Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.
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e-mail: shkoh@postech.ac.kr
e-mail: gregc@jhu.edu
e-mail: suresh@mecheng.iisc.ernet.in
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January 2009
Research Papers
A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations
Sung K. Koh,
Sung K. Koh
Department of Mechanical Engineering,
e-mail: shkoh@postech.ac.kr
Pohang University of Science and Technology
, Pohang, 790-784, Republic of Korea
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Gregory S. Chirikjian,
Gregory S. Chirikjian
Department of Mechanical Engineering,
e-mail: gregc@jhu.edu
Johns Hopkins University
, Baltimore, MD 21218
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G. K. Ananthasuresh
G. K. Ananthasuresh
Department of Mechanical Engineering,
e-mail: suresh@mecheng.iisc.ernet.in
Indian Institute of Science
, Bangalore, 560012, India
Search for other works by this author on:
Sung K. Koh
Department of Mechanical Engineering,
Pohang University of Science and Technology
, Pohang, 790-784, Republic of Koreae-mail: shkoh@postech.ac.kr
Gregory S. Chirikjian
Department of Mechanical Engineering,
Johns Hopkins University
, Baltimore, MD 21218e-mail: gregc@jhu.edu
G. K. Ananthasuresh
Department of Mechanical Engineering,
Indian Institute of Science
, Bangalore, 560012, Indiae-mail: suresh@mecheng.iisc.ernet.in
J. Comput. Nonlinear Dynam. Jan 2009, 4(1): 011012 (12 pages)
Published Online: December 12, 2008
Article history
Received:
June 18, 2007
Revised:
May 20, 2008
Published:
December 12, 2008
Citation
Koh, S. K., Chirikjian, G. S., and Ananthasuresh, G. K. (December 12, 2008). "A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations." ASME. J. Comput. Nonlinear Dynam. January 2009; 4(1): 011012. https://doi.org/10.1115/1.3007903
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