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

•Concentric tube robots (CTR) are interesting for surgical applications.•Evaluation of stability and number of equilibria for given actuation inputs remains difficult.•A generic numerical framework for cardinality and stability assessment is proposed.•Continuation method, dynamic relaxation and bifu...

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Published in:Mechanism and machine theory Vol. 132; pp. 176 - 192
Main Authors: Peyron, Q., Rabenorosoa, K., Andreff, N., Renaud, P.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.02.2019
Elsevier
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ISSN:0094-114X, 1873-3999
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Abstract •Concentric tube robots (CTR) are interesting for surgical applications.•Evaluation of stability and number of equilibria for given actuation inputs remains difficult.•A generic numerical framework for cardinality and stability assessment is proposed.•Continuation method, dynamic relaxation and bifurcation analysis are associated.•Accuracy of the framework is demonstrated by generating reference results.•New results about 3-tube CTR follow-the-leader deployment are presented. 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.
AbstractList •Concentric tube robots (CTR) are interesting for surgical applications.•Evaluation of stability and number of equilibria for given actuation inputs remains difficult.•A generic numerical framework for cardinality and stability assessment is proposed.•Continuation method, dynamic relaxation and bifurcation analysis are associated.•Accuracy of the framework is demonstrated by generating reference results.•New results about 3-tube CTR follow-the-leader deployment are presented. 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.
Concentric tube robot (CTR) is a promising class of continuum robots for medical interventions given their compactness and dexterity. Their dexterity is in particularbeingusedtoachievesocalledFollow-the-Leader(FTL)deployments, wherethetippathdrawstheshapeoftherobot. Duringthiskindofdeployment theycanhoweverbesubjecttoelasticinstabilities, andthenumberofreachable 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.
Author Andreff, N.
Peyron, Q.
Rabenorosoa, K.
Renaud, P.
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Keywords Follow-the-leader deployment
Continuation method
Stability evaluation
Concentric tube robot
Bifurcation analysis
Language English
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Snippet •Concentric tube robots (CTR) are interesting for surgical applications.•Evaluation of stability and number of equilibria for given actuation inputs remains...
Concentric tube robot (CTR) is a promising class of continuum robots for medical interventions given their compactness and dexterity. Their dexterity is in...
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StartPage 176
SubjectTerms Automatic
Bifurcation analysis
Computer Science
Concentric tube robot
Continuation method
Data Structures and Algorithms
Engineering Sciences
Follow-the-leader deployment
Stability evaluation
Title A numerical framework for the stability and cardinality analysis of concentric tube robots: Introduction and application to the follow-the-leader deployment
URI https://dx.doi.org/10.1016/j.mechmachtheory.2018.10.020
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