Title :
Redundant robotic chains on Riemannian manifolds
Author :
Altafini, Claudio
Author_Institution :
Int. Sch. for Adv. Studies, Scuola Int. Superiore di Studi Avanzati, Trieste, Italy
Abstract :
A geometric framework for the study of redundant robotic chains is proposed. Once a suitable metric for the workspace of the end-effector is chosen, the forward kinematic map from joint space to workspace can be described in terms of Riemannian submersions. Consequently, the inverse kinematics admits an interpretation in terms of horizontal lift of the Riemannian submersion. It is shown that for the most common class of robotic manipulators, those composed of one degree of freedom lower-pair joints, the commonly used Moore-Penrose pseudoinversion corresponds exactly to the horizontal lift of vector fields from workspace to joint space.
Keywords :
manipulator dynamics; redundant manipulators; vectors; Moore-Penrose pseudoinversion; Riemannian manifolds; Riemannian submersions; forward kinematic map; geometric framework; horizontal lift; inverse kinematics; one degree of freedom lower-pair joints; redundant robotic chains; robotic manipulators; Control systems; Equations; Extraterrestrial measurements; Force control; Kinematics; Manipulators; Mechanical variables control; Orbital robotics; Robots; Torque control;
Conference_Titel :
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on
Print_ISBN :
0-7803-7516-5
DOI :
10.1109/CDC.2002.1184737