Investigation of the Application of Riemann Geometry to Robot Manipulators

Abstract

In this survey, we show that the posture set of an articulated manipulator of a robot can be represented by a Riemannian manifold and its application to a specific motion. The posture of an articulated manipulator is captured by a set of rotational quantities at each joint. By considering the pairs of rotational quantities as coordinates, the set of manipulator's postures can be expressed in terms of coordinates, and by introducing an appropriate metric, the manipulator can be considered as a Riemannian manifold, and the behavior of an articulated manipulator can be expressed in terms of a Riemannian manifold.