A Sliding-Rod Variable-Strain Model for Concentric Tube Robots

Renda, Federico; Messer, Conor; Rucker, D. Caleb; Boyer, Frédéric

doi:10.1109/lra.2021.3063704

Cited by 17 publications

(18 citation statements)

References 24 publications

(47 reference statements)

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“…Apart from the numerical implementations presented in this paper, other numerical methods can be used. For instance, the BVP of the Newtonian approach can be solved with finite differences or spectral methods, while [32]- [34] present different numerical methods for the Lagrangian approach. In what follows, we compare the derivation of the Newtonian approach solved with a shooting method and the derivation of the Lagrangian approach solved with Newton-Raphson's method.…”

Section: Discussionmentioning

confidence: 99%

“…Note that this is different from [32], where the resolution is performed by the explicit time integration of an overdamped equivalent system. Also, compared to [32]- [34] regarding the Lagrangian approach, this paper further extends the simulations to Reissner rods (i.e. considering shear and extension).…”

Section: B Numerical Implementation Of the Lagrangian Approachmentioning

confidence: 95%

“…In other words, to improve the intelligibility of the approach, we bring back TACR modeling to the canonical Lagrangian methodology. Note that this choice contrasts with recent publications on the topic, where the Lagrangian model is obtained either by projection of Cosserat partial differential equations with Jacobian matrices [33], [34], or by feeding a continuous Newton-Euler inverse algorithm with specific inputs [32].…”

Section: Lagrangian Model Of Tacrsmentioning

confidence: 99%

“…It should be noted here that, although expressions (49) and (50) are equivalent and dual to each other, choosing one or the other to calculate the generalized external forces, leads to fundamentally different algorithms. In details, if one uses (49), as in [33], [34], the external forces of (46) are calculated with Jacobian matrices according to a matrix projective process, often called Kane's method in the mechanical literature [43]. On the other hand, if one uses (50) as in [32], the same forces are calculated by solving the inverse BVP (51).…”

Section: B Reduced Static Balancementioning

confidence: 99%

“…Lately, another approach for solving the same mechanical problem was proposed based on a Lagrangian viewpoint [32]- [34]. In essence, the Lagrangian approach for mechanics is based on two key ingredients: first the concept of configuration space, second a variational principle that allows the static or dynamic balance on this space to be derived [35].…”

Section: Introductionmentioning

confidence: 99%

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Cosserat Rod Modeling of Continuum Robots from Newtonian and Lagrangian Perspectives

et al. 2023

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Cosserat rod theory proved efficient modeling performances in robotics, especially in the context of continuum robots, in the past decade. The implementation of such theory is far from being unique and straightforward. We consider the illustrative example of multi-segment, general routing tendon actuated continuum robots in their nominal static operating regime. This paper details two main approaches based on Cosserat rod modeling, namely the Newtonian and Lagrangian approaches. We provide a walk-through guide regarding theoretical derivations and numerical implementation of both approaches, together with a proof of equivalence. This comparative study is supplemented with novel contributions and extensions of each approach and in-depth discussion of their performances and applicability, as well as highlighting their special features.

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Section: Discussionmentioning

confidence: 99%

Section: B Numerical Implementation Of the Lagrangian Approachmentioning

confidence: 95%

Section: Lagrangian Model Of Tacrsmentioning

confidence: 99%

Section: B Reduced Static Balancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cosserat Rod Modeling of Continuum Robots from Newtonian and Lagrangian Perspectives

et al. 2023

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Multibody dynamic modeling of the behavior of flexible instruments used in cervical cancer brachytherapy

Straathof,

Meijaard,

van Vliet‐Pérez

et al. 2024

Medical Physics

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BackgroundThe steep radiation dose gradients in cervical cancer brachytherapy (BT) necessitate a thorough understanding of the behavior of afterloader source cables or needles in the curved channels of (patient‐tailored) applicators.PurposeThe purpose of this study is to develop and validate computer models to simulate: (1) BT source positions, and (2) insertion forces of needles in curved applicator channels. The methodology presented can be used to improve the knowledge of instrument behavior in current applicators and aid the development of novel (3D‐printed) BT applicators.MethodsFor the computer models, BT instruments were discretized in finite elements. Simulations were performed in SPACAR by formulating nodal contact force and motion input models and specifying the instruments’ kinematic and dynamic properties. To evaluate the source cable model, simulated source paths in ring applicators were compared with manufacturer‐measured source paths. The impact of discrepancies on the dosimetry was estimated for standard plans. To validate needle models, simulated needle insertion forces in curved channels with varying curvature, torsion, and clearance, were compared with force measurements in dedicated 3D‐printed templates.ResultsComparison of simulated with manufacturer‐measured source positions showed 0.5–1.2 mm median and <2.0 mm maximum differences, in all but one applicator geometry. The resulting maximum relative dose differences at the lateral surface and at 5 mm depth were 5.5% and 4.7%, respectively. Simulated insertion forces for BT needles in curved channels accurately resembled the forces experimentally obtained by including experimental uncertainties in the simulation.ConclusionThe models developed can accurately predict source positions and insertion forces in BT applicators. Insights from these models can aid novel applicator design with improved motion and force transmission of BT instruments, and contribute to the estimation of overall treatment precision. The methodology presented can be extended to study other applicator geometries, flexible instruments, and afterloading systems.

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Visual servoing of continuum robots: Methods, challenges, and prospects

Nazari

Zareinia

Janabi–Sharifi

2022

Robotics Computer Surgery

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Background Recent advancements in continuum robotics have accentuated developing efficient and stable controllers to handle shape deformation and compliance. The control of continuum robots (CRs) using physical sensors attached to the robot, particularly in confined spaces, is difficult due to their limited accuracy in three‐dimensional deflections and challenging localisation. Therefore, using non‐contact imaging sensors finds noticeable importance, particularly in medical scenarios. Accordingly, given the need for direct control of the robot tip and notable uncertainties in the kinematics and dynamics of CRs, many papers have focussed on the visual servoing (VS) of CRs in recent years. Methods The significance of this research towards safe human‐robot interaction has fuelled our survey on the previous methods, current challenges, and future opportunities. Results Beginning with actuation modalities and modelling approaches, the paper investigates VS methods in medical and non‐medical scenarios. Conclusions Finally, challenges and prospects of VS for CRs are discussed, followed by concluding remarks.

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A Sliding-Rod Variable-Strain Model for Concentric Tube Robots

Cited by 17 publications

References 24 publications

Cosserat Rod Modeling of Continuum Robots from Newtonian and Lagrangian Perspectives

Cosserat Rod Modeling of Continuum Robots from Newtonian and Lagrangian Perspectives

Multibody dynamic modeling of the behavior of flexible instruments used in cervical cancer brachytherapy

Visual servoing of continuum robots: Methods, challenges, and prospects

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