About this Journal Submit a Manuscript Table of Contents
Advances in Mechanical Engineering
Volume 2010 (2010), Article ID 284976, 9 pages
Research Article

Application of the Rotation Matrix Natural Invariants to Impedance Control of Rotational Parallel Robots

1Dipartimento di Meccanica e Costruzione delle Macchine, Università di Genova, Via Opera Pia 15A, 16145 Genova, Italy
2Dipartimento di Meccanica, Università Politecnica delle Marche, Via Brecce Bianche 12, 60131 Ancona, Italy

Received 17 June 2009; Accepted 10 November 2009

Academic Editor: Zhen Huang

Copyright © 2010 L. Bruzzone and M. Callegari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Force control of parallel robots with rotational degrees of freedom through impedance algorithms is considerably influenced by the representation method of the end-effector orientation. Using the natural invariants of the rotation matrix and the angular velocity vector in the impedance control law has some theoretical advantages, which derive from the Euclidean-geometric meaning of these entities. These benefits are particularly evident in case of robotic architectures with three rotational degrees of freedom (serial or parallel wrists with spherical motion). The behaviour of a 3-CPU parallel robot controlled by an impedance algorithm based on this concepts is assessed through multibody simulations, and the results confirm the effectiveness of the proposed approach.