Abstract:

An algorithm is given for calculating the curvature of 3-dimensional curves from measurements made along the curve by a robot desiring to determine the curve.

It is well known that such curves are fixed by their curvature and torsion parameters measured in terms of the arc length along the curve. We have shown [1] that these parameters form a convenient characterization for use by robots, especially since the curvature and torsion can nicely be evaluated in terms of local Euler angles. However, in making such evaluations it becomes necessary to correctly position the normal vector which in turn determines the curvature, the latter being the reciprocal of the radius of the oscillating circle at a given point [2, p. 101]. In this paper we develop an algorithm for positioning this normal and for evaluating the oscillating circle's radius using the vector analysis formulation developed in [2].

[1] R. W. Newcomb and D. Panagiotopoulos, "Equations for Robot 3D Curve Determination Decisions," Proceedings of the 22nd IEEE Conference on Decision & Control, Vol. 3,San Antonio, December 16, 1983, pp. 1222 - 1223.

[2] I. D. Faux and M. J. Pratt, "Computational Geometry for Design and Manufacture," Ellis Horwood Ltd, Chichester, 1979.