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IROS
2007
IEEE

Task-induced symmetry and reduction in kinematic systems with application to needle steering

10 years 5 months ago
Task-induced symmetry and reduction in kinematic systems with application to needle steering
— 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 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 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.
Vinutha Kallem, Dong Eui Chang, Noah J. Cowan
Added 03 Jun 2010
Updated 03 Jun 2010
Type Conference
Year 2007
Where IROS
Authors Vinutha Kallem, Dong Eui Chang, Noah J. Cowan
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