machine possible because a corresponding measuring machine for Must be available. For real sizes of machines with egg However, this is a travel range of more than 300 mm and more practically no longer feasible.  

It is also known (DE 196 34 575 A1) that a tool and / or a workpiece holder via rods with drive units is flexibly connected. We can differ between two reference points at least align an unloaded measuring arm freely. Its location is in a reference space. As soon as the position of the tool and / or workpiece holder and the orientation of this holder bearing rods deviate from a predetermined target position, leads this leads to a change of position and position of the unloaded Messar mes. Its location and orientation is recorded and evaluated, whereby the deviating position of the tool and / or workpiece holder can be recorded and corrected if necessary.  

The problem of calibration is explained in more detail with reference to FIGS. 1 to 4. In the drawing shows

Fig. 1 is a schematic representation of a known hexapod machine,

Fig. 2, the corresponding orientation of the inserted coordinate systems and vectors

Fig. 3 is a schematic representation of a known Linapod- machine,

Fig. 4 shows the associated orientation of the introduced coordinate systems and vectors.

In Fig. 1, an immovable table is indicated as a platform 1 on which the basic coordinate system B = (x _B , y _B , z _B ) is defined ( Fig. 2). A movable platform 2 has the platform coordinate system P = (x _p , y _p , z _p ). The platforms 1, 2 are six Akto ren 3 against each other in six degrees of freedom movable-jointed by the length of the actuators is changed 3, wherein the Akto ren 3 at one end through hinges 4 on the fixed platform 1 and at the other end via joints 5 to the movable Platform 2 are bound to. For an exact control of the platform 2 , the position of the center points 6 , 7 of the gimbals or ball joints 4 , 5 , on both platforms 1 , 2 and all lengths I _{i0 of} the actuators 3 for a selectable reference position with the count index j = 0 be known as precisely as possible. In fact, this is not achievable even with highly precise manufacturing and assembly. One therefore starts from a reference position j = 0, which can in principle be set as desired. In order to determine the position of the articulation centers 6 , 7 and the lengths I _{i0 of} the actuators 3 in the fully assembled state of the machine, taking into account all coordinates and lengths of the flowing factors, the problem arises with six actuators with the counting index i = 1, ... to determine 6 following 42 scalar sizes:

• - The 3 coordinates of the six joint centers 6 of the immobile platform 1 described by the vector ^B _i in the base coordinate system ^B , together 18 scalar quantities;
• - The 3 coordinates of the six joint center points 7 of the movable platform 2 described by the vector ^P _i in the platform coordinate system P, a total of 18 scalar variables and
• - The lengths I _{i0 of} the six actuators 3 in the reference position, together six scalar quantities.

Next, FIG. 2 is a distance vector ^B _j, which describes the displacement of the platform coordinate system P relative to the Basiskoordi natensystem B. The Pythagorean theorem for determining the length of the i-th actuator (I _i0 + ΔI _ij ) in the j-th positioning attempt is therefore easy to obtain ( FIG. 2):

∥R _j . ^P _i + ^B _j - ^B _i ∥ - (I _i0 + ΔI _ij ) = 0 (*)

With

• - R _{j represents} the 3 × 3 rotation matrix (see Weck, M., Werkzeugmaschi NEN manufacturing systems, volume 3.2 Automation and control technology, 2nd edition, Düsseldorf, VDI Verlag, 1995, p. 334), which for each position j describes the rotation of a platform-fixed platform coordinate system P = (x _p , y _p , z _p ) assigned to a movable platform 2 relative to one of the other platform 1 assigned basic coordinate system B = (x _B , y _B , z _B ) and whose entries consist of sine and cosine functions of the three rotation angles,
• the vector ^P _i for each of the actuators 3 with index i describes the hinge point coordinates of the movable platform 2 to be determined in the platform coordinate system P,
• the vector ^B _{j describes} the distance between the origin of the base coordinate system B and the origin of the platform coordinate system P in the base coordinate system B,
• the vector ^B _i for each of the actuators 3 describes the pivot point coordinates of the fixed platform 1 to be determined in the basic coordinate system B,
• I _{i0 are} the length of the actuators 3 in a reference position,
• - ΔI _{ij are} the actuator length changes specified or measured during the positioning tests,

being the center of the joints

5

the one with the rotation matrix R _j

and the vector ^P _i

moving platform

2nd

according to the equation

∥R _j . ^P _i + ^B _ji ∥ = ^B _i

were transferred to the fixed coordinate system B.

The equation (*) links actuator lengths, position and orientation of the movable platform 2 and position of the articulation points 6 , 7 with one another. In principle, it is possible to carry out positioning tests in which defined actuator lengths are specified in the control and the distance vector ^B _j and the three rotations of the platform are measured directly. The entries in the rotation matrix R _j can be calculated from the angles of the three rotations of the platform. If the hexapod has a corresponding measuring system, it can be assumed that the actual actuator length changes ΔI _ij correspond to the target values of the control. This means that the quantities ΔI _ij , ^B _j , R _{j are} known from each positioning experiment _j . ^B _i , ^P _i , I _{i0 are unknown} .

A scalar equation can be set up for each actuator (i = 1, ..., 6) from the equation (*) for each positioning attempt. A total of 6 scalar equations are obtained per positioning attempt. The required 42 independent nonlinear equations for the 42 unknowns can be established by 7 independent experiments (positioning). These 42 equations can be grouped into 6 linearly independent systems of equations, each with 7 unknowns. For each actuator i there is a system of equations with 7 nonlinear equations to determine the 7 unknowns I _i0 , ^P _i and ^P _i :

Other formulations of the calibration problem can be found in the book Merlet J.-P., Les robots paralleles, Hermes, Paris, 1997, p. 95 Find.

What has been said so far also largely applies to the calibration process of a Linapod machine. The use of the Pythagoras Theo rem for determining the fixed length of bars 8 '( Fig. 3 and Fig. 4) leads to the following mathematical relationship:

∥R _j . ^P _i + ^B _j - ^B _i - _i (I _i0 + ΔI _ij ) ∥ - s _i = 0 (* '),

in which

• - R _j , ^P _i , ^B _j , I _i0 , ΔI _ij , have the same meaning as the corresponding quantities in equation (*) for the deleted platforms or actuators ( FIGS. 3, 4),
• - the vector
  describes the spatially fixed direction vector of the linear displacement of a joint 4 'assigned to the immobile platform 1 ' by the associated i-th actuator 3 ',
• the vector ^B _i for each of the actuators 3 'describes the hinge point coordinates to be determined and assigned to the fixed platform 1 ' in the original position in the base coordinate system B,
  the vector ^B _i0 for each of the actuators 3 'describes the joint point coordinates to be determined and assigned to the fixed platform 1 ' in the reference position in the base coordinate system B and
• - s _i denotes the fixed length of the rod 8 'assigned to the i-th actuator.

Fig. 3 shows a schematic representation of a Linapod machine. An immovable table is indicated as platform 1 'on which the basic coordinate system B = (x _B , y _B , z _B ) is defined ( FIG. 4). A movable platform 2 'has the platform coordinate system P = (x _p , y _p , z _p ). The platforms 1 ', 2 ' are movable by means of six actuators 3 'against each other in six degrees of freedom, by means of the actuators 3 ', the joints 4 'assigned to the immobile platform 1 ' are linearly displaced. The rods 8 'of constant length are supported in these joints 4 ' and via further joints arranged on the movable platform 2 '. For exact control of the platform 2 ', as with the Hexapod, the position of the center points 6 ', 7 'of the gimbal or ball joints 4 ', 5 'must be at the platforms 1 ', 2 'and all lengths I _{i0 of} the displacement the joints 4 'by the actuators 3 ', here the lengths of the respective actuator 3 'corresponding directly, for a selectable reference position with the counting index j = 0 and the fixed length of the actuators 3 ' associated rods 8 'to be known as precisely as possible. In this case, the problem arises of determining the following 60 scalar quantities:

• - The coordinates of each 3 6 base joint center points ^B _i in the original position relative to the stationary Tischkoordina tensystem B, together 18 scalar quantities.
• - The 3 coordinates of the base _{joint center points} ^B _i0 in the reference position, based on the fixed table coordinate system B, together 18 scalar sizes. The origin and reference position together clearly determine the position and orientation of the tours.
• - The 3 coordinates of the 6 platform joint center points ^P _i , based on the platform coordinate system P, together 18 scalar quantities.
• - The length of the 6 bars s _i , together 6 scalar sizes.

The required 60 independent nonlinear equations for the 60 unknowns can thus be established through 10 independent experiments (positioning). These 60 equations can be grouped into 6 linearly independent systems of equations, each with 10 Un known ones. For each actuator i there is an equation system with 10 nonlinear equations for determining the 10 ^P _i , ^B _i , ^B _i0 and s _i :

There is currently no special procedure for measuring Linapo known because these machines are still in the prototype stage are located. Using the procedure for Hexapo listed above In principle, the measuring process for linapods could also be done carry out. With the Hexapod determine the inevitable Monta error the deviations of the articulation points immediately. On the other hand with the Linapod the displacements of the (moving) joint points of the table indirectly due to orientation and position errors of the guides.

The difficulty of the measurement method described lies in the exact determination of the position and orientation of the platform and in the enormous effort. Especially the measurement of the Ori The movable platform is difficult to measure.

The invention has for its object the generic Train the process so that the parallel manipulator is precise and can be automated and calibrated with little effort.

This object is fiction, in the generic method according to ge with the characterizing features of claim 1 solves.

The basic idea of the process is that the positioning try instead of measuring all the parameters that determine the location and Orientation of the moving platform completely ren, parameters are measured, which are measured only with low can be determined according to the effort and an automation Allow calibration procedure. Because with every attempt less information than in the procedure described above However, this means that the number of expe riments must be increased. The disadvantage of analyzing more measuring points With this method, having to settle is made easier by the better Justifiability justified.

It is technically much easier and more precise to measure only stand lengths as specified in claim 2. The fol lowing approach therefore assumes that for each Positionierver only the distance between the centers of the movable platform 2 (z. B. the tool holder) and the immobile platform 1 ( Fig. 1) is measured. This distance corresponds to the length of the vector ^B _j from FIG. 2. The measuring method is again based on the system of equations (*), which describes the relationship between actuator lengths and the position of the platform in space. Instead of measuring the distance vector ^B _j and the rotation angles for R _j , these 6 scalar values (3 coordinates and 3 angles) are considered as 6 additional unknowns per positioning attempt. In an experiment, one obtains six scalar equations with 42 + 6 = 48 unknowns from equation (*).

For each positioning attempt in the work area, the length d _{j of} the vector is determined from the base to the platform coordinate system. The length of the vector indicates the distance between the reference point on the machine table and the platform (e.g. the tool holder) and can be determined by measuring the length. This gives an additional equation for each positioning attempt j:

∥ ^B _j ∥ = d _j (**)

Carrying out a positioning test thus yields 6 equations from (*) (based on the 6 actuator length changes ΔI _ij ) and equation (**) from the measurement ∥ ^B _j ∥. In total, the first experiment provides 7 equations with 48 unknowns (3 coordinates by 6 actuators for ^P _i and ^B _i , 6 actuator lengths in the starting position I _i0 3 coordinates ^B _j and three angles in R _j ). Each further experiment gives another 7 equations, but only 6 further unknowns in ^B _j and R _j , since the other values are constant regardless of the experiments. With the implementation of 42 position measurements, an equation system with 294 equations and 294 unknowns is available, which can be solved to determine the joint coordinates.

The described procedure, used to calibrate a Linapod machine, shows hardly any differences. In this case too, instead of measuring the distance vector ^B _j and the rotation angles for the calculation of R _j , these 6 scalar values (3 coordinates and 3 angles) are considered as 6 additional unknowns per positioning attempt. In an experiment, one obtains six scalar equations with 60 + 6 = 66 unknowns from the equation (* '). For each positioning attempt in the work area, the length d _{j of} the vector is determined from the base to the platform coordinate system. This gives an additional equation (**) for each positioning attempt j. In total, the first experiment yields 7 equations with 66 unknowns (3 coordinates each with 6 actuators for ^P _i and ^B _i and ^B _i0 , 6 rod lengths s _i , 3 coordinates ^B _j and three angles in R _j ). Each further attempt gives 7 more equations, but only 6 more unknowns. With the implementation of 60 position measurements, a system of equations with 420 equations and 420 unknowns is available that can be solved to determine the joint coordinates.

The system of equations described above is about quadratic homogeneous systems of equations. Such glide systems can be solved iteratively. Possible solutions are optimization methods that cover the sum of squares of the Minimize mistakes. There are special least square Procedures, but also general optimization procedures to be selected. The Newton-Gauss method is one of them promising approach.

The calibration method according to the invention is further explained with reference to FIGS. 5 and 6. In the drawing shows

Figure 5 measurements. A linear scale for performing Abstandsmes,

Fig. 6 shows schematically a measurement setup for determining the distance of the points assigned between the fixed and movable platform.

Specially designed linear scales appear to be a promising approach for determining the position of the tool center point. Such a linear scale consists of a two- or multi-stage telescopic leg 9 , at the ends of which precision balls 10 , 11 are attached. The length d of the measuring system can be varied within a certain range. For length determination, a laser interferometer 12 is built into the telescopic leg 9 . As can be seen from Fig. 6, the stationary platform 1 , the machine table of a hexapod and the movable plattform 2 are each provided with a flat plate 13 , 14 , each of which contains a ball holder for the precision balls 10 , 11 . If the recordings of the plates 13 , 14 of the linear scale 9 lie as such reference points in the respective origin of the platform or base coordinate system, the measured length corresponds to the amount of the distance vector ^B _j . Since only one distance measurement is required in each case, the linear scale 9 can remain in the recording from experiment to experiment. The different room positions can thus be approached automatically and the measurement of the distance for each room position can be carried out automatically.

To the 42 unknowns described above in the Hexapod or corresponding to 60 to be determined in the linapodeinmeßverfahren other approaches are applicable. Here, between the measuring effort (automatability, number and costs of the required termed measuring equipment) and the solution effort of the equation system compromised.  

On the one hand, the actuator length changes .DELTA.I _ij can also be measured, for example by linear scales present in the machine. In the method described above, it is assumed that the values ΔI _ij correspond to the setpoints of the control. If the remaining deviation between the target and actual length of the actuators cannot be neglected, the measurement mentioned increases the accuracy of the measuring method.

Furthermore, instead of or in addition to equation (**), the equation (s) can be drawn up:

• - Which describe the position of at least any point of the movable platform 2 or 2 ', which is recorded during the calibration process, in at least one spatial coordinate
• and / or the change in angle of at least one actuator 3 with respect to at least one platform 1 , 2 or correspondingly at least one rod 8 'with respect to at least one platform 1 ', 2 'and / or the angle of rotation of at least one of the joints 4 , 5 or 4 ' and 5 '

and corresponding sizes measured during the positioning tests become. The additional ones determined in such a procedure Information allows the number of positioning attempts to be read and the solution of the corresponding system of equations facilitate.

Individual sizes can also be determined on a coordinate measuring machine before assembly of the hexapod or linapod machine, e.g. For example, the coordinates of the platform joints ^P _i and / or the actuator length I _i0 can be measured. This further reduces the number of unknowns and thereby the number of necessary positioning attempts.

In this way, the invention allows the effort of calibration process and automate it.

Reference list

1

,

1

'' immobile platform

2nd

,

2nd

'' movable platform

3rd

,

3rd

'' Actuators

4th

,

4th

'Joints

1

5

,

5

'Joints

2nd

6

,

6

'' Center of the joint

1

7

,

7

'' Center of the joint

2nd

8th

'' Rod of constant length

9

Linear scale

10th

end ball

9

11

end ball

9

12th

Laser interferometer

13

Plate on

1

14

Plate on

2nd

Claims (5)

1. A method for calibrating a parallel manipulator, in particular a hexapod or linapod, in which rods of variable length (actuators 3 ) or corresponding rods ( 8 ') of constant length at one end by joints ( 5 ; 5. ) On a movable platform ( 2 ; 2 ') ') are connected, which position the platform ( 2 ; 2 ') in space above an immovable, machine-fixed platform ( 1 ; 1 ') by means of computer-controlled actuators ( 3 ; 3 '), where the actuators ( 3 ) are in each other support an immovable platform ( 1 ) associated joints ( 4 ) or correspondingly support the rods ( 8 ') in the joints ( 4 ') assigned to the platform ( 1 '), which are moved with the actuators ( 3 '), wherein the actual coordinates of the joint centers containing the assembly and / or manufacturing errors are calculated from the variables characterizing the actual Cartesian position and orientation of the platform ( 2 ; 2 '), characterized in that that it consists of the following process steps:

• a) Moving the movable platform ( 2 ; 2 ') by actuating the actuators identified by a counting index i ( 3 ; 3 ') into different positions characterized by a counting index j, j being the number and type of parameters to be measured is determined
• b) measurement of parameters that partially characterize the position and orientation of the movable platform ( 2 ; 2 ') relative to the immobile platform ( 1 ; 1 ') and / or
• c) measuring parameters which indirectly characterize the position and orientation of the movable platform ( 2 ; 2 ') relative to the immobile platform ( 1 ; 1 '),
• d) Calculation of the actual joint point coordinates (coordinates of the centers of the joints ( 4 , 5 ; 4 ', 5 ')) from an equation system formed according to the number and type of parameters to be measured.

2. Calibration method according to claim 1, characterized in that the distance between each of the movable or fixed platform ( 1 , 2 ; 1 ', 2 ') assigned points is determined, these points being fixed during the calibration process with respect to the corresponding Platforms are held. 3. Calibration method according to claim 1 or 2, characterized in that in the measurement of the position errors of at least any point of the movable platform ( 2 ; 2 ') that is recorded during the calibration process is determined in at least one spatial coordinate. 4. Calibration method according to one of claims 1 to 3, characterized in that during the measurement, the angle change of at least one actuator ( 3 ) with respect to at least one platform ( 1 , 2 ) or accordingly at least one sta bes ( 8 ') with respect to at least one platform ( 1 ', 2 ') is measured and / or the angle of rotation of at least one of the gels ke ( 4 , 5 ; 4 ', 5 '). 5. Calibration method according to one of claims 1 to 4, characterized in that coordinates of the platforms ( 1 , 2 ; 1 ', 2 ') associated joints ( 4 , 5 ; 4 ', 5 ') are partially measured directly.