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
Mechanics of precurved-tube continuum robots
IEEE Transactions on Robotics
Three dimensional statics for continuum robotics
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Design and control of concentric-tube robots
IEEE Transactions on Robotics
Equilibrium Conformations of Concentric-tube Continuum Robots
International Journal of Robotics Research
An Investigation of the Intrinsic Force Sensing Capabilities of Continuum Robots
IEEE Transactions on Robotics
Geometrically Exact Models for Soft Robotic Manipulators
IEEE Transactions on Robotics
Mechanics Modeling of Tendon-Driven Continuum Manipulators
IEEE Transactions on Robotics
Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
International Journal of Robotics Research
Percutaneous intracardiac beating-heart surgery using metal MEMS tissue approximation tools
International Journal of Robotics Research
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Continuum robots, which are composed of multiple concentric, precurved elastic tubes, can provide dexterity at diameters equivalent to standard surgical needles. Recent mechanicsbased models of these "active cannulas" are able to accurately describe the curve of the robot in free space, given the preformed tube curves and the linear and angular positions of the tube bases. However, in practical applications, where the active cannula must interact with its environment or apply controlled forces, a model that accounts for deformation under external loading is required. In this paper, we apply geometrically exact rod theory to produce a forward kinematic model that accurately describes large deflections due to a general collection of externally applied point andor distributed wrench loads. This model accommodates arbitrarily many tubes, with each having a general preshaped curve. It also describes the independent torsional deformation of the individual tubes. Experimental results are provided for both point and distributed loads. Average tip error under load was 2.91 mm (1.5%-3% of total robot length), which is similar to the accuracy of existing free-space models.