# A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Koh, Sung K and Chirikjian, Gregory S and Ananthasuresh, GK (2009) A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations. In: Journal of Computational and Nonlinear Dynamics, 4 (1). 011012-1.

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## Abstract

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.

Item Type: Journal Article Copyright of this article belongs to The American Society of Mechanical Engineers. attitude control;fully-reversed sequences of rotations;noncommutativity of finite rigid rotations;Jacobian algorithm; inverse. kinematics; motion planning Division of Mechanical Sciences > Mechanical Engineering Id for Latest eprints 27 Aug 2009 05:55 19 Sep 2010 05:30 http://eprints.iisc.ac.in/id/eprint/19885