Robot arm motion design by Frenet-Serret and Rotation Minimizing Frames

Abstract

The purpose of this paper is to represent that the techniques of computer aided geometric design such as spatial rational frames could be applied to robot kinematics for arm motion design and to computer graphics for generating smooth animation of a rigid body specially in complicated sets of control points and orientations. In application requiring control of the orientation of a rigid body, as its center of mass executes a given path, alignment of body's principal axes with the Frenet-Serret frame at each point appears to be the solution. However, the other useful orthonormal frames can be defined along a space curve. An important example is rotation minimizing frame. Rotation minimizing frames are employed in robotics application where the axis of a tool or probe should remain tangential to a given spatial path while minimizing changes of orientation about this axis.