Task-Induced Symmetry and Reduction With Application to Needle Steering

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Lie group symmetry in a mechanical system can lead to a dimensional reduction in its dynamical equations. Typically, the symmetries that one exploits are intrinsic to the mechanical system at hand, e. g., invariance of the system's Lagrangian to some group of motions. In the present work we consider symmetries that arise from an extrinsic control task, rather than the intrinsic structure of the configuration space, constraints, or system dynamics. We illustrate this technique with several examples. In the examples, the reduction enables us to design essentially global feedback controllers on the reduced systems. We also demonstrate how the proposed technique dovetails with Lagrangian reduction. We apply task-induced symmetry and reduction to a recently developed 6 DOF kinematic model of steerable bevel-tip needles. The resulting controllers cause the needle tip to track a subspace of its configuration space. We envision that the methodology presented in this paper will form the basis for a new planning and control framework for needle steering.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2010-03
Language
English
Article Type
Article
Keywords

SYSTEMS

Citation

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, v.55, no.3, pp.664 - 673

ISSN
0018-9286
DOI
10.1109/TAC.2009.2039241
URI
http://hdl.handle.net/10203/220795
Appears in Collection
EE-Journal Papers(저널논문)
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