Method for ascertaining a rough trajectory from a specified contour

Abstract

The invention relates to a method for ascertaining a rough trajectory from a specified contour for controlling a machine tool which has at least two mutually redundant drive devices for carrying out superimposed movements, wherein the contour is determined by a contour function which is defined in portions at least by contour nodal points P.sub.0-P.sub.n+1 with ascending indices and contour portion functions p.sub.0-p.sub.n assigned to the contour nodal points P.sub.0-P.sub.n+1 and has a contour starting nodal point P.sub.0, wherein the rough trajectory is determined by a rough trajectory function which is defined in portions by rough trajectory nodal points Q.sub.0 to Q.sub.n+1 with ascending indices and has a rough trajectory starting nodal point Q.sub.0, wherein the rough trajectory starting nodal point Q.sub.0 is equated to the contour starting nodal point P.sub.0 and then in a first iteration step, on the basis of the contour nodal points P.sub.j to P.sub.n+1, the index value k of which is greater than or equal to the index value j of the respective rough trajectory starting nodal point that contour nodal point P.sub.k which has the smallest possible index value k and the distance of which from the rough trajectory starting nodal point Q.sub.j still just satisfies a specified distance condition is ascertained, and in a second iteration step, a respective following rough trajectory nodal point Q.sub.j+1 which follows the respective rough trajectory starting nodal point Q.sub.j and lies on a connecting line between Q.sub.j and P.sub.k or between Q.sub.j and a centroid of the portion contour P.sub.j to P.sub.k is ascertained.

Claims

1. A method for controlling a machine tool having at least two mutually redundant drive devices for carrying out superimposed movements following a contour function, the method comprising: determining a specified contour for controlling the machine tool by the contour function defined in portions by contour nodal points (P.sub.0-P.sub.n+1) with ascending indices and contour portion functions (p.sub.0-p.sub.n) assigned to the contour nodal points (P.sub.0-P.sub.n+1) and has a contour starting nodal point (P.sub.0); determining a rough trajectory by a rough trajectory function defined in portions by rough trajectory nodal points (Q.sub.0-Q.sub.n+1) with ascending indices, the rough trajectory having a rough trajectory starting nodal point (Q.sub.0); equating the rough trajectory starting nodal point (Q.sub.0) to the contour starting nodal point (P.sub.0); carrying out an iteration process comprising a first iteration step and a second iteration step based on a respective rough trajectory starting nodal point (Q.sub.j) and beginning at the rough trajectory starting nodal point (Q.sub.0), wherein: the first iteration step comprises ascertaining, based on the contour nodal points (P.sub.j-P.sub.n) having an index value (k) greater than or equal to an index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), a contour nodal point (P.sub.k) having a lowest possible index value (k) and a distance of the contour nodal point (P.sub.k) from the rough trajectory starting nodal point (Q.sub.j) satisfies a specified distance condition, and the second iteration step comprises ascertaining a respective following rough trajectory nodal point (Q.sub.j+1) which follows the respective rough trajectory starting nodal point (Q.sub.j) and lies on a first connecting line between the respective rough trajectory starting nodal point (Q.sub.j) and the contour nodal point (P.sub.k) ascertained in the first iteration step, or lies on a second connecting line between the respective rough trajectory starting nodal point (Q.sub.j) and a centroid of a portion contour between the contour nodal point (P.sub.j) and the contour nodal point (P.sub.k), and the distance of the contour nodal point (P.sub.k) from the rough trajectory starting nodal point (Q.sub.j) corresponds to a factor-weighted distance of the contour nodal point (P.sub.k) ascertained in the first iteration step from the rough trajectory starting nodal point (Q.sub.j), wherein the factor is obtained from a quotient of trajectory length (s.sub.j) of the contour portion function (p.sub.j), the index value (j) of the trajectory length (s.sub.j) of the contour portion function (p.sub.j) is equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), and ascertaining a sum of trajectory lengths (s.sub.j-s.sub.k−1) of the contour portion functions (p.sub.j-p.sub.k−1) between the contour nodal point (P.sub.j) and the contour nodal point (P.sub.k) ascertained in the first iteration step, where the index value (j) of the contour nodal point (P.sub.j) is equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j); and directing the movement of one of the at least two mutually redundant drive devices based on the ascertained rough trajectory nodal point (Q.sub.j+1).

2. The method of claim 1, wherein the contour function is a spline.

3. The method of claim 2, wherein the spline is a first order spline, a third order spline, or fifth order spline.

4. The method of claim 1, wherein the specified distance condition comprises a first and a second distance subcondition, wherein the contour nodal point (P.sub.k) to be ascertained must satisfy at least one of the distance subconditions, wherein the first distance subcondition requires that, for the contour nodal point (P.sub.k) to be ascertained, a sum of the trajectory lengths (s.sub.j-s.sub.k) between the contour nodal point (P.sub.j), the index value (j) of the sum of the trajectory lengths (s.sub.j-s.sub.k) between the contour nodal point (P.sub.j) is equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), and the contour nodal point (P.sub.k) to be ascertained is less than or equal to a predetermined limit value (Δ) and a sum of the trajectory lengths (s.sub.j-s.sub.k+1) between the contour nodal point (P.sub.j), the index value (j) of the sum of the trajectory lengths (s.sub.j-s.sub.k+1) between the contour nodal point (P.sub.j) is equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), and the contour nodal point (P.sub.k+1) immediately following the contour nodal point (P.sub.k) to be ascertained is greater than the predetermined limit value (Δ), and wherein the second distance subcondition requires that, for the contour nodal point (P.sub.k) to be ascertained, the distance between the contour nodal point (P.sub.j), the index value (j) of the contour nodal point (P.sub.j) equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), and the respective rough trajectory starting nodal point (Q.sub.j) is less than or equal to half the predetermined limit value (Δ) and the distance between the contour nodal point (P.sub.k+1) immediately following the contour nodal point (P.sub.k) to be ascertained and the respective rough trajectory starting nodal point (Q.sub.j) is greater than half the predetermined limit value (Δ).

5. The method of claim 4, wherein the predetermined limit value (Δ) corresponds to a maximum displacement of one of the redundant drive devices.

6. The method of claim 1, wherein the rough trajectory function is further defined by respective rough trajectory portion functions (q.sub.0-q.sub.n) assigned to the rough trajectory nodal points (Q.sub.0-Q.sub.n+1) such that in the second iteration step, the respective rough trajectory portion function (q.sub.j) assigned to the respective rough trajectory starting nodal point (Q.sub.j) is formed by a linear function.

7. The method of claim 1, wherein the rough trajectory function is further defined by respective rough trajectory portion functions (q.sub.0-q.sub.n) assigned to the rough trajectory nodal points (Q.sub.0-Q.sub.n+1) generated via a spline interpolation of the rough trajectory nodal points (Q.sub.0-Q.sub.n).

8. A system for controlling a machine tool, the system comprising: the machine tool comprising at least two mutually redundant drive devices for carrying out superimposed movements following a contour function; and a computer numerical control (CNC) device configured to: determine a specified contour for controlling the machine tool by the contour function defined in portions by contour nodal points (P.sub.0-P.sub.n+1) with ascending indices and contour portion functions (p.sub.0-p.sub.n) assigned to the contour nodal points (P.sub.0-P.sub.n+1) and has a contour starting nodal point (P.sub.0), determine a rough trajectory by a rough trajectory function defined in portions by rough trajectory nodal points (Q.sub.0-Q.sub.n+1) with ascending indices, the rough trajectory having a rough trajectory starting nodal point (Q.sub.0), equate the rough trajectory starting nodal point (Q.sub.0) to the contour starting nodal point (P.sub.0), carry out an iteration process comprising a first iteration step and a second iteration step based on a respective rough trajectory starting nodal point (Q.sub.j) and beginning at the rough trajectory starting nodal point (Q.sub.0), wherein: the first iteration step comprises ascertaining, based on the contour nodal points (P.sub.j-P.sub.n) having an index value (k) greater than or equal to an index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), a contour nodal point (P.sub.k) having a lowest possible index value (k), and a distance of the contour nodal point (P.sub.k) from the rough trajectory starting nodal point (Q.sub.j) that satisfies a specified distance condition, and the second iteration step comprises ascertaining a respective following rough trajectory nodal point (Q.sub.j+1) which follows the respective rough trajectory starting nodal point (Q.sub.j) and lies on a first connecting line between the respective rough trajectory starting nodal point (Q.sub.j) and the contour nodal point (P.sub.k) ascertained in the first iteration step, or lies on a second connecting line between the respective rough trajectory starting nodal point (Q.sub.j) and a centroid of a portion contour between the contour nodal point (P.sub.j) and the contour nodal point (P.sub.k), and the distance of the contour nodal point (P.sub.k) from the rough trajectory starting nodal point (Q.sub.j) corresponds to a factor-weighted distance of the contour nodal point (P.sub.k) ascertained in the first iteration step from the rough trajectory starting nodal point (Q.sub.j), wherein the factor is obtained from a quotient of trajectory length (s.sub.j) of the contour portion function (p.sub.j), where the index value (j) of the trajectory length (s.sub.j) of the contour portion function (p.sub.j) is equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), and ascertaining a sum of trajectory lengths (s.sub.j-s.sub.k−1) of the contour portion functions (p.sub.j-p.sub.k−1) between a contour nodal point (P.sub.j) of the contour nodal points (P.sub.j-P.sub.n) and the contour nodal point (P.sub.k) ascertained in the first iteration step, where the index value (j) of the trajectory length (s.sub.j) of the contour portion function (p.sub.j) is equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), and direct the movement of one of the at least two mutually redundant drive devices based on the ascertained rough trajectory nodal point (Q.sub.j+1).

9. The system of claim 8, wherein the contour function is a spline.

10. The system of claim 9, wherein the spline is a first order spline, a third order spline, or fifth order spline.

11. The system of claim 8, wherein the specified distance condition comprises a first and a second distance subcondition, wherein the contour nodal point (P.sub.k) to be ascertained must satisfy at least one of the distance subconditions, wherein the first distance subcondition requires that, for the contour nodal point (P.sub.k) to be ascertained, a sum of the trajectory lengths (s.sub.j-s.sub.k) between the contour nodal point (P.sub.j), the index value (j) of which the sum of the trajectory lengths (s.sub.j-s.sub.k) between the contour nodal point (P.sub.j) is equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), and the contour nodal point (P.sub.k) to be ascertained is less than or equal to a predetermined limit value (Δ) and a sum of the trajectory lengths (s.sub.j-s.sub.k+1) between the contour nodal point (P.sub.j), the index value (j) of the sum of the trajectory lengths (s.sub.j-s.sub.k+1) between the contour nodal point (P.sub.j) is equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), and the contour nodal point (P.sub.k+1) immediately following the contour nodal point (P.sub.k) to be ascertained is greater than the predetermined limit value (Δ), and wherein the second distance subcondition requires that, for the contour nodal point (P.sub.k) to be ascertained, the distance between the contour nodal point (P.sub.j), the index value (j) of the contour nodal point (P.sub.j) equal to the index value (j) of the respective rough trajectory starting nodal point (Q.sub.j), and the respective rough trajectory starting nodal point (Q.sub.j) is less than or equal to half the predetermined limit value (Δ) and the distance between the contour nodal point (P.sub.k+1) immediately following the contour nodal point (P.sub.k) to be ascertained and the respective rough trajectory starting nodal point (Q.sub.j) is greater than half the predetermined limit value (Δ).

12. The system of claim 11, wherein the predetermined limit value (Δ) corresponds to a maximum displacement of one of the redundant drive devices.

13. The system of claim 8, wherein the rough trajectory function is further defined by respective rough trajectory portion functions (q.sub.0-q.sub.n) assigned to the rough trajectory nodal points (Q.sub.0-Q.sub.n+1) such that in the second iteration step, the respective rough trajectory portion function (q.sub.j) assigned to the respective rough trajectory starting nodal point (Q.sub.j) is formed by a linear function.

14. The system of claim 8, wherein the rough trajectory function is further defined by respective rough trajectory portion functions (q.sub.0-q.sub.n) assigned to the rough trajectory nodal points (Q.sub.0-Q.sub.n+1) generated via a spline interpolation of the rough trajectory nodal points (Q.sub.0-Q.sub.n).

Description

DRAWINGS

(1) Further advantages are revealed by the drawings and the associated description of the drawings. The drawings show exemplary embodiments of the invention. The drawings, description and claims contain numerous features in combination. A person skilled in the art will expediently also consider these features individually and combine them into meaningful further combinations.

(2) In the Figures:

(3) FIG. 1 shows a schematic diagram of an iteration of a method according to the invention for ascertaining a rough trajectory, and

(4) FIG. 2 shows a schematic diagram of a specified contour and an associated rough trajectory ascertained by means of the method according to the invention.

(5) The method according to the invention is described below by way of example on the basis of a trajectory division of a two-dimensional contour which is defined in an (X, Y) plane, wherein generalisation to other dimensions is, of course, possible. Trajectory division proceeds for example for a machine tool which has two redundant drive devices for each direction of movement. The contour may be described, for example, by first, third or fifth order splines, as is conventional for the operation CNC machine tools. Other contour descriptions may, however, also be available.

(6) A contour portion j is defined by a starting point or contour nodal point P.sub.j=(x.sub.j, y.sub.j), a parameterisation interval [0,s.sub.j] and a contour portion function p.sub.j, wherein s.sub.j is the arc length of the contour portion and the contour portion function p.sub.j describes the course of the contour portion. In the examples according to FIGS. 1 and 2, the functions p.sub.j are linear functions.

(7) The contour for which the rough trajectory is to be ascertained is accordingly defined by a function (P.sub.j, s.sub.j, p.sub.j), j=n.

(8) It should be noted that, instead of parameterisation on the basis of trajectory length s.sub.j, it is also possible to select any desired other parameterisation, for example parameterisation with time or in Cartesian x, y coordinates.

(9) The aim now, with the assistance of the method according to the invention, is to ascertain a smoothed rough trajectory (Q.sub.j, s.sub.j, q.sub.j), j=n for controlling the low-dynamic drive devices, such that the distance of this rough trajectory does not exceed a specified limit value. The rough trajectory must thus satisfy the following condition:
∥p.sub.j(s)−q.sub.j(s)∥≤Δ,s∈[0,s.sub.j],j=0, . . . ,n.

(10) The method according to the invention is an iterative method. A rough trajectory starting nodal point Q.sub.0 is firstly equated to the starting nodal point P.sub.0 of the contour. At least the following two steps are carried out within an iteration j.

(11) In a first step, a first contour nodal point P.sub.k with k j which satisfies either the first or the second of the following two conditions is sought:

(12) $\begin{array}{cc}\underset{l=j}{\overset{k}{.Math.}}{s}_l\le \Delta ,\underset{l=j}{\overset{k+1}{.Math.}}{s}_l>\Delta ,& \left(1\right)\end{array}$

(13) $\begin{array}{cc}{.Math..Math.P_k\left(s\right)-Q_j\left(s\right).Math..Math.}_p\le \frac{\Delta }{2},{.Math..Math.P_{k+1}\left(s\right)-Q_j\left(s\right).Math..Math.}_p>\frac{\Delta }{2}.& \left(2\right)\end{array}$

(14) Just one of the two conditions 1 or 2 is regularly applied for one pass of the method. The condition to be applied may be permanently set or be selected on the basis of contour characteristics such as continuity, curvature behaviour etc. It is also conceivable for one of the two conditions to be applied in portions.

(15) If no such point can be located for condition (1), or if k=j for condition (2), the contour nodal point P.sub.k to be ascertained is defined as the contour nodal point P.sub.j+1.

(16) FIG. 1 illustrates ascertaining the contour nodal point P.sub.k with the lowest possible index value k for p=∞, i.e. the maximum norm. By calculating the distance according to the maximum norm, a search window F within which the contour nodal point to be ascertained must be situated has the shape of a square with edge length Δ. As is clearly apparent from FIG. 1, point P.sub.k is still just within the search window F, while the next point P.sub.k+1 is already situated outside the search window. In this respect, the contour nodal point P.sub.k which still just satisfies a distance norm is sought, while the next point P.sub.k+1 already no longer satisfies said norm. In practical terms, the point P.sub.k+1 is firstly sought as the point which breaches distance condition and thus identifies the preceding point P.sub.k.

(17) In a second iteration step, the equation

(18) $S=\underset{l=j}{\overset{k-1}{.Math.}}{s}_l,$
calculates the sum S of the trajectory lengths s.sub.j to s.sub.k of the contour portion functions p.sub.j to p.sub.k between the contour nodal point P.sub.j, the index value j of which is equal to the index value j of the respective rough trajectory starting nodal point Q.sub.j and the contour nodal point P.sub.k ascertained in the first iteration step. The summed trajectory lengths s.sub.j to s.sub.k are denoted Σs.sub.l in FIG. 1. On the basis of S, s.sub.j, Q.sub.j and P.sub.k, a following rough trajectory nodal point

(19) $Q_{j+1}=Q_j+\frac{s_j}{s}\left(P_k-Q_j\right)$
and an assigned rough trajectory portion function

(20) $q_j\left(s\right)=Q_j+\frac{s}{s_j}\left(Q_{j+1}-Q_j\right)$
are ascertained.

(21) The dashed line which connects the rough trajectory starting nodal point Q.sub.j and the following rough trajectory nodal point Q.sub.j+1 represents the rough trajectory portion function q.sub.j.

(22) The next iteration j+1 is then carried out, wherein the value of the following rough trajectory nodal point Q.sub.1+1 ascertained in iteration j forms the new rough trajectory starting nodal point in the next iteration j+1.

(23) FIG. 2 shows is a further contour (P.sub.j, s.sub.j, p.sub.j) for which a rough trajectory (Q.sub.j, Q.sub.j) is likewise ascertained by the method according to the invention.

(24) Ascertaining respective rough trajectory nodal points Q.sub.j+1 on the basis of a rough trajectory starting nodal point Q.sub.j by locating a contour nodal point P.sub.k still just within the search window F and the associated rough trajectory portion function q.sub.j(s) here proceeds in the same manner as has been described with reference to FIG. 1.