A numerical framework for the stability and cardinality analysis of concentric tube robots: Introduction and application to the follow-the-leader deployment

Abstract

Concentric tube robot (CTR) is a promising class of continuum robots for medical interventions given their compactness and dexterity. Their dexterity is in particular being used to achieve so called Follow-the-Leader (FTL) deployments, where the tip path draws the shape of the robot. During this kind of deployment they can however be subject to elastic instabilities, and the number of reachable configurations may vary for a given state of actuators. These cardinality and stability changes need therefore to be predicted during CTR design. Available methods and results are limited, with restrictive assumptions on number and properties of tubes. We therefore propose in this paper a numerical framework for the cardinality and stability assessment of CTR. It is based on the association of dynamic relaxation, continuation method and bifurcation analysis. The numerical framework is validated by reproducing reference results on the stability and cardinality of two-tube robots. Then, new results on three-tube CTR deploying in a FTL manner are presented. The framework genericity allows in particular to provide new insights on the behaviour of CTR with helical-shaped tubes.

Singularity Conditions for Continuum Parallel Robots

“…It is possible to approximate the expression of h by using finite differences [6]. Thus, let us discretize the rod into N rigid elements of equal length ei = L i /N j (Fig.…”

An Analytical Formulation for the Geometrico-Static Problem of Continuum Planar Parallel Robots

“…1(a)), L is the rod length, and s is the curvilinear abscissa along the rod. It is possible to approximate the expression of θ by using finite differences [11]. For this, let us discretize the rod into N elements of equal length e = L/N (Fig.…”

“…Most of these mechanisms feature a serial architecture, in which rigid bodies and joints are replaced by an assembly of slender rods deformed by wires, electromagnets, fluidic actuators or other types of actuation. Continuum robots, inspired by biological systems such as trunks, tentacles, and snakes, have been used in many applications in which the problem of manipulation in confined, or hard-to-reach workspace, is crucial, like minimally invasive surgery [8,9,11].…”

SLAM-Based Follow-the-Leader Deployment of Concentric Tube Robots

“…CTRs can exhibit instabilities during deployment [16], [17]. Global stability criterion exist only for CTRs made of two constant-curvature tubes.…”

“…The chosen mathematical function enabling such possibility is a sigmoid. In this work, we use the formulation given in (17):…”