Polynomial and spline interpolation of machine tool orientations

• US 20030125830A1
• Filed: 12/23/2002
• Published: 07/03/2003
• Est. Priority Date: 12/21/2001
• Status: Active Grant

• Current Assignee: Siemens AG
• Original Assignee: Siemens AG
• Inventors: Munz, Martin
• Granted Patent: US 6,735,495 B2
• Time in Patent Office: Days
• US Class Current: 700/189
• CPC Class Codes: G05B 19/4103 Digital interpolation
• CPC Class Codes: G05B 2219/34089 Parametric, polynomial representation of path per axis as function of time
• CPC Class Codes: G05B 2219/34135 Spline
• CPC Class Codes: G05B 2219/34142 Polynomial
• CPC Class Codes: G05B 2219/50349 Obtain normal vector of two points on surface, interpolate in between

Abstract

In a method and apparatus for guiding the motion of a moveable machine element, the orientation of the machine element is defined by an orientation vector that can be programmed in each set. The orientation vector can be obtained by a linear great circle interpolation in a plane spanned by a start vector and an end vector. In more general cases, polynomials can be used in the program, enabling an almost arbitrary definition of the path that determines how the end vector is obtained. The interpolated orientation vector can also be rotated out of the plane by an arbitrary angle. An extended interpolation permits a representation of orientation changes on a conical surface having an arbitrary orientation in space. This enables the orientation axes to move across several sets with continuous velocity and acceleration.

Claims

1. A control method for guiding a motion of a movable machine element of a numerically controlled industrial processing machine, such as a machine tool, a robot and the like, comprising the steps of:

orienting the machine element in a workspace using orientation vectors;

subdividing an orientation and a motion path of the machine element into a plurality of sequential contiguous motion segments;

changing the orientation of the machine element within a motion segment by tilting an orientation vector from a start vector to an end vector about a first angle in a plane spanned by the start vector and end vector and about a second angle perpendicular to the plane, and

interpolating the first and second angles of the orientation vectors over several motion segments.

2. The control method of claim 1, wherein the first and second angles are interpolated by a polynomial interpolation.

3. The control method of claim 1, wherein the first and second angles are interpolated by a spline interpolation.

4. The control method of claim 1, wherein the first and second angles are interpolated on a surface of a cone.

5. The control method of claim 4, wherein the first angle represents a rotation angle of an orientation vector about a center axis of the cone and the second angle represents an apex angle of the cone.

6. The control method of claim 2, wherein polynomial coefficients used in the polynomial interpolation are selected so that the orientation vectors of the machine elements move with at least one of continuous velocity and continuous acceleration.

7. The control method of claim 3, wherein spline coefficients used in the spline interpolation are selected so that the orientation vectors of the machine elements move with at least one of continuous velocity and continuous acceleration.

8. A numerical controller for guiding a motion of a movable machine element of a numerically controlled industrial processing machine, such as a machine tool, a robot and the like, comprising:

means for orienting the machine element in a workspace using orientation vectors;

means for subdividing an orientation and a motion path of the machine element into a plurality of sequential contiguous motion segments;

means for changing the orientation of the machine element within a motion segment by tilting an orientation vector from a start vector to an end vector about a first angle in a plane spanned by the start vector and end vector and about a second angle perpendicular to the plane, and means for interpolating the first and second angles of the orientation vectors over several motion segments.

9. The controller of claim 8, wherein the first and second angles are interpolated by a polynomial interpolation.

10. The controller of claim 8, wherein the first and second angles are interpolated by a spline interpolation.

11. The controller of claim 8, wherein the first and second angles are interpolated on a surface of a cone.

12. The controller of claim 11, wherein the first angle represents a rotation angle of an orientation vector about a center axis of the cone and the second angle represents an apex angle of the cone.

13. The controller of claim 9, wherein polynomial coefficients used in the polynomial interpolation are selected so that the orientation vectors of the machine elements move with at least one of continuous velocity and continuous acceleration.

14. The controller of claim 10, wherein spline coefficients used in the spline interpolation are selected so that the orientation vectors of the machine elements move with at least one of continuous velocity and continuous acceleration.