Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
A New Robotic System for Visually Controlled Percutaneous Inerventions under CT Fluoroscopy
MICCAI '00 Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention
Design, analysis and experimentation: the fundamentals of continuum robotic manipulators
Design, analysis and experimentation: the fundamentals of continuum robotic manipulators
Nonholonomic Modeling of Needle Steering
International Journal of Robotics Research
ACM SIGGRAPH 2008 papers
Mechanics of precurved-tube continuum robots
IEEE Transactions on Robotics
Torsional kinematic model for concentric tube robots
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Mechanics of bending, torsion, and variable precurvature in multi-tube active cannulas
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
International Journal of Robotics Research
Geometric integration on Euclidean group with application to articulated multibody systems
IEEE Transactions on Robotics
Image-Guided Robotic Flexible Needle Steering
IEEE Transactions on Robotics
Mechanics Modeling of Tendon-Driven Continuum Manipulators
IEEE Transactions on Robotics
A novel mechatronic tool for computer-assisted arthroscopy
IEEE Transactions on Information Technology in Biomedicine
Mechanics of bending, torsion, and variable precurvature in multi-tube active cannulas
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
International Journal of Robotics Research
A geometrically exact model for externally loaded concentric-tube continuum robots
IEEE Transactions on Robotics
Percutaneous intracardiac beating-heart surgery using metal MEMS tissue approximation tools
International Journal of Robotics Research
International Journal of Robotics Research
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Robots consisting of several concentric, preshaped, elastic tubes can work dexterously in narrow, constrained, and/or winding spaces, as are commonly found in minimally invasive surgery. Previous models of these â聙聹active cannulasâ聙聺 assume piecewise constant precurvature of component tubes and neglect torsion in curved sections of the device. In this paper we develop a new coordinate-free energy formulation that accounts for general preshaping of an arbitrary number of component tubes, and which explicitly includes both bending and torsion throughout the device. We show that previously reported models are special cases of our formulation, and then explore in detail the implications of torsional flexibility for the special case of two tubes. Experiments demonstrate that this framework is more descriptive of physical prototype behavior than previous models1 it reduces model prediction error by 82% over the calibrated bending-only model, and 17% over the calibrated transmissional torsion model in a set of experiments.