DE102017200084A1 - A method of providing a motion contour for a manipulator along predetermined landmarks - Google Patents

Abstract

The invention relates to a method for providing a manipulator movement contour (18) along a course of predetermined landmarks (Q), comprising computing a plurality of filter points (F) within a filter tolerance region (16) around the landmarks (Q) such that each filter point (F) at a nearest landmark (Q) of the predetermined landmarks (Q) is located at an inner side of the course of the landmarks (Q) with respect to a change of direction. The method further comprises calculating a smoothed motion contour (18) by means of a spline approximation from the filter points (F) such that the smoothed motion contour (18) extends within a smoothing tolerance range around the filter points (F). The invention further relates to a computing unit and a computer program for carrying out the method.

Description

The present invention relates to a method for providing a motion contour for a manipulator along a course of predetermined landmarks. The invention is thus in the field of automation technology and the control or regulation of machine tools, in particular for applications in the fields of numerically controlled or NC-programmed milling (NC = numerical control), the jet cutting, such as by means of laser and / or Plasma and / or water, the turning and / or the movement of robots.

State of the art

In the context of the automation of work and / or process steps, it may be desirable to automatically move a machine or a manipulator along predetermined orientation points, for example around the manipulator along the predetermined orientation points or within a predetermined tolerance range along or around the predetermined one Guide around points. This may be desirable, for example, in applications in which a workpiece is to be milled and / or cut and / or sawn with the manipulator within a tolerance range around the predetermined orientation points.

It is desirable to provide a motion contour for the manipulator, which not only meets the requirements of the landmarks and the tolerance range, but also has a c ² -stetigen course in which the manipulator is not exposed to sudden changes in direction, speed and acceleration ,

A movement contour for a manipulator can conventionally be composed of several, in particular linear, subsegments, for example of linear subsegments between the individual, predetermined orientation points. In order to avoid excessively high loads on the manipulator or on the automation system, it may be advantageous or necessary to smooth the movements according to the individual subsegments in order to eliminate contour creases, ie only c ⁰ continuous transitions.

It is therefore desirable to provide a method, for example as part of the NC firmware, which produces a smooth (in particular c ² -steady) contour.

Disclosure of the invention

According to the invention, a method for providing a movement contour for a manipulator along a course of predefined orientation points as well as a computing unit and a computer program for carrying it out with the features of the independent patent claims are proposed. Advantageous embodiments are the subject of the dependent claims and the following description.

The invention avoids abrupt changes in speed and / or changes in direction resulting in high accelerations and / or jerks, i. Acceleration changes, and therefore can lead to high loads for the manipulator or for the automation system. This also unwanted oscillations of the manipulator and / or the automation system, which lead to mechanical loads and / or reduce precision in the orientation, positioning and / or movement of the manipulator and / or the automation system, avoided.

In one aspect, the invention relates to a method of providing a motion contour for a manipulator along a course of predetermined landmarks. The method includes calculating a plurality of filter points within a filter tolerance range around the landmarks such that each filter dot is located at a nearest landmark of the predetermined landmarks on an interior of the course of the landmarks with respect to a direction change. The method further comprises calculating a smoothed motion contour by means of a spline approximation from the filter points such that the smoothed motion contour extends within a smoothing tolerance range around the filter points.

The orientation points can be predetermined, for example, to set a desired course of a cutting contour and / or a milling contour, which is to be generated by means of the manipulator. In particular, the invention may be advantageous for providing at least partially curved movement contours, ie for movement contours which are not exclusively along one Straight line, although the invention is also applicable to a straight course of landmarks.

The calculation of the filter points can be done using any type of geometric filters that filter points can create such that the filter points based on the respective landmarks, but at least partially take a position deviating from the landmarks due to the filtering.

Within the scope of the invention, there are many points of interest (e.g., landmarks, filter points, and checkpoints). It should be noted that such a point is not just a 2- or 3-dimensional point in space, such as P = (x, y, z), but may be a multi-dimensional point. For example, in the NC area, a point not only includes the position of a tool - this is referred to as the TCP (tool center point) - but also the orientation of the tool. The orientation of a rotationally symmetric tool (milling cutter, laser beam, etc.) can e.g. are described by a directional vector in space Rho = (Rho_x, Rho_y, Rho_z). Such points are then 6-dimensional, i. P = (x, y, z, Rho_x, Rho_y, Rho_z). The orientation of a non-rotationally symmetric tool, e.g. The gripper of a robot is preferably described by a quaternion Q = (Qw, Qx, Qy, Qz) such that the points of the form P = (x, y, z, Qw, Qx, Qy, Qz), i. 7-dimensional.

The invention offers the advantage that motion contours can be provided which have smaller curvatures and / or smaller changes in curvature than motion contours provided by conventional methods. As a result, accelerations and / or jerks acting on the manipulator and / or on the entire automation system can be reduced at otherwise the same web speed.

Furthermore, the invention offers the advantage that according to the invention a better reproducibility can be achieved, i. that deviations between various provided movement contours, which are based on the same or similarly positioned landmarks, are less than provided by conventional methods motion contours. This advantage results in particular from the fact that according to the invention filtering, i. determining filter points, and smoothing by means of a spline approximation, which have a filter tolerance range or a smoothing tolerance range. This has the advantage, in particular in applications such as the line milling of a free-form surface, that a particularly high quality of a milling line constancy can be achieved since, according to the invention, the milling line constancy preferably essentially depends on a size or width of the smoothing tolerance range, but not on a size or width of the filter tolerance range. Compared to conventional methods in which, for example, only smoothing with a large smoothing tolerance range without prior filtering is used, according to the present invention, a much smaller smoothing tolerance range can be used or achieved, for which reason a higher milling line consistency can be achieved according to the invention.

In addition, the invention has the advantage that a movement contour can be provided which is continuous and twice continuously differentiable. In particular, a motion contour can be provided which is c ² continuous, ie that the second derivative of the motion contour is also continuous and therefore no abrupt changes of a curvature of the motion contour occur. This has the advantageous effect that the occurrence of abrupt changes in movement or changes in direction of a manipulator following the movement contour can be avoided particularly effectively. In particular, a more homogeneous velocity profile and / or a more homogeneous movement can be achieved in this way than with conventional methods, which often rely only on providing filter points and in which the provided motion contour corresponds to a c1-continuous filter point curve, ie only the first derivative the motion contour is steady.

Preferably, a sum of the filter tolerance range and the smoothing tolerance range is at least locally, but preferably over the entire course of the predetermined orientation points, less than or equal to a predetermined total tolerance range around the predetermined orientation points. This has the advantage that any given total tolerance range can be divided into the filter tolerance range and the smoothing tolerance range. Since, for example, only the smoothing tolerance range is decisive for a milling line constancy, a significantly higher milling line constancy can thus be achieved than would be possible if only a smoothing occurs in which the smoothing tolerance range is equal to the total tolerance range. In addition, it can be ensured that, despite the calculation of filter points and additionally performing a smoothing according to the invention a predetermined tolerance range or total tolerance range can be maintained. Particularly preferably, the filter tolerance range and the smoothing tolerance range are selected such that the filter tolerance range is significantly greater than the smoothing tolerance range. For example, the filter tolerance range and the smoothing tolerance range may each be 0.5 times the total tolerance range. Preferably, the filter tolerance range is 0.6 times and the smoothing tolerance range is 0.4 times the total tolerance range. More preferably, the filter tolerance range is 0.7 times and the smoothing tolerance range is 0.3 times the total tolerance range. More preferably, the filter tolerance range is 0.8 times and the smoothing tolerance range is 0.2 times the total tolerance range. Most preferably, the filter tolerance range is 0.9 times and the smoothing tolerance range is 0.1 times the total tolerance range. This has the advantage that despite a large total tolerance range, a small smoothing tolerance range and thus a high milling line constancy can be achieved.

Preferably, the filtering points are calculated by means of an average filter or a moving average. The mean value filter or the moving average is in particular a geometry filter, which is pushed over the course of the landmarks or is applied to the course of the landmarks. The mean value filter generates at least one filter point for each landmark. The use of a mean value filter for calculating the filter points has the advantage that the calculation of filter points can be done in a particularly simple manner and / or with little computational effort. Particularly preferably, the filter points are calculated in such a way that there are two, three or more filter points between two consecutive orientation points.

Preferably, the calculation of a filter point of the plurality of filter points for the nearest landmark takes place taking into account a region of the course of the given landmarks surrounding the nearest landmark. In particular, a radius of curvature and / or a bend angle between connection vectors of the nearest landmark to adjacent landmarks can be taken into account. Preferably, a length of the moving average or the mean value filter can be adapted to the radius of curvature and / or the bend angle. For example, at a small or acute kink angle, a short filter length may be appropriate to ensure positioning of the calculated filter point within the filter tolerance range, while at long kink angles a long filter length may be used without positioning the calculated filter point the filter tolerance range leaves.

Preferably, the length of the filter is automatically determined or fixed. In this case, the predefined orientation points and the filter tolerance range particularly preferably determine the length of the filter and thus a behavior of the filter. An exemplary algorithm for determining the filter is explained in the description of the figures.

Preferably, the calculation of a filter point for the nearest landmark takes place taking into account at least one neighboring landmark of the nearest landmark. In particular, several neighboring landmarks can be taken into account for the calculation of a filter point for a particular landmark. For example, the moving average or the mean value filter may extend beyond the nearest landmark and at least one, preferably several, neighboring landmarks. This has the advantage that a homogeneous course of the filter points can be achieved, since in the positioning or calculation of the filter points a larger area of the course of the landmarks is taken into account than in a case in which only the nearest landmark is taken into account for which one Filter point to be created. Preferably, the filter points are calculated such that the filter points are at regular intervals, i. equidistant, are arranged.

The spline approximation preferably approximates a profile of the filter points by means of a spline curve. This has the advantage that, in addition to the use of the mean value filter or for the calculation of the filter points, a further smoothing takes place on the basis of the filter points. This offers in particular the advantage that, although the course of the filter points may be discontinuous and / or may not be continuously differentiable or may only be continuously differentiable or c ¹ -continuous, by a subsequent approximation or smoothing by means of the spline Approximation provided motion contour can be provided as a c ² continuous function. In other words, a movement contour based on the filter points can be achieved by the spline approximation of the course of the filter points, which is continuous even in its second derivative. Preferably, the filter points are arranged at equal intervals, ie equidistant.

Preferably, the spline curve is formed by means of a plurality of control points, the control points being calculated on the basis of the filter points. In other words, based on the filter points, the control points are calculated, which in turn influence the spline curve and / or at least partially determine and / or at least partially determine. This is a particularly effective way to approach or smooth the profile of the filter points by means of a spline approximation. The control points are points that influence the course of the spline curve, whereby the spline curve does not necessarily run through the control points themselves. For a spline curve or a spline nth degree at least n + 1 checkpoints must be provided. This offers the advantage that a particularly smooth or smoothed motion contour can be achieved with little computational effort by combination of the calculation of filter points, for example by means of an average filter, and the use of a spline for the provision. The spline curve and thus also the smoothed motion contour thus do not necessarily run through the control points and / or through the filter points. In particular, a smoothed motion contour can be designed in such a way that it does not extend through a control point or through a filter point.

Preferably, the spline curve is formed or calculated in such a way that the spline curve is arranged within, in particular completely inside, the smoothing tolerance range. For example, the spline curve may be calculated using an iterative method, for example, the iterative process being continued until the entire spline curve is located within the smoothing tolerance range. This ensures that the entire spline curve is within the smoothing tolerance range.

More preferably, the spline curve is a spline curve at least 3rd degree. This offers the advantage that a homogeneous motion contour can be provided in a particularly effective manner, which is c ² -continuous.

Most preferably, the spline curve is a B-spline curve. This has the advantage that resulting linear systems of equations are particularly easy to solve. Furthermore, due to local characteristics, a B-spline curve can be changed in a simple manner by an optionally subsequent shifting of control points.

An arithmetic unit according to the invention, e.g. a control unit of a milling machine is, in particular programmatically, adapted to perform a method according to the invention.

The implementation of the method in the form of a computer program, for example, NC firmware of an NC-controlled machine is advantageous because this causes very low costs, especially if an executive controller is still used for other tasks and therefore already exists. Suitable data carriers for providing the computer program are in particular magnetic, optical and electrical memories, such as e.g. Hard drives, flash memory, EEPROMs, DVDs, etc. It is also possible to download a program via computer networks (Internet, intranet, etc.).

Further advantages and embodiments of the invention will become apparent from the description and the accompanying drawings.

It is understood that the features mentioned above and those yet to be explained below can be used not only in the particular combination indicated, but also in other combinations or in isolation, without departing from the scope of the present invention.

The invention is illustrated schematically by means of exemplary embodiments in the drawing and will be described in detail below with reference to the drawing.

list of figures

• 1A to 1D show in a schematic representation the calculation of filter points according to a preferred embodiment.
• 2 shows a schematic representation of the calculation of filter points according to a second preferred embodiment.
• 3 shows a schematic representation of the calculation of filter points according to a third preferred embodiment.
• 4A to 4D show in a schematic representation a method for calculating a spline curve according to a preferred embodiment.
• 5 shows an exemplary course of a smoothed motion contour according to a preferred embodiment.
• 6 to 8th show by means of a course of landmarks preferred filtering options.

Detailed description of the drawing

Based on 1A to 1D is based on a history 10 from predetermined orientation points Q, or Q1 to QN, a calculation of filter points F, or F1 to FN, according to a preferred embodiment of the invention explained. To calculate the filter points F, a geometric filter is used, which is used as a mean value filter 12 is trained. The mean value filter 12 has a length L, wherein in the in 1A present situation of the mean value filter 12 two half-segments 12a and 12b having a respective length of L / 2.

The mean value filter extends in 1A between the landmarks Q1 and Q2 such that the mean value filter 12 along connecting lines 14 or connection vectors 14 runs, the adjacent landmarks of the landmarks Q1 to Q3 each connect in a straight line. The connecting lines 14 serve only to illustrate and are not required for the provision of a smoothed motion contour.

The mean value filter 12 calculates a (preferably arithmetic) mean over its length as a filter point (eg F1). As in the in 1 Case shown the course of the average filter 12 between Q1 and Q2 is rectilinear, the calculated filter point is also on the connecting line 14 between the landmarks Q1 and Q2. According to the in the 1A to 1D the embodiment shown has the mean value filter 12 a length L which is shorter than a distance between two adjacent landmarks Q1 to Q3.

1B shows a further step in which the filter point F1 has already been calculated and placed and now another filter point F2 is to be calculated along the course of the landmarks Q1 to Q3. According to 1B The mean value filter 12 extends to a part along the connecting line 14 between the landmarks Q1 and Q2 and, on the other hand, along the connecting line 14 between the landmarks Q2 and Q3. At landmark Q2, the course of the landmarks makes Q1 to Q3, and hence the gradient of the average filter 12 a kink with a kink angle a. Since in this case the mean value filter does not extend exclusively along a straight line, but runs over the bend (change of direction), the calculation of the filter point F2 leads to a positioning of the filter point F2 away from the connecting line 14 namely, on an inner side of the course of the landmarks Q1 to Q3 with respect to the change of direction. The length L of the mean value filter 12 depends on the bending angle α. The sharper or smaller the angle α, the smaller the length L of the average filter is preferably 12 , This can prevent that from passing through the mean value filter 12 calculated filter points are too far away from the nearest landmark Q2 and, in particular, are not placed outside a filter tolerance range.

Also in 1C showing a more advanced process of calculating the filter values, the average filter extends 12 over the kink at landmark Q2, so that in this case too the mean value filter positions a filter point F3 on the inside of the course with respect to the change of direction.

In the same way, the calculation or positioning of the filter point F4 takes place in FIG 1D , In 1D can also be seen from a course of the filter points F1 to F4 that the filter points F1 to F4 follow a rounded course, which has no hard corners, such as the course of the landmarks Q1 to Q3.

2 shows a further preferred embodiment in which for the calculation of a filter point FK of the plurality of filter points F1 to FN in each case a plurality of orientation points Q2 to Q6 is taken into account. For this purpose, the mean value filter extends 12 take into account the majority of landmarks Q2 to Q6. In this way, a single filter point can be calculated from a plurality of orientation points Q2 to Q6. Alternatively, however, a plurality of filter points F1 to FN, the plurality being equal to or larger than the plurality of landmarks Q1 to Q7. In other words, the number of filter points may be greater than, equal to or less than the number of landmarks. Even if a plurality of orientation points Q2 to Q6 are taken into account or used in the calculation of a specific filter point FK, so that, for example, the mean value filter extends over it or detects it, then further filter points FK can also be calculated which also at least part of the already take into account landmarks Q2 to Q6.

The calculated filter point FK results from the averaging on an inner side with respect to a change in direction of the course of the predetermined orientation points Q1 to Q7, the direction change of the profile being determined at the orientation point Q4 closest to the filter point FK (see FIG 2 ).

Further shows 2 also a schematically illustrated filter tolerance range 16 , If the orientation points Q1 to Q7 are arranged along a one-dimensional course in a two-dimensional plane, the filter tolerance range 16 For example, be arranged as a tolerance band around the course of the landmarks Q1 to Q7 around. If the orientation points Q1 to Q7 are arranged along a one-dimensional course in a three-dimensional volume, the filter tolerance range 16 For example, be arranged as a filter tube around the course of the landmarks Q1 to Q7 around. The filter tolerance range 16 sets a range around the course of the landmarks Q1 to Q7 around, in which the calculated filter points FK are to be placed, so that the desired smoothed motion contour remains within a predetermined total tolerance range. Preferably, therefore, is the filter tolerance range 16 smaller than the total tolerance range. This also allows the smoothing tolerance range (not shown) to be out of the filter tolerance range 16 can extend or expand on the side facing away from the course of the landmarks Q1 to Q7, without necessarily leaving the total tolerance range.

3 shows a further embodiment for the calculation of the filter points, wherein it is ensured that the filter points F1 and F2 are arranged within the filter tolerance range. This is taken into account or ensured in particular by the fact that at acute or small bending angles, such as at the orientation point Q2, the mean value filter 12 has a smaller length L or the half segments 12a and 12b have a smaller length L / 2 than at larger buckling angles, such as at the landmark Q3. As a result, it can be easily avoided that at acute buckling angles, a distance between the calculated filter point F1 and the nearest orientation point Q2 becomes so great that the filter point F1 is positioned outside the filter tolerance range. In other words, it can be ensured that the distance between a filter point and the nearest landmark is less than or equal to the maximum allowable distance according to the filter tolerance range.

Also is in 3 clearly recognizable that the filter points F1 and F2 are each arranged on the inside of the course of the landmarks Q1 to Q4, that are each arranged on an inner side of the bending angle at the nearest landmark.

Based on 4A to 4D is an example of a method for calculating a spline curve 20 , in particular a B-spline curve, based on the filter points F explained, but the invention is not limited to this example.

wobei P₀,..,P_n die Kontrollpunkte der Spline-Kurve bezeichnen und u den Spline-Parameter bezeichnet. Der Term N_i,0(u) bezeichnet B-Spline-Basisfunktionen, welche durch die folgenden Zusammenhänge rekursiv definiert sind: $$N_{i\mathrm{,0}}\left(u\right)=\{\begin{array}{cc}1& U_i\le u\le U_{i+1}\\ 0& sonst\end{array}$$

$$N_{i\text{,}p}\left(u\right)=\frac{u-U_i}{U_{i+p}-U_i}{N}_{i\text{,}p-1}\left(u\right)+\frac{U_{i+p+1}-u}{U_{i+p+1}-U_{i+1}}{N}_{i+\mathrm{1,}p\mathrm{-}\text{1}}\left(u\right)$$

wobei U_i Knotenpunkte des Knotenvektors $\overrightarrow{U}=\left\{U_0\mathrm{,...,}{U}_m\right\}$

mit U_i ≤ U_i+1 bezeichnen.A B-spline curve of degree p is defined by: $$\overrightarrow{C}\left(u\right)={\displaystyle \underset{i=0}{\overset{n}{\Sigma }}{N}_{i\text{.}p}\left(u\right){\overrightarrow{P}}_i}$$

where P ₀ , .., P _n denote the control points of the spline curve and u denotes the spline parameter. The term N _{i, 0} (u) denotes B-spline basis functions, which are recursively defined by the following relationships: $$N_{i\mathrm{,\; 0}}\left(u\right)=\{\begin{array}{cc}1& U_i\le u\le U_{i+1}\\ 0& sOnst\end{array}$$

$$N_{i\text{.}p}\left(u\right)=\frac{u-U_i}{U_{i+p}-U_i}{N}_{i\text{.}p-1}\left(u\right)+\frac{U_{i+p+1}-u}{U_{i+p+1}-U_{i+1}}{N}_{i+\mathrm{1,}p\mathrm{-}\text{1}}\left(u\right)$$

where U _i nodes of the node vector $\overrightarrow{U}=\left\{{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="DE102017200084A1\_0034.png,DE102017200084A1\_0036.png"\; state="\{\{state\}\}">U</figure-callout>}}_0\mathrm{,\; ...,}{U}_m\right\}$

with U _i ≤ U _{i + 1} .

sind somit die B-Spline-Basisfunktionen N_i,p(u) eindeutig bestimmt. Die Anzahl der Knotenpunkte U_i beläuft sich auf m + 1 und die Anzahl der Kontrollpunkte P_i auf n + 1, wobei m , n und der Grad p des Splines dem Zusammenhang m = n + p + 1 genügen.Through the node vector $\overrightarrow{U}$

Thus, the B-spline basis functions N _{i, p} (u) are uniquely determined. The number of nodes U _i is m + 1 and the number of control points P _i is n + 1, where m, n and the degree p of the spline satisfy the relationship m = n + p + 1.

mit den m + 1 Knotenpunkten U_i und der Spline-Kurve 20. Die Spline-Kurve 20 bzw. B-Spline-Kurve $\overrightarrow{C}\left(u\right)$

für U₀ ≤ u ≤ U_m ist dabei durch den Knotenvektor $\overrightarrow{U}$

und die Kontrollpunkte P_i eindeutig bestimmt. Die Spline-Kurve 20 startet im Kontrollpunkt P₀ und endet im Kontrollpunkt P_n, wenn der Knotenvektor $\overrightarrow{U}$

sowohl an seinem Beginn als auch an seinem Ende jeweils eine Anzahl von p + 1 gleichen Knotenpunkten U_i aufweist. 4A shows an exemplary course of the n + 1 control points P _i , the node vector $\overrightarrow{U}$

with the m + 1 nodes U _i and the spline curve 20 , The spline curve 20 or B-spline curve $\overrightarrow{C}\left(u\right)$

for U ₀ ≤ u ≤ U _m is the node vector $\overrightarrow{U}$

and the control points P _i uniquely determined. The spline curve 20 starts at the control point P ₀ and ends at the control point P _n when the node vector $\overrightarrow{U}$

has at its beginning as well as at its end in each case a number of p + 1 identical nodes U _i .

erfolgt gemäß dem erläuterten Beispiel anhand der vorgegebenen Orientierungspunkte Q, welche in 4B als Q_k mit k = 0,.., r dargestellt sind. Insbesondere zeigt 4B den Zusammenhang zwischen den vorgegebenen Orientierungspunkten Q_k und dem Knotenvektor $\overrightarrow{U}\text{,}$

welcher die Knotenpunkte U₀ bis U_r+6 umfasst. Die Knotenpunkte werden dabei, abgesehen von den gleichen Knotenpunkten am Beginn und am Ende des Knotenvektors $\overrightarrow{U}\text{,}$

entsprechend den jeweiligen Abständen zwischen den aufeinanderfolgenden Orientierungspunkten Q_k gesetzt bzw. bestimmt. Beispielsweise haben dabei die Knotenpunkte U_i die folgende Form: $$U_0=U_1=U_2=U_3=0$$

$$U_i=U_{i-1}+\left|Q_{i-3}-Q_{i-4}\right|\text{, }i=\mathrm{4,..,}r+3$$

$$U_{r+6}=U_{r+5}=U_{r+4}=U_{r+3}$$

The creation of the node vector $\overrightarrow{U}$

takes place according to the illustrated example on the basis of the predetermined orientation points Q, which in 4B are represented as Q _k with k = 0, .., r. In particular shows 4B the relationship between the given landmarks Q _k and the node vector $\overrightarrow{U}\text{.}$

which comprises the nodes U ₀ to U _{r + 6} . The nodes are thereby, apart from the same nodes at the beginning and at the end of the node vector $\overrightarrow{U}\text{.}$

is set or determined according to the respective distances between the successive landmarks Q _k . For example, the nodes U _{i have} the following form: $${\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="DE102017200084A1\_0034.png,DE102017200084A1\_0036.png"\; state="\{\{state\}\}">U</figure-callout>}}_0=U_1={\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102017200084A1\_0032.png"\; state="\{\{state\}\}">U</figure-callout>}}_2={\mathrm{<figure-callout\; id="3"\; label="U"\; filenames="DE102017200084A1\_0033.png,DE102017200084A1\_0034.png"\; state="\{\{state\}\}">U</figure-callout>}}_3=0$$

$$U_i=U_{i-1}+\left|Q_{i-3}-Q_{i-4}\right|\text{.}i=\mathrm{4,\; ..,}\mathrm{<figure-callout\; id="3"\; label="r\; +"\; filenames="DE102017200084A1\_0033.png,DE102017200084A1\_0034.png"\; state="\{\{state\}\}">r\; </figure-callout>}+3$$

$$U_{r+6}=U_{r+5}=U_{r+4}=U_{r+3}$$

In other words, the distances between the successive nodes U _i and U _{i + 1 are determined} according to the respective distances between the successive landmarks Q _i and Q _{i + 1} .

Das beispielhaft verwendete Geometriefilter ist dabei ein Mittelwertfilter, welches über das Polygon bzw. über den Verlauf der Orientierungspunkte Q₀ bis Q_r geschoben wird. Dabei wird eine Mehrzahl von Filterpunkten F bzw. F_kf, d.h. von F₀ bis F_nf, erzeugt, wobei die Filterpunkte F₀ bis F_nf entlang eines Verlaufs einer Filterpunktkurve liegen, die durch die Kreise in 4C dargestellt ist. Die Länge des Filters 12 (nicht gezeigt) wird dabei derart verändert, dass an jedem Orientierungspunkt ${\overrightarrow{Q}}_i$

der zugehörige Filterpunkt F_kf nicht außerhalb des Filtertoleranzbereichs 16 (siehe 2) liegt. Mit anderen Worten genügen die Filterpunkte der Bedingung: $$\left|Q_k-F_{kf}\right|\le E_f\text{,}$$

wobei E_f den Filtertoleranzbereich um die Orientierungspunkte herum bezeichnet. 4C shows a schematic representation of the relationship between the filter points F, the landmarks Q and the node vector $\overrightarrow{U}\text{,}$

The geometry filter used by way of example is an average value filter which is pushed over the polygon or over the course of the orientation points Q ₀ to Q _r . In this case, a plurality of filter points F and F _kf , ie, from F ₀ to F _nf , generated, wherein the filter points F ₀ to F _nf along a curve of a filter point curve are, by the circles in 4C is shown. The length of the filter 12 (not shown) is thereby changed so that at each landmark ${\overrightarrow{Q}}_i$

the associated filter point F _kf not outside the filter tolerance range 16 (please refer 2 ) lies. In other words, the filter points satisfy the condition: $$\left|Q_k-F_{kf}\right|\le e_f\text{.}$$

where E _f denotes the filter tolerance range around the landmarks.

Further shows 4C for some of the filter points F _kf, the associated parameter values u _{kf of} some filter points F _kf on the node vector $\overrightarrow{U}\text{,}$

ist dabei wie mit Bezug auf 4C erläutert berechnet bzw. vorgegeben, wobei der Kotenvektor $\overrightarrow{U}$

aus den Knotenpunkten U₀ bis U_m besteht. Für die Berechnung der Spline-Kurve 20 bzw. der B-Spline-Kurve sind neben den Knotenvektor $\overrightarrow{U}$

auch Kontrollpunkte erforderlich, weshalb die Kontrollpunkte P₀ bis P_n mit n = m - 4 auf Basis der Filterpunkte F berechnet werden. Gemäß dem erläuterten Beispiel werden die Kontrollpunkte P₀ bis P_n durch das Lösen des folgenden, überbestimmten Gleichungssystems bestimmt: $$\overrightarrow{C}\left(u_{kf}\right)={\overrightarrow{F}}_{kf}$$

mit kf = 0,.., nf, oder anders ausgedrückt $${\displaystyle \sum _{i=0}^n{N}_{i\mathrm{,3}}\left(u_{kf}\right)}{\overrightarrow{P}}_i={\overrightarrow{F}}_{kf}$$

mit kf = 0,.., nf. Das überbestimmte Gleichungssystems kann mittels eines Verfahrens der linearen Ausgleichsrechnung gelöst werden, welches z.B. in dem Lehrbuch Stoer: „Numerische Mathematik 1“, Springer Verlag beschrieben ist.Based on 4D is the calculation of a smoothed motion contour by means of a spline approximation on the basis of the filter points F and the approaching of the course of the filter points F _kf by means of a spline curve 20 or a B-spline curve explained. The node vector $\overrightarrow{U}$

is like with respect to 4C explained calculated or given, wherein the Kotenvektor $\overrightarrow{U}$

consists of the nodes U ₀ to U _m . For the calculation of the spline curve 20 and the B-spline curve are in addition to the node vector $\overrightarrow{U}$

Also control points are required, which is why the control points P ₀ to P _n with n = m - 4 are calculated on the basis of the filter points F. According to the illustrated example, the control points P ₀ to P _{n are} determined by solving the following, overdetermined system of equations: $$\overrightarrow{C}\left(u_{kf}\right)={\overrightarrow{F}}_{kf}$$

with kf = 0, .., nf, or in other words $${\displaystyle \underset{i=0}{\overset{n}{\Sigma }}{N}_{i3}\left(u_{kf}\right)}{\overrightarrow{P}}_i={\overrightarrow{F}}_{kf}$$

kf = 0, .., nf The overdetermined system of equations can be solved by means of a method of linear compensation calculation, which is described for example in the textbook Stoer: "Numerical Mathematics 1", Springer Verlag.

zwischen der Spline-Kurve 20 und den Filterpunkten F_kf überprüft. Solange eine Maximalabweichung $$D^{\text{max}}=\underset{kf=\mathrm{0,..,}nf}{\text{max}}{D}_{kf}$$

kleiner als der Glättungstoleranzbereich ist, werden Knoten aus dem Knotenvektor $\overrightarrow{U}$

(und damit Kontrollpunkte) entfernt. Das Minimieren der Kontrollpunktanzahl ergibt in der Folge ein Entfernen kurzer NC-Sätze (Kompressoreigenschaft) und damit eine geringere Belastung der NC-Rechenzeit. Dies wirkt sich wiederum vorteilhaft auf die Geschwindigkeitsführung aus.From a solution of said, overdetermined system of equations, the control points P ₀ to P _{n result} . After the calculation of the control points P ₀ to P _n , the distances become $$D_{kf}=\left|\overrightarrow{C}\left(u_{kf}\right)-{\overrightarrow{F}}_{kf}\right|$$

between the spline curve 20 and the filter points F _kf checked. As long as a maximum deviation $$D^{\text{Max}}=\underset{kf=\mathrm{0,\; ..,}nf}{\text{Max}}{D}_{kf}$$

is less than the smoothing tolerance range, nodes become nodes from the node vector $\overrightarrow{U}$

(and thus checkpoints) away. The minimization of the number of control points results in the removal of short NC blocks (compressor characteristic) and thus a lower load on the NC computation time. This in turn has an advantageous effect on the speed control.

For example, the removal is done according to an algorithm described in Les Piegl, Wayne Tiller: "The Nurbs Book", Springer Verlag.

von der ursprünglichen Kurve C(u) in einem abgegrenzten Bereich um U_k. Für die Abweichung kann eine obere Schranke B_k angegeben werden. B_k hängt von der Kontrollpunkt- und Knotenverteilung ab. Im Detail gilt für einen B-Spline vom Grad 3 mit Einfachknoten $$\left|\stackrel{⌢}{C}\left(u\right)-C\left(u\right)\right|\le N_{k-\mathrm{2,3}}\left(u\right)B_k$$

The removal of a node U _k and the corresponding control point leads to a deviation of the new curve $\stackrel{⌢}{C}\left(u\right)$

from the original curve C (u) in a delimited area around U _k . For the deviation, an upper limit B _{k can be} specified. B _k depends on the control point and node distribution. In detail applies to a B-spline of degree 3 with simple nodes $$\left|\stackrel{⌢}{C}\left(u\right)-C\left(u\right)\right|\le N_{k-2.3}\left(u\right)B_k$$

It is important here that the two curves deviate only in the u-range in which the basic function N _k-2,3 (u) is different from zero, ie in the interval U _k-2 <= u <U _{k +2} .

With the above mathematical relationship can be determined before removing the node U _k , whether the new curve leaves the tolerance range E _b or not. If she leaves, the knot is not removable.

The bounds B _{k are} now calculated for all internal nodes U ₄ to U _m-4 . For the smallest B _k it is checked whether the curve leaves the tolerance range. If not, the node is removed. Then the new bounds B _{k are} calculated and the node with the smallest Bk is removed again. The process is repeated until no more nodes are removable.

Subsequently, the spline approximation can be performed with the remaining control points.

After a plurality of iteration steps, each calculating a spline curve 20 based on the reduced nodes and then removing nodes, there is a spline curve 20 or B-spline curve, which remains within the smoothing tolerance range with radius E _b around the filter points, without leaving the smoothing tolerance range.

4D shows a spline curve 20 or a B-spline curve with n + 1 control points P _i , which were calculated on the basis of the nf +1 filter points F _nf and a spline curve 20 determine the course of the filter points F _nf , so as to provide a smoothed motion contour 10 provide.

5 shows an exemplary course of a smoothed motion contour 18 along with the course of the landmarks Q1 to Q11. The smoothed motion contour 18 was provided by means of the filter points F1 to F15 calculated on the basis of the orientation points Q1 to Q11, a spline curve being based on or using the filter points F1 to F11 20 was calculated. The spline curve 20 includes several spline segments 20a which adjoin one another at junctions (not shown). The nodes may or may not necessarily coincide with the filter points. 4 clarifies that the smoothed motion contour 18 on an inner side of the course of the landmarks Q1 to Q11. By calculating the smoothed motion contour 18 using a spline approximation or spline curve 20 , the control points (not shown) were calculated on the basis of the filter points F1 to F15, a c ² -stetige motion contour 18 to be provided.

Based on 6 to 8th An example method for determining or calculating the filter or filter points is explained, but the invention is not restricted to this:

6 shows a point polygon with the landmarks Q ₁ to Q ₈ . In the first step, a maximum possible filter length ML _{k is} determined for each orientation point Q _k . In this filter length, the distance between Q _k and its associated pixel or filter point Fkf just has the predetermined value Ef. In the present example, the orientation point Q _{3 is assigned} a maximum possible filter length of ML ₃ = 0.6. On a less sharp kink, for example at Q ₅ , ML ₅ = 5.0. The determination of the ML _k is generally not analytically possible and is carried out by means of an iterative method. In places with small angle changes, ML _k can become arbitrarily large. To prevent this, an upper limit is expediently set for ML _k .

To further explain the algorithm is sufficient a one-dimensional representation of the facts, as in the 7 and 8th shown. On a u-scale (from which the node vector U is derived later), the distances of the landmarks Q _k are plotted as u-values, ie u _{k + 1} -u _k = | Q _{k + 1} -Q _k |. On this scale, the point Q3 is plotted as u ₃ , as well as the length ML ₃ = 0.6 and the respective filter point. The thin arrows represent the filter center. Filter points can be set as required.

The 7 and 8th now show the successive shifting of the filter from u ₁ to u ₈ . During the shift there are phases with constant, increasing and decreasing filter length. The phases are marked on the right with thick arrows.

row 1 : If u ₁ = 0, ML ₁ = 0 and the filter starts with L = 0 and grows. When the filter length has grown to 1.0, its right edge reaches the location u ₁ = 1.0. Since ML ₁ = 4.0> 1.0, the filter may continue to grow.

row 2 : The right edge reaches u ₃ = 1.5 with a filter length of 1.5. The center of the filter (thin arrow) is at the position u = 0.75. If needed could be there as well as in line 1 an intermediate filter point can be generated. Since L = 1.5 is greater than ML ₃ = 0.6, the filter must now decrease.

row 3 : The filter decreases while its right edge stays on u ₃ . With a filter length of L = 1.0, the filter center reaches u ₂ = 1.0. There, a filter point F (open circle) is generated. The distance of this pixel F to Q ₂ is now smaller than Ef, since Ef would only result with a filter length of L = ML ₂ = 4.0.

row 4 : The filter continues to decrease until it reaches the required L = ML ₃ = 0.6.

row 5 : The filter is pushed over u ₃ with a constant length. There again a filter point is generated. This now has the distance Ef of Q ₃ , since L = ML ₃ = 0.6.

row 6 : The filter is pushed on with a constant length L = 0.6 until its left edge leaves u ₃ .

• Zeile 1: Die Filterlänge L wächst bei konstantem linkem Rand auf u₃. Die Filtermitte erreicht u₄. Dort wird ein Filterpunkt erzeugt. Der rechte Filterrand erreicht u₅. Die Filterlänge ist L = 1,0.
• Zeile 2: Da ML₅ = 5,0 größer ist als L, wächst L bei konstantem linkem Rand auf u₃ weiter an, bis der rechte Rand u₇ erreicht. In diesem Zustand ist L = 2,0 und die Filtermitte liegt zufällig bei u₅. Dort wird ein Filterpunkt erzeugt.
• Zeile 3: Wegen ML₅ = 1,0 muss jetzt die Filterlänge auf L = 1,0 abnehmen. Dies geschieht bei konstantem rechtem Rand auf u₅, bis L = 1,0
• Zeile 4: Das Filter wird bei konstanter Länge L = 1,0 über u₇ geschoben. Der rechte Rand erreicht die Endstelle u₈.
• Zeile 5: L nimmt bei konstantem rechtem Rand bei u₈ ab. Bei L = 0,7 könnte beispielsweise ein Zwischenfilterpunkt erzeugt werden.
• Zeile 6: Der Endpunkt ist erreicht. L hat auf 0 abgenommen. Der letzte Filterpunkt liegt exakt auf Q₈.

The sequel is in 8th shown:

• row 1 : The filter length L grows to u ₃ with a constant left edge. The filter center reaches u ₄ . There a filter point is generated. The right filter edge reaches u ₅ . The filter length is L = 1.0.
• row 2 Since ML ₅ = 5.0 is larger than L, L continues to grow to u ₃ at a constant left edge until the right edge reaches u ₇ . In this state L = 2.0 and the filter center happens to be at u ₅ . There a filter point is generated.
• row 3 : Due to ML ₅ = 1.0, the filter length now has to decrease to L = 1.0. This happens at constant right edge on u ₅ , until L = 1.0
• row 4 : The filter is pushed over u ₇ at a constant length L = 1.0. The right edge reaches the terminal u ₈ .
• row 5 : L decreases at constant right edge at u ₈ . For example, if L = 0.7, an intermediate filter point could be generated.
• row 6 : The endpoint is reached. L has decreased to 0. The last filter point is exactly on Q ₈ .

Claims (14)

A method of providing a manipulator motion contour (18) along a course of predetermined landmarks (Q) comprising the steps of: Calculating a plurality of filter points (F) within a filter tolerance range (16) around the orientation points (Q) such that each filter point (F) at a nearest orientation point (Q) of the predetermined orientation points (Q) at an inner side of the orientation of the landmarks (Q) Q) is arranged with respect to a change of direction; - Calculating a smoothed motion contour (18) by means of a spline approximation on the basis of the filter points (F) such that the smoothed motion contour (18) extends within a smoothing tolerance range around the filter points (F). Method according to Claim 1 wherein a sum of the filter tolerance range (16) and the smoothing tolerance range is at least in places, but preferably over the entire course of the predetermined orientation points (Q), less than or equal to a predetermined total tolerance range around the predetermined orientation points (Q). Method according to Claim 1 or 2 , wherein the calculation of the filter points (F) by means of an average filter (12). Method according to one of the preceding claims, wherein the calculation of a filter point (F) of the plurality of filter points (F) for the nearest landmark (Q) taking into account a region of the course of the predetermined landmarks (Q) surrounding the nearest landmark (Q). Method according to Claim 4 in which a size of the area taken into account in calculating a filter point (F) of the plurality of filter points (F) for the nearest landmark (Q) has a radius of curvature and / or a bend angle (a) of the course of the predetermined landmarks (Q) nearest landmark (Q). Method according to one of the preceding claims, wherein the calculation of the filter point (F) for the nearest landmark (Q) taking into account at least one adjacent landmark (Q) of the nearest landmark (Q). Method according to one of the preceding claims, wherein the spline approximation approximates a profile of the filter points (F) by means of a spline curve (20). Method according to Claim 7 wherein the spline curve (20) is preferably a spline curve (20) of at least the third degree and / or a B-spline curve. Method according to one Claim 7 or 8th in which the spline curve (20) is formed by means of a plurality of control points, the control points (P) being calculated on the basis of the filter points (F). Method according to Claim 9 wherein the spline curve (20) is calculated such that the spline curve (20) is located within the smoothing tolerance range about the filter points (F). Method according to one of the preceding claims, wherein the spline approximation is such that the smoothed motion contour (18) is continuously differentiable at least twice. Arithmetic unit which is adapted to carry out a method according to one of the preceding claims. Computer program, which causes a computing unit, a method according to one of Claims 1 to 11 when executed on the computing unit. Machine-readable storage medium with a computer program stored thereon Claim 13 ,

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