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.

Implicit active constraints for safe and effective guidance of unstable concentric tube robots

“…The motivation for these restrictions is: a) the end-effectors positions of connected vertices/ configurations should be close; b) the differences in joint-space should be limited, ensuring small joint-velocities when transitioning from one configuration to the next one; and c) vertex centre-line should be similar, as encoded in (8). Note that these hard restrictions to edge insertion guarantee a sparse graph, which results in faster shortest-path queries.…”

“…CTR mechanics have thus far been investigated extensively, with reliable models existing for torsionally compliant kinematics and equilibrium conformations [7], [8]. The latter result from the instability of CTR, which under certain configurations rapidly release energy after sufficient torsional wind-up of their tubular components [9].…”

On-line collision-free inverse kinematics with frictional active constraints for effective control of unstable concentric tube robots

“…For concentric tube robots accurate algebraic close-form description of the forward kinematic is not available [5], [6]. The kinematic models are currently based on boundary value problems, solving differential equations iteratively [12] which is computationally intensive [15], [16].…”

“…Concentric tube robots are continuum robots that exhibit shape control through the relative rotation and telescopic translation of pre-curved super-elastic tubes [5], [6]. With their dimensions being comparable to catheters, concentric tube robots have been proposed for several clinically-critical interventions that require navigation through the vasculature [7], the nasal cavities [8], and the urinary tracts [9].…”

Some Aspects Regarding the Information Security Management System within Organizations – Adopting the ISO/IEC 27001:2013 Standard

“…In [1][2][3][4], were analyzed the kinematic models by the "backbone curve". The papers [5][6][7] derived a new kinematic model by using the differential geometry, [8,12] studied the manipulability of continuum robots. Cable-driven continuum robot control with variable stiffness was studied in [13].…”