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A Jacobian-Based Algorithm for the Attitude Control of a Rigid Body Undergoing Fully-Reversed Sequences of Rotations

[+] Author Affiliations
Sung K. Koh

Pohang University of Science & Technology, Pohang, South Korea

Gregory S. Chirikjian

Johns Hopkins University, Baltimore, MD

G. K. Ananthasuresh

India Institute of Science, Bangalore, India

Paper No. DETC2007-34927, pp. 1255-1263; 9 pages
doi:10.1115/DETC2007-34927
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 31st Mechanisms and Robotics Conference, Parts A and B
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4809-4 | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

Jacobian-based control algorithms for the attitude control of a rigid body undergoing a series of forward and reverse rotations are proposed in this paper. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is singular as well as a null matrix at the identity that makes the conventional Jacobian formulation break down. In order to handle the singularities involved in FR rotations, the Jacobian algorithm is reformulated and implemented so as to synthesize the FR rotation for a desired orientation change. We introduce the single-step and multiple-step Jacobian methods in this paper. The single-step Jacobian method synthesizes a specific FR rotation that enables the rigid body to reach a given desired orientation through a single step. The multiple-step Jacobian method synthesizes physically feasible FR rotations on an incremental optimal path to a desired orientation. A comparison with existing control algorithms for FR motions verifies the fast convergence property of the Jacobian-based algorithm and the accuracy of the solutions.

Copyright © 2007 by ASME
Topics: Algorithms

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