Characterisation of Frenet-Serret and Bishop motions with applications to needle steering

Journal article

Selig, JM (2013). Characterisation of Frenet-Serret and Bishop motions with applications to needle steering. Robotica. 31 (6), pp. 981 - 992. https://doi.org/10.1017/S026357471300026X
AuthorsSelig, JM
Abstract

Frenet-Serret and Bishop rigid-body motions have many potential applications in robotics, graphics and computer-aided design. In order to study these motions, new characterisations in terms of their velocity twists are derived. This is extended to general motions based on any moving frame to a space curve. Furthermore, it is shown that any such general moving frame motion is the product of a Frenet-Serret motion with a rotation about the tangent vector. These ideas are applied to a simple model of needle steering. A simple kinematic model of the path of the needle is derived. It is then shown that this leads to Frenet-Serret motions of the needle tip but with constant curvature. Finally, some remarks about curves with constant curvature are made. © Cambridge University Press 2013.

Year2013
JournalRobotica
Journal citation31 (6), pp. 981 - 992
PublisherCambridge University Press (CUP)
ISSN0263-5747
Digital Object Identifier (DOI)https://doi.org/10.1017/S026357471300026X
Publication dates
Print01 Sep 2013
Publication process dates
Deposited21 Jun 2016
Accepted13 Mar 2013
Accepted author manuscript
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