Elastic rod dynamics: Validation of a real-time implicit approach

Till, John; Rucker, D. Caleb

doi:10.1109/iros.2017.8206139

Cited by 17 publications

(18 citation statements)

References 20 publications

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“…A related statement of Kirchhoff rod dynamics was developed by Till and Rucker (2017a). The derivation here is more general: we consider the effects of shear, extension, and rotational inertia of the rod cross-section.…”

Section: Cosserat Models and Methodsmentioning

confidence: 99%

“…In addition, for the slower modes of interest, the rotational inertia of the cross-section ρ J often has a negligible effect compared with that of the linear mass distribution ρ A , which can reduce complexity further (Till and Rucker, 2017a). We will primarily rely on the full Cosserat rod equations in (7) throughout the paper, but the Kirchhoff assumption can be a useful step to reduce the problem’s complexity and improve computational efficiency in some scenarios.…”

Section: Cosserat Models and Methodsmentioning

confidence: 99%

“…As described by Till and Rucker (2017a), at very small timesteps implicit discretization inherently has a “catastrophic cancelation” loss of floating-point precision caused by subtracting nearly equal numbers. For example, the backward Euler method relies on the calculation…”

Section: Cosserat Models and Methodsmentioning

confidence: 99%

“…Our preliminary work on this topic was presented by Till and Rucker (2017a), where we proposed and validated an implicit discretization approach for a dynamic Kirchhoff rod with negligible cross-section rotational inertia. Beyond this, our additional advances here include (1) derivation and application to the full Cosserat rod model including shear, extension, and rotational cross-section inertia, (2) a performance characterization of several variants of the method on a benchmark test problem, (3) additional experimental validation and speed characterization of the full Cosserat model and a tendon robot model, and (4) derivation and application of our method to three different continuum and soft robot designs, including a novel soft robot model, with real-time simulation demonstration in each case.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Real-time dynamics of soft and continuum robots based on Cosserat rod models

Till

Aloi

Rucker

2019

The International Journal of Robotics Research

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255

185

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The dynamic equations of many continuum and soft robot designs can be succinctly formulated as a set of partial differential equations (PDEs) based on classical Cosserat rod theory, which includes bending, torsion, shear, and extension. In this work we present a numerical approach for forward dynamics simulation of Cosserat-based robot models in real time. The approach implicitly discretizes the time derivatives in the PDEs and then solves the resulting ordinary differential equation (ODE) boundary value problem (BVP) in arc length at each timestep. We show that this strategy can encompass a wide variety of robot models and numerical schemes in both time and space, with minimal symbolic manipulation required. Computational efficiency is gained owing to the stability of implicit methods at large timesteps, and implementation is relatively simple, which we demonstrate by providing a short MATLAB-coded example. We investigate and quantify the tradeoffs associated with several numerical subroutines, and we validate accuracy compared with dynamic rod data gathered with a high-speed camera system. To demonstrate the method’s application to continuum and soft robots, we derive several Cosserat-based dynamic models for robots using various actuation schemes (extensible rods, tendons, and fluidic chambers) and apply our approach to achieve real-time simulation in each case, with additional experimental validation on a tendon robot. Results show that these models capture several important phenomena, such as stability transitions and the effect of a compressible working fluid.

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Section: Cosserat Models and Methodsmentioning

confidence: 99%

Section: Cosserat Models and Methodsmentioning

confidence: 99%

Section: Cosserat Models and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Real-time dynamics of soft and continuum robots based on Cosserat rod models

Till

Aloi

Rucker

2019

The International Journal of Robotics Research

Self Cite

255

185

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show abstract

“…Fras et al [27] described the design and implementation of a static model used for position estimation of a flexible modular medical manipulator equipped with optic-fiber based sensors. Till and Rucker [28] exhibited low numerical damping, handled arbitrarily large time steps, and provided an accurate, high-order representation of the rod shape in steady state. Hadi Sadati et al [29] introduced a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic method.…”

Section: Introductionmentioning

confidence: 99%

Research on Stiffness of Multibackbone Continuum Robot Based on Screw Theory and Euler-Bernoulli Beam

Wang

2018

Mathematical Problems in Engineering

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Continuum robots have become a focus for extensive research, since they can work well in complex and confined environments. The main contribution of this paper is to establish a stiffness model of a single section multibackbone continuum robot and analyze the effect of the structural parameters of continuum robot on the overall rotation and translation stiffness. First, a stiffness model which indicates the end configuration of continuum robot under external load is deduced by the screw theory and Euler-Bernoulli beam. Then, the stiffness elements are fully analyzed, therefore, obtaining the influence of the structural parameters of continuum robot on the stiffness elements. Meanwhile, a numerical analysis of stiffness elements is given. Furthermore, the minimum and maximum rotation/translation stiffness are introduced to analyze the effect of the structural parameters of continuum robot on the overall rotation and translation stiffness. Finally, the experiments are used to validate the proposed stiffness model. The experimental results show that the proposed stiffness model of continuum robot is correct and the errors are less than 7%.

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On Singularity and Instability in a Planar Parallel Continuum Mechanism

Altuzarra

Campa

2020

Springer Proceedings in Advanced Robotics

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Elastic rod dynamics: Validation of a real-time implicit approach

Cited by 17 publications

References 20 publications

Real-time dynamics of soft and continuum robots based on Cosserat rod models

Real-time dynamics of soft and continuum robots based on Cosserat rod models

Research on Stiffness of Multibackbone Continuum Robot Based on Screw Theory and Euler-Bernoulli Beam

On Singularity and Instability in a Planar Parallel Continuum Mechanism

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