title: Equilibrium Conformations of Concentric-tube Continuum Robots.
abstract: 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 "active cannulas" 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 models; 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.
authors.affiliation: Department of Mechanical Engineering, Vanderbilt University, 2301 Vanderbilt Place, PMB 351592, Nashville, TN 37235-1592, USA.
authors.forename: D Caleb
authors.initials: DC
authors.lastname: Rucker
authors.affiliation: Department of Mechanical Engineering, Vanderbilt University, 2301 Vanderbilt Place, PMB 351592, Nashville, TN 37235-1592, USA.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Webster
authors.affiliation: Department of Mechanical Engineering, John Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA.
authors.forename: Gregory S
authors.initials: GS
authors.lastname: Chirikjian
authors.affiliation: Department of Mechanical Engineering, John Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA.
authors.forename: Noah J
authors.initials: NJ
authors.lastname: Cowan
keywords: active cannula; concentric tube robot; continuum robot; elastica; flexible arms; kinematics; mechanics; medical robots; snake-like robot; variational calculus