Method and apparatus for determining position and orientation

Abstract

The invention relates to a method and a device for determining position and orientation, wherein the method uses a measuring body having a predetermined polyhedral basic form, which basic form makes a contour line with at least three measurement marks available, and the method has the following steps: capturing a set of measurement data coordinates using a surface profiler, the set of measurement data coordinates comprising at least two measurement values ​​for each of the corresponding measurement marks, wherein the measurement values ​​represent the contour line, evaluating the measured values ​​of the set of measurement data coordinates and the known values ​​of the geometry of the measuring body, thereby determining the z-axis rotation angle of the measuring body around its z-axis, the y-axis rotation angle of the measuring body around the y-axis of a sensor head of the surface profiler, the x-axis rotation angle of the measuring body around the x-axis of the sensor head, and evaluating the measured values ​​of the set of measurement data coordinates, the known values ​​of the geometry of the measuring body and the known rotation angle, thereby determining the translational displacement of the measuring body in the x-axis, y-axis and z-axis directions of the sensor head.

Description

Technical Field

[0001] The invention relates to a method for determining a position and an orientation. The invention also relates to a computer program product and a device for determining a position and an orientation, and a measuring body. Background Art

[0002] It is necessary to capture the displacement of an object on a test bench or inspection bench in all three spatial axes and the rotation about all three rotation axes. The object may be, for example, a gearbox or a traction motor associated with a motor vehicle or other object.

[0003] This type of displacement and rotation can be captured by measuring the corresponding linear acceleration and rotation rate and subsequently integrating them in order to determine distance and angle values. However, the sensors required for this purpose are sensitive to shocks and vibrations. In addition, these sensors are frequency-dependent, causing their output signals to scatter and be subject to offsets, so that single or double integration produces signal drift. Therefore, especially slow movements can only be captured to a limited extent.

[0004] Sampling measurement or contactless measurement requires three sensors for the three spatial axes and three more sensors for angle measurement. It also requires access from three sides, which is not always available.

[0005] Optical triangulation and subsequent evaluation with two cameras requires the use of three measuring bodies in order to be able to determine the displacement of the object in the direction of all three spatial axes and the rotation about all three rotation axes. However, the two cameras must be arranged with a minimum distance between each other and the object, which is very demanding given the unavailable space in the engine compartment or underbody area of ​​a motor vehicle.

[0006] It would therefore be desirable to demonstrate a method by which the measurement of displacements of an object in the direction of all three spatial axes and rotations about all three rotational axes can be improved. Summary of the invention

[0007] The object of the invention is achieved by a method for determining position and orientation, wherein a measuring volume having a predetermined polyhedral basic form is used, which makes available a contour line with at least three measurement markings, the method comprising the following steps:

[0008] capturing a set of measurement data coordinates using a surface profiler, the set of measurement data coordinates comprising at least two measurement values ​​for each of the corresponding measurement marks, wherein the measurement values ​​represent a profile line,

[0009] evaluating the measured values ​​of the measurement data coordinate set and the known values ​​of the measurement body geometry to determine a z-axis rotation angle of the measurement body about its z-axis, a y-axis rotation angle of the measurement body about a y-axis of a sensor head of the surface profiler, and an x-axis rotation angle of the measurement body about an x-axis of the sensor head, and

[0010] The measured values ​​of the measurement data coordinate set, the known values ​​of the geometry of the measuring body and the known rotation angles are evaluated in order to determine the translational displacement of the measuring body in the direction of the x-axis, y-axis and z-axis of the sensor head.

[0011] A measuring head is thus used, which is assigned to the object to be monitored. The measuring body can be a separate component which is detachably or permanently connected to the object, or the measuring body is formed on the object, i.e. the object and the measuring body are formed from a single piece and / or a consistent material. The measuring body makes it possible to capture a contour line by means of a surface profiler, wherein the path of the contour line through the measuring marks is characterized in such a way that the displacement of the object in the direction of all three spatial axes and the rotation angle around all three rotation axes can be determined. Since all the measuring marks are located in one or the same plane, each measuring mark is described by only two measured values. In other words, the contour line can be described by means of the height information related to the interval starting from the starting point, wherein, within certain limits, the measuring marks are assigned together in each case to one feasible position of the measuring body. Together with the known values ​​of the measuring body geometry, this allows surprisingly simple determination of the displacement of the object in the direction of all three spatial axes and the rotation angle around all three rotation axes.

[0012] According to one form of embodiment, the measuring body has five planar boundary surfaces, two of which each have a triangular basic form and three of which each have a trapezoidal basic form, wherein the corresponding measurement mark is arranged at the transition between one of the boundary surfaces and the adjacent boundary surface. The line between the two measurement marks, the line through the other measurement mark perpendicular to the connecting line of the first-mentioned measurement mark and the known value are evaluated to determine the z-axis rotation angle. The two measurement values ​​can be the first and last measurement marks along the contour line. In other words, another of the at least three measurement marks is arranged between the first and last measurement marks. The known value can be the inclination angle of the intersection line of the selected surface (for example, the boundary surface with a trapezoidal basic form). The z-axis rotation angle around the vertical axis can thus be determined.

[0013] According to another form of embodiment, a measuring body having a contour with at least four measuring markings is used. This simplifies the evaluation of the measured values.

[0014] According to another form of embodiment, the measuring body has six planar boundary surfaces, five of which have a trapezoidal basic form and one of the six planar boundary surfaces has a rectangular basic form, wherein the corresponding measurement marks are arranged at the transition between one of the boundary surfaces and the adjacent boundary surface. In other words, four measurement marks are only assigned to the three boundary surfaces on the upper side of the measuring body. As a result, the displacement of the object in the direction of all three spatial axes and the rotation angle around all three rotation axes can be realized by sampling only three boundary surfaces. This reduces the time required for sampling.

[0015] According to another form of embodiment, two measuring marks are arranged at the transition between a boundary surface with a rectangular basic form and a corresponding adjacent boundary surface with a trapezoidal basic form. As a result, the displacement of the object in the direction of all three spatial axes and the rotation angles about all three rotation axes can be determined in a particularly simple and therefore economical manner in terms of computing resources.

[0016] According to another form of embodiment, the measuring body is designed to be axisymmetric. For example, the measuring body can be designed to be axisymmetric with respect to its x-axis or longitudinal axis. This simplifies the determination of the displacement of the object in the direction of all three spatial axes and the rotation angles about all three rotation axes and thus results in a method that is particularly economical in terms of computing resources.

[0017] According to another form of embodiment, the measuring body has a substantially wedge-shaped design. A substantially wedge-shaped basic form here refers to two boundary surfaces that intersect at an acute angle, for example a boundary surface with a rectangular basic form and a boundary surface with a trapezoidal basic form, for example, located opposite the boundary surface. This also simplifies the determination of the displacement of the object in the direction of all three spatial axes and the rotation angles about all three rotation axes, thereby resulting in a method that is particularly economical in terms of computing resources.

[0018] According to another form of embodiment, in particular when a measuring body with at least four measuring marks is used, a first partial line segment and a second partial line segment of a line segment between two measuring marks and a known value are evaluated to determine the z-axis rotation angle. The two measured values ​​may be the first and last measuring marks along the contour line. In other words, the other two of the at least four measuring marks are arranged between the first measuring mark and the last measuring mark. The known value may be the angle between two lines that coincide with the edges of two selected boundary surfaces of the measuring body. Thus, the z-axis rotation angle about the vertical axis can be determined in a particularly simple and thus economical manner in terms of computing resources.

[0019] According to another form of embodiment, the system of equations is solved mathematically to determine the z-axis rotation angle. For this purpose a numerical determination of the roots can be performed.

[0020] According to another form of embodiment, the y-axis rotation and the angle value and the line segment length of the measuring body about its y-axis are determined, and the z-axis rotation, the y-axis rotation and the angle value and the line segment length are evaluated to determine the y-axis rotation angle. As a result, the y-axis rotation angle about the transverse axis can be determined in a particularly simple and thus economical manner in terms of computing resources.

[0021] According to another form of embodiment, two of the measured values ​​are evaluated in order to determine the x-axis rotation angle. These two measured values ​​can again be the first and last measurement mark along the contour line. Thus, the x-axis rotation angle about the longitudinal axis can be determined in a particularly simple and thus economical manner in terms of computing resources.

[0022] The invention also includes a computer program product for carrying out the method, such a device and such a measuring body. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The present invention will now be described with reference to the accompanying drawings, in which:

[0024] Figure 1 A schematic diagram of a device for determining position and orientation is shown for carrying out an exemplary embodiment of a method according to the invention;

[0025] Figure 2 According to the first form of embodiment, Figure 1 A perspective view of the measuring body shown in;

[0026] Figure 3 Shows Figure 2 A plan view of the measuring body shown in ;

[0027] Figure 4 Shows Figure 2 A side view of the measuring body shown in;

[0028] Figure 5 Shows Figure 2 A front view of the measuring body shown in ;

[0029] Figure 6 Shows Figure 2 A cross-sectional view of the measuring body shown in FIG.

[0030] Figure 7 An auxiliary perspective view for illustrating the method is shown;

[0031] Figure 8 A perspective view of a further measuring body according to a second form of embodiment is shown. DETAILED DESCRIPTION

[0032] First reference Figure 1 .

[0033] A device 2 is shown for determining the position and orientation of an object O. The object O may be part of a plane having, for example, a gearbox or a traction motor. In the present form of embodiment, the device 2 is designed to capture displacements within a range of + / -10 mm and rotation angles within a range of + / -10°.

[0034] In the present form of embodiment, the device 2 comprises a surface profiler 4 which is designed for contactless (e.g. optical) capture of the surface topography. For this purpose, a measuring body 6 is sampled with a sensor head 8 of the surface profiler 4, which in the present form of embodiment is fixed to the object O. In contrast to the present form of embodiment, the measuring body 6 can also be formed on the object O.

[0035] exist Figure 1 In FIG. 1 , the longitudinal axis or x-axis x of the sensor head 8 is also shown. s , transverse axis or y axis s and the vertical axis or z axis s and the longitudinal axis or x-axis x of the object O t , transverse axis or y axis t and the vertical axis or z axis t .

[0036] Now we will refer to Figures 2 to 5 First, the measuring body 6 will be described in detail.

[0037] In the present form of embodiment, a measuring body 6 with four measuring markings P1 , P2 , P3 , P4 is shown.

[0038] In the present form of embodiment, the measuring body 6 has a wedge-shaped basic form. The measuring body 6 of the present form of embodiment also includes six planar boundary surfaces 10a, 10b, 10c, 10d, 10e, 10f. Five boundary surfaces 10a, 10b, 10c, 10d, 10e each have a trapezoidal basic form, while one boundary surface 10f has a rectangular basic form.

[0039] In the following detailed description of the five boundary surfaces 10a, 10b, 10c, 10d, 10e, each having a trapezoidal basic form, the corresponding two parallel sides are referred to as the base sides of the corresponding trapezoid. The longer of the two corresponding base sides is referred to as the base of the corresponding trapezoid, and the two adjacent (generally non-parallel) sides are referred to as legs.

[0040] The first boundary surface 10a and the second boundary surface 10b opposite to the first boundary surface 10a are each formed as a trapezoid having equal sides, that is, a symmetrical trapezoid, and the two surfaces are arranged parallel to each other. The respective normal vectors of the first boundary surface 10a and the second boundary surface 10b are aligned with the longitudinal axis or x t The axes coincide.

[0041] The third boundary surface 10c and the fourth boundary surface 10d opposite to the third boundary surface 10c are both asymmetric trapezoids. The respective bases of the third boundary surface 10c and the fourth boundary surface 10d are adjacent to the second boundary surface 10b, and the respective shorter base sides are adjacent to the first boundary surface 10a. In other words, the respective directions in which the third boundary surface 10c and the fourth boundary surface 10d gradually decrease have the same orientation. The normal vector of the third boundary surface 10c has an x ​​component, a y component, and a z component, wherein the x component is from x to z. t The axis deviation angle β0 = 45° (with the z component from z t axis deviates from a 45° angle), and the y component changes from y t The axis deviates from the angle α0=15°. The normal vector of the fourth boundary surface 10d also has an x ​​component, a y component and a z component, wherein the x component is from the x t The axis deviation angle β0 = 45° (with the z component from z t axis deviates from a 45° angle), and the y component changes from y t The axis is offset by an angle of α0 = 15°. However, the third boundary surface 10c and the fourth boundary surface 10d are not arranged parallel to each other but are arranged in an intersecting plane.

[0042] The fifth boundary surface 10e is formed as an isosceles or symmetrical trapezoid. The base of the fifth boundary surface 10e is adjacent to the base of the second boundary surface 10b, and the shorter base of the fifth boundary surface 10e is adjacent to the base of the first boundary surface 10a. Each waist of the fifth boundary surface 10e is adjacent to the corresponding waist of the corresponding boundary surface 10c and 10d. The normal vector of the fifth boundary surface 10e is adjacent to the vertical axis or z t The axes coincide. The measuring body 6 is connected to the object O via a fifth boundary surface 10e, and the object O forms an extension of the fifth boundary surface 10e due to the flat extent of its plane.

[0043] The sixth boundary surface 10f has t The sixth boundary surface 10f is a rectangle with two horizontal sides in the direction of the zt axis or the transverse axis and two vertical sides perpendicular to these horizontal sides. The corresponding horizontal sides of the sixth boundary surface 10f are adjacent to the corresponding shorter base sides of the first boundary surface 10a and the second boundary surface 10b, and the corresponding vertical sides are adjacent to the corresponding waists of the corresponding boundary surfaces 10c and 10d. The normal vector of the sixth boundary surface 10f deviates from the zt axis or the vertical axis by an angle of α0=15°.

[0044] The measuring body 6 of the present form of embodiment is designed to be axisymmetric, in particular by selecting the angles on both sides to be α0=15° and β0=45°, relative to the xt axis or longitudinal axis.

[0045] Different from the current embodiment, the measuring body 2 according to another embodiment can be designed to have axial asymmetry. The measuring body 6 can also include a boundary surface designed as a non-isosceles triangle and / or an asymmetric trapezoid. In other words, Figures 3 to 5 The angles α0 and β0 shown in can have different values ​​on both sides of the corresponding extension axis. Figure 3 and Figure 4 The angles α0 in do not have to have the same value.

[0046] Now refer to Figure 6 .

[0047] The height profile along the contour line is shown, as well as the result of sampling an object O using a surface profiler 4 through a measuring body 6. The contour line is characterized by four measuring marks P1, P2, P3, P4. Each of the four measuring marks P1, P2, P3, P4 is arranged in a bending region or transition region between a starting surface and an adjacent further boundary surface 10a, 10b, 10c, 10d, 10e, 10f.

[0048] The two measuring marks P1 and P4 define the start and end points of the contour line, respectively, while the other two measuring marks P2 , P3 are arranged at the transition between the sixth boundary surface 10 f and the respectively adjacent third boundary surface 10 c and fourth boundary surface 10 d .

[0049] Since the measuring markers P1, P2, P3, P4 are located in one plane, the measuring markers P1, P2, P3, P4 can each be described by a value pair, namely in each case by z t The value in the axis or vertical axis direction and y t Description of the value in the axial or transverse axial direction.

[0050] Due to the shape of the measuring body 6, at x t The linear or translational movement in the axis direction results in a change in the height (i.e., z-coordinate or z-value) of the measuring markers P2 and P3 and a change in the y-spacing of the measuring markers P1 and P4. t Movement in the axial direction results in an increase or decrease in the y coordinates or y values ​​of all measurement markers P1, P2, P3, P4, and in the z t Movement in the axial direction results in an increase or decrease in the z-coordinate or z-value of all measurement markings P1 , P2 , P3 , P4 .

[0051] Around x t A rotational movement about an axis results in a rotation in the corresponding plane. As long as the rotational movement is less than the angle α0 = 15°, the tThe rotation of the axis changes the angles δ and ε in the same way, that is, each increases or decreases together. On the other hand, as long as the rotational movement is less than the angle α0 = 15°, the rotation around z t Rotation of the axis changes the angles δ and ε in opposite ways, ie the angle δ decreases and the angle ε increases, or the angle δ increases and the angle ε decreases.

[0052] Thus, all the necessary information is available to determine the position of the object O in all three spatial axes x t ,y t 、z t The displacement in the φ, θ and Ψ directions and the rotation angles around all three rotation axes Φ, θ and Ψ.

[0053] Now we will refer to Figure 7 Describe the evaluation of measurement data.

[0054] Sampling the measurement volume 6 with the surface profiler 4 delivers a data set representing the height profile along the contour line. It comprises a plurality of value pairs, each value pair comprising a y value for a corresponding position along the contour line and a z value for the corresponding height at that position.

[0055] In order to determine the value pairs corresponding to the measurement markers P1, P2, P3, P4, the data sets are evaluated based on the changes or gradients of the corresponding y values ​​and / or the changes in the gradients. The following set of measurement data coordinates M is the result for the measurement markers P1, P2, P3, P4:

[0056] P1 (P1y | P1z), P2 (P2y | P2z), P3 (P3y | P3z), P4 (P4y | P4z)

[0057] These coordinates and the coordinate representation of the points thereafter are relative to the coordinate system of the sensor head 8 .

[0058] Then a series of auxiliary variables are determined.

[0059] The first auxiliary variable P5 is the intersection of the first auxiliary straight line through the measurement markers P1 and P2 and the second auxiliary straight line through the measurement markers P3 and P4. The following applies to the y value P5y:

[0060]

[0061] The following applies to the z-value P5z:

[0062]

[0063] A further auxiliary variable P6 is the center between the measuring marks P2 and P3, which lies in the y0 plane of the measuring volume 6. The following applies to the corresponding y- and z-values:

[0064]

[0065] Another auxiliary variable P0 is the intersection of the first auxiliary straight line through the measuring markers P1 and P4 and the second auxiliary straight line through the auxiliary variables P5 and P6. It lies both in the y0 plane of the measuring volume 6 and in the z0 plane of the measuring volume 6. The following applies to the y value P0y:

[0066]

[0067] The following applies for the z-value P0z:

[0068]

[0069] The line segments u (connecting the measurement marker P4 and the auxiliary variable P5), v (connecting the measurement marker P1 and the auxiliary variable P5), w (connecting the measurement marker P4 and the measurement marker P1), w1 (connecting the measurement marker P1 and the auxiliary variable P0), and w2 (connecting the measurement marker P4 and the auxiliary variable P0) are additionally determined as further auxiliary variables using the Pythagorean theorem:

[0070]

[0071] You can also use trigonometric functions or the law of cosines or the Pythagorean theorem to determine the following auxiliary variables, i.e., line segments and angles:

[0072]

[0073] In another step, it is then determined that t The following applies to the line segments w1 and w2:

[0074]

[0075]

[0076] Then we get the ratio w2 / w1:

[0077]

[0078] Solving for Ψ2 yields:

[0079]

[0080] In a further step, determine the t The following applies to line segments b and d:

[0081]

[0082] By rearranging and substituting into b = w1cos(α0 - Ψ2), we get:

[0083]

[0084] Arranging for Θ2 yields:

[0085]

[0086] In a further step, determine the s The rotation angle of the axis is θ1. For line segment d, according to the rotation θ2, we have:

[0087]

[0088] For line segment c, according to the rotation angle θ1 and the rotation angle Ψ2, we have:

[0089]

[0090] Arrangement and insertion finally yield:

[0091]

[0092] Furthermore, in a further step, the rotation around x is determined s The rotation angle Φ0 of the axis. For this purpose the first measurement mark P1 and the last measurement mark P4 are evaluated. For the rotation angle Φ0 we have:

[0093]

[0094] Finally, in a further step, the distance Δ between the auxiliary point P0 and the measurement reference point MP is determined. The following applies:

[0095]

[0096] The determined angles Ψ2, Θ1 and Φ0 describe the rotation of the measuring volume 6 about the fixed origin and can now be used for coordinate transformation into a spatially fixed reference system. Each point of the measuring volume 6 can be transformed into the reference coordinate system by three subsequent rotations of the angles -Ψ, -Θ and -Φ.

[0097] This can be realized for a vector r''' (having a length Δ and defined by being located on the x-axis of the measuring volume 6 ) from the auxiliary point P0 to the measuring reference point MP:

[0098]

[0099]

[0100]

[0101]

[0102] Here (x | y | z) is the vector r, which connects the auxiliary point P0 to the measurement reference point MP, expressed in the coordinate system of the sensor head 8. The coordinates of the measurement point in the spatially fixed reference coordinate system describe the displacement of the measuring volume 6. The following equation applies to the displacement:

[0103]

[0104] Note that P0x = 0 since the point lies in the sampling plane.

[0105] In the present form of embodiment, the rotational movement of the measuring body 6 is described by means of a combination of three subsequent rotations through the angles Ψ, Θ and Φ. However, this is only one possible way of describing the rotation of the measuring body 6.

[0106] For a clearer description, the three axes (unit vectors) of the coordinate system of the measuring volume 6 can be expressed in the reference coordinate system, using the same matrix operations as above. The projection of these vectors onto the plane of the reference coordinate system helps to visualize the rotation:

[0107] The following applies to the y-axis of measuring volume 6 in the coordinate system of measuring volume 6 :

[0108]

[0109] Then, to express r2''' in the reference coordinate system, we have:

[0110]

[0111] For the angle Φ between the vector r2''' projected onto the yz plane of the reference coordinate system and the y axis of the reference coordinate system, we obtain:

[0112]

[0113] The following applies to the z-axis of measuring volume 6 in the coordinate system of measuring volume 6 :

[0114]

[0115] Then, for the representation of r3''' in the reference coordinate system, we have:

[0116]

[0117] For the angle θ between the vector r3''' projected onto the zx plane of the reference coordinate system and the z axis of the reference coordinate system, we have:

[0118]

[0119] The following applies to the x-axis of measuring volume 6 in the coordinate system of measuring volume 6 :

[0120]

[0121] Then, for the representation of r1''' in the reference coordinate system, we have:

[0122]

[0123] For the angle Ψ between the vector r1''' projected onto the xy plane of the reference coordinate system and the x-axis of the reference coordinate system, we have:

[0124]

[0125] Thus, the displacement of the object O in the direction of all three spatial axes and the rotation about all three rotation axes can be more clearly displayed using the measuring body 6 .

[0126] Now refer to Figure 8 Firstly, the measuring body 6 ′ according to the second form of embodiment is described in detail.

[0127] In the second form of embodiment, the measuring body 6 ′ has three measuring markings P1 ′, P2 ′, P3 ′.

[0128] The measuring body 6' according to the second form of embodiment also has a wedge-shaped basic form. However, the measuring body 6' according to the second form of embodiment comprises five planar boundary surfaces 10a', 10b', 10c', 10d', 10e'. Two boundary surfaces 10a', 10b' each have a triangular basic form, while three boundary surfaces 10c', 10d', 10e' have a trapezoidal basic form.

[0129] The first boundary surface 10a' and the second boundary surface 10b' opposite to the first boundary surface 10a' are both formed as isosceles triangles and are arranged parallel to each other. The corresponding normal vectors of the first boundary surface 10a' and the second boundary surface 10b' are aligned with the longitudinal axis or x t The axes coincide.

[0130] The third boundary surface 10c', the fourth boundary surface 10d' and the fifth boundary surface 10e' are all symmetrical trapezoids. The corresponding bases of the third boundary surface 10c', the fourth boundary surface 10d' and the fifth boundary surface 10e' are adjacent to the second boundary surface 10b', and the corresponding shorter base sides are adjacent to the first boundary surface 10a'. In other words, the corresponding directions in which the corresponding third boundary surface 10c', the fourth boundary surface 10d' and the fifth boundary surface 10e' gradually become smaller have the same orientation.

[0131] The measuring volume 6 ′ is connected to the object O via the fifth boundary surface 10 e ′, while the object O forms an extension of the fifth boundary surface 10 e ′ due to its planar extent.

[0132] The measuring body 6 ′ according to the second form of embodiment is designed to be axisymmetric in the present form of embodiment.

[0133] Different from the second embodiment, the measuring body 6' can also include a boundary surface designed as a non-isosceles triangle and / or an asymmetric trapezoid. In addition, the measuring body 6' according to the second embodiment can be designed to be axially asymmetric.

[0134] In terms of evaluating the measurement data, when using the measuring body 6' according to the second form of embodiment, only three measurement markings P1', P2', P3' are available. The measurement markings P2 and P3 of the measuring body 6 according to the first form of embodiment are missing. If the two measuring bodies 6, 6' are compared, it is further shown that the measurement marking P2' of the measuring body 6' according to the second form of embodiment corresponds to the auxiliary variable P5 in the evaluation of the measurement data when using the measuring body 6 according to the first form of embodiment.

[0135] The measurement data coordinate set M' obtained using the measurement volume 6' with three measurement markings P1', P2', P3' according to the second form of embodiment has, for example, the following format:

[0136] P1' (P1y, P1z), P2' (P2y, P2z), P3' (P3y, P3z)

[0137] Without the measuring marks P2 and P3 of the measuring body 6 according to the first form of embodiment, the auxiliary variables P6 and P0 cannot be determined as above. Therefore, the line segments w1, w2 and d are not available. When the measuring body 6' according to the second form of embodiment is used, the line segments w1, w2 and d are not available. t The determination of the rotation angle Ψ2 of the axis can be achieved by solving the following system of equations:

[0138]

[0139] The system of equations can be solved analytically. Alternatively, the system of equations can be solved using numerical determination of the roots in order to determine the rotation angle Ψ2. Also optionally, a neural network can also be used after a training phase, or a lookup table can be used.

[0140] By knowing the rotation angle Ψ2 about the zt axis, the line segment lengths w1, w2 and d can also be determined using the formulas further shown above. The method can then be used to continue calculating other variables to be solved using the measuring body 6 according to the first form of embodiment.

[0141] Reference numerals list

[0142] 2 Devices

[0143] 4Surface Profiler

[0144] 6 Measurement body

[0145] 6' measuring body

[0146] 8 sensor heads

[0147] 10a Boundary surface

[0148] 10b Boundary surface

[0149] 10c Boundary surface

[0150] 10d boundary surface

[0151] 10e boundary surface

[0152] 10f boundary surface

[0153] 10a' boundary surface

[0154] 10b' boundary surface

[0155] 10c' boundary surface

[0156] 10d' boundary surface

[0157] 10e' boundary surface

[0158] aAuxiliary value

[0159] bAuxiliary value

[0160] b2 auxiliary value

[0161] c auxiliary value

[0162] d auxiliary value

[0163] d2 auxiliary value

[0164] M measurement data coordinate group

[0165] M' measurement data coordinate group

[0166] MP measurement reference point

[0167] OObject

[0168] P0 auxiliary marker

[0169] P1 measurement mark

[0170] P2 measurement marker

[0171] P3 measurement marker

[0172] P4 measurement mark

[0173] P5 auxiliary variables

[0174] P6 auxiliary variables

[0175] P1' measurement mark

[0176] P2' measurement mark

[0177] P3' measurement marker

[0178] u-segment

[0179] v Line segment

[0180] w line segment

[0181] w1 line segment

[0182] w2 segment

[0183] x0 value

[0184] x s The x-axis of the sensor head

[0185] x t The x-axis of the measuring body

[0186] y s Y axis of the sensor head

[0187] y t Measuring volume's y-axis

[0188] z s The z-axis of the sensor head

[0189] z t The z-axis of the measuring volume

[0190] α0 angle

[0191] β0 angle

[0192] δ angle

[0193] Δ Spacing

[0194] ε angle

[0195] θ Rotation axis

[0196] Θ1 around y s Rotation angle of the axis

[0197] Θ2 around y t Rotation angle of the axis

[0198] ΦRotation axis

[0199] Φ0 around x s Rotation angle of the axis

[0200] ΨRotation axis

[0201] Ψ2 around z t Rotation angle of the axis

Claims

1. A method for determining the position and orientation of an object using a measuring body (6, 6'), wherein the measuring body (6, 6') has a predetermined polyhedral basic form, which makes a contour line with at least three measurement marks (P1, P2, P3, P4; P1', P2', P3') available, the method comprising the following steps: capturing a set of measurement data coordinates (M, M') with a surface profiler (4), the set of measurement data coordinates (M, M') comprising at least two measurement values ​​for each of the corresponding measurement marks (P1, P2, P3, P4; P1', P2', P3'), wherein the measurement values ​​represent the contour line, Evaluation of the measured values ​​of the set of measured data coordinates (M, M') and the known values ​​(α0, x 0MP ), thereby determining the displacement of the measuring body (6, 6') about its z-axis (z t ), a z-axis rotation angle (Ψ2) of the measuring body (6, 6') around the y-axis (y s ), a y-axis rotation angle (θ1) of the measuring body (6, 6') around the x-axis (x s ), and Evaluation of the measured values ​​of the set of measured data coordinates (M, M'), the known values ​​of the geometry of the measuring volume (6, 6') (α0, x 0MP ) and the known rotation angles (Ψ2, Θ1, Φ0), thereby determining the x-axis (x s ), the y-axis (y s ) and the z axis (z s ) direction to determine the position and orientation of the object.

2. The method according to claim 1, wherein the measuring body (6') has five planar boundary surfaces (10a', 10b', 10c', 10d', 10e'), wherein two of the boundary surfaces (10a', 10b') each have a triangular basic form and three of the boundary surfaces (10c', 10d', 10e') each have a trapezoidal basic form, wherein the respective measuring marking (P1', P2', P3') is arranged at the transition between one of the boundary surfaces (10c', 10d', 10e') and the immediately adjacent boundary surface (10c', 10d', 10e'). 3 . The method according to claim 1 , wherein the measuring body ( 6 ) is used which has the contour line with at least four of the measuring markings ( P1 , P2 , P3 , P4 ).

4. The method according to claim 3, wherein the measuring body (6) has six planar boundary surfaces (10a, 10b, 10c, 10d, 10e, 10f), wherein five of the six planar boundary surfaces (10a, 10b, 10c, 10d, 10e, 10f) have a trapezoidal basic form and one of the six planar boundary surfaces (10a, 10b, 10c, 10d, 10e, 10f) has a rectangular basic form, wherein the respective measuring marking (P1, P2, P3, P4) is arranged at the transition between one of the planar boundary surfaces (10a, 10b, 10c, 10d, 10e, 10f) and the adjacent planar boundary surface (10a, 10b, 10c, 10d, 10e, 10f).

5. The method according to claim 4, wherein the two measuring marks (P2, P3) are arranged at the transition between the planar boundary surface (10f) having the rectangular basic form and the respectively adjacent planar boundary surface (10a, 10b, 10c, 10d, 10e) having the trapezoidal basic form. 6 . The method according to claim 1 , wherein the measuring body ( 6 , 6 ′) is designed to be axisymmetric. 7 . The method according to claim 1 , wherein the measuring body ( 6 , 6 ′) has a wedge-shaped basic form.

8. The method according to claim 5, wherein a first partial line segment (w1) and a second partial line segment (w2) of a line segment between two of the measurement markings (P1, P4) and a known value (α0) are evaluated to determine the z-axis rotation angle (Ψ2), wherein: The first partial line segment (w1) is a line segment connecting one of the two measurement marks (P1, P4) and a first auxiliary variable (P0), the second partial line segment (w2) is a line segment connecting the other of the two measurement marks (P1, P4) and the first auxiliary variable (P0), and the known value (α0) is an angle between two lines that coincide with edges of two selected boundary surfaces of the measurement body (6).

9. The method of claim 1, wherein the z-axis rotation angle (Ψ2) is determined by mathematically solving a system of equations.

10. The method according to claim 8, wherein a y-axis rotation angle (θ2) and an angle value (δ) as well as a line segment length (v) of the measuring body (6) about its y-axis are determined, and wherein the z-axis rotation angle (Ψ2), the y-axis rotation angle (θ2) and the angle value (δ) as well as the line segment length (v) are evaluated to determine the y-axis rotation angle (θ1), wherein The angle value (δ) is a second auxiliary variable, and the line segment length (v) is a line segment length connecting the measurement mark (P1) and the third auxiliary variable (P5).

11. The method according to claim 10, wherein the measured values ​​(P 1y , P 1z ;P 4y , P 4z ), thereby determining the x-axis rotation angle (Φ0).

12. A computer program product designed to perform the method of any one of claims 1 to 11.

13. A device (2) for determining the position and orientation of an object using a measuring body (6, 6'), the measuring body (6, 6') having a predetermined polyhedral basic form, the polyhedral basic form making available a contour line with at least three measurement marks (P1, P2, P3, P4; P1', P2', P3'), wherein the device (2) is designed to capture a set of measurement data coordinates (M, M') using a surface profiler (4), the set of measurement data coordinates (M, M') comprising at least two measurement values ​​for each of the respective measurement marks (P1, P2, P3, P4; P1', P2', P3'), wherein the measurement values ​​represent the contour line, and the device (2) is designed to evaluate the measurement values ​​of the set of measurement data coordinates (M, M') and known values ​​(α0, x) of the geometry of the measuring body (6, 6'). 0MP ), thereby determining the displacement of the measuring body (6, 6') about its z-axis (z t ), a z-axis rotation angle (Ψ2) of the measuring body (6, 6') around the y-axis (y s ), and the measurement body (6, 6') around the x-axis (x s ), and the device (2) is designed to evaluate the measured values ​​of the measurement data coordinate set (M, M'), the known values ​​of the geometry of the measurement body (6, 6') (α0, x 0MP ) and the known rotation angles (Ψ2, Θ1, Φ0), thereby determining the x-axis (x s ), the y-axis (y s ) and the z axis (z s ) direction to determine the position and orientation of the object.

14. The device (2) according to claim 13, wherein the measuring body (6') has five planar boundary surfaces (10a', 10b', 10c', 10d', 10e'), wherein two of the boundary surfaces (10a', 10b') each have a triangular basic form and three of the boundary surfaces (10c', 10d', 10e') each have a trapezoidal basic form, wherein the corresponding measuring markings (P1', P2', P3') are arranged at the transition between one of the boundary surfaces (10c', 10d', 10e') and the adjacent boundary surface (10c', 10d', 10e'). 15 . The device ( 2 ) according to claim 13 , wherein the measuring body ( 6 ) has a contour with at least four of the measuring markings ( P1 , P2 , P3 , P4 ).

16. The device (2) according to claim 15, wherein the measuring body (6) has six planar boundary surfaces (10a, 10b, 10c, 10d, 10e, 10f), wherein five of the six planar boundary surfaces (10a, 10b, 10c, 10d, 10e, 10f) have a trapezoidal basic shape and one of the six planar boundary surfaces (10a, 10b, 10c, 10d, 10e, 10f) has a rectangular basic form, wherein the respective measuring marking (P1, P2, P3, P4) is arranged at the transition between one of the planar boundary surfaces (10a, 10b, 10c, 10d, 10e, 10f) and the immediately adjacent planar boundary surface (10a, 10b, 10c, 10d, 10e, 10f).

17. The device (2) according to claim 16, wherein two of the measuring marks (P2, P3) are arranged at the transition between the planar boundary surface (10f) having the rectangular basic form and the corresponding adjacent planar boundary surface (10a, 10b, 10c, 10d, 10e) having the trapezoidal basic form. 18 . The device ( 2 ) according to claim 13 , wherein the measuring body ( 6 , 6 ′) is designed to be axisymmetric.

19. The device (2) according to claim 13, wherein the measuring body (6, 6') has a wedge-shaped basic form.

20. The device (2) according to claim 17, wherein the device (2) is designed to evaluate a first partial segment (w1) and a second partial segment (w2) of a line segment between two measurement markings (P1, P4) and a known value (α0) in order to determine the z-axis rotation angle (Ψ2), wherein: The first partial line segment (w1) is a line segment connecting one of the two measurement marks (P1, P4) and a first auxiliary variable (P0), the second partial line segment (w2) is a line segment connecting the other of the two measurement marks (P1, P4) and the first auxiliary variable (P0), and the known value (α0) is an angle between two lines that coincide with edges of two selected boundary surfaces of the measurement body (6).

21. The device (2) according to claim 13, wherein the device (2) is designed to use a numerical solution of a system of equations in order to determine the z-axis rotation angle (Ψ2).

22. The device (2) according to claim 20, wherein the device (2) is designed to determine the y-axis rotation angle (θ2) and the angle value (δ), as well as the line segment length (v) of the measuring body (6) around its y-axis, and to evaluate the z-axis rotation angle (Ψ2), the y-axis rotation angle (θ2) and the angle value (δ), as well as the line segment length (v), so as to determine the y-axis rotation angle (θ1), wherein: The angle value (δ) is a second auxiliary variable, and the line segment length (v) is a line segment length connecting the measurement mark (P1) and the third auxiliary variable (P5).

23. The device (2) according to claim 22, wherein the device (2) is designed to evaluate the measured values ​​(P 1y , P 1z ;P 4y , P 4z ), thereby determining the x-axis rotation angle (Φ0).

24. A measuring body (6, 6') for a device (2) as claimed in any one of claims 13 to 23.

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