A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations
- Title
- A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations
- Date Issued
- 2009-01
- Publisher
- ASME-AMER SOC MECHANICAL ENG
- 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. [DOI: 10.1115/1.3007903]
- Keywords
- attitude control; fully-reversed sequences of rotations; noncommutativity of finite rigid rotations; Jacobian algorithm; inverse kinematics; motion planning; RIGID-BODY; STABILIZATION
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29025
- DOI
- 10.1115/1.3007903
- ISSN
- 1555-1423
- Article Type
- Article
- Files in This Item:
- There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.