Characterisation of Frenet-Serret and Bishop motions with applications to needle steering
Selig, JM (2013). Characterisation of Frenet-Serret and Bishop motions with applications to needle steering. Robotica. 31 (6), pp. 981 - 992.
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.
|Journal citation||31 (6), pp. 981 - 992|
|Publisher||London South Bank University|
|Digital Object Identifier (DOI)||doi:10.1017/S026357471300026X|
|01 Sep 2013|
|Publication process dates|
|Deposited||21 Jun 2016|
|Accepted||13 Mar 2013|
|Accepted author manuscript|
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