Spatial Continuum Models of Rods Undergoing Large Deformation and Inflation

Tunay, I.

doi:10.1109/tro.2012.2232532

Cited by 64 publications

(49 citation statements)

References 25 publications

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“…3) Variable Curvature (VC) kinematics [9] with Cosserat rod model (or equivalent beam theory method), as explained in [10,11] which leads to an optimization boundary value problem (BVP). Tunay presented an approximate solution for the weak-form integral equations resulting from this BVP in a finite element discretized form [12]. 4) Approximate solutions based on the identification of the system with a polynomial [13], or shape function based series solutions [5] which construct a setup-specific model.…”

Section: Introductionmentioning

confidence: 99%

Mechanics of Continuum Manipulators, a Comparative Study of Five Methods with Experiments

Sadati

Naghibi

Shiva

et al. 2017

Towards Autonomous Robotic Systems

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Abstract.: Investigations on control and optimization of continuum manipulators have resulted in a number of kinematic and dynamic modeling approaches each having their own advantages and limitations in various applications. In this paper, a comparative study of five main methods in the literature for kinematic, static and dynamic modeling of continuum manipulators is presented in a unified mathematical framework. The five widely used methods of Lumped system dynamic model, Constant curvature, two-step modified constant curvature, variable curvature Cosserat rod and beam theory approach, and series solution identification are re-viewed here with derivation details in order to clarify their methodological differences. A comparison between computer simulations and experimental results using a STIFF-FLOP continuum manipulator is presented to study the advantages of each modeling method.

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Section: Introductionmentioning

confidence: 99%

Mechanics of Continuum Manipulators, a Comparative Study of Five Methods with Experiments

Sadati

Naghibi

Shiva

et al. 2017

Towards Autonomous Robotic Systems

View full text Add to dashboard Cite

show abstract

“…5) approximate identification based series-solutions where coefficients of a simple [18] or complex [19] series are identified using experimental results to construct a hardware-specific model. 6) Numerical finite element methods using Euler-Bernoulli [20] or Galerkin weakform series-solution [21] mechanics and VC kinematics.…”

mentioning

confidence: 99%

“…Use of series-solution based models for identification of kinematic map by Godage [8] have shown to be realtime but with a complex hard to interpret shape function and limitations related to identification based methods. Seriessolution based Galerkin method for static modeling of complex deformation in a discretized finite element domain by Tunay [21] is accurate and comprehensive, but with a complex shape function and limitations related to finite element and Cosserat rod method.…”

mentioning

confidence: 99%

Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz–Galerkin Methods

Sadati

Naghibi

Walker

et al. 2018

IEEE Robot. Autom. Lett.

110

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Abstract-To address the challenges with real-time accurate modeling of multi-segment continuum manipulators in presence of significant external and body loads, we introduce a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic method. By combining a modified Lagrange polynomial series solution, based on experimental observations, with Ritz and Ritz-Galerkin methods, the infinite modeling state space of a continuum manipulator is minimized to geometrical position of a handful of physical points (in our case two). As a result, a unified easy to implement vector formalism is proposed for nonlinear impedance and configuration control. We showed that by considering the mechanical effects of axial highly elastic deformation, the model accuracy is increased by up to 6%. The proposed model predicts experimental results with 6-8% (4-6 [mm]) mean error for the Ritz-Galerkin method in static cases and 16-20% (12-14 [mm]) mean error for the Ritz method in dynamic cases, in planar and general 3D motions. Comparing to five different models in the literature, our approximate solution showed to be more accurate with the smallest possible number of modeling states and suitable for real-time modeling, observation and control applications.

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“…Here, to shift the local coordinate systemof each secondary backbone into the global coordinate system -, an adjoint action of Lie group SE(3) on its Lie algebra is introduced by a 6 × 6 matrix representation [21]:…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…Krishnan et al [20] studied serial and parallel concatenation of building blocks. Tunay [21] proposed a concept of equivalent bending stiffness 2 Mathematical Problems in Engineering to establish the kinematic model of continuum robot. Gao et al [22] established a mathematical model for predicting the loaded posture of a single section continuum manipulator.…”

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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Spatial Continuum Models of Rods Undergoing Large Deformation and Inflation

Cited by 64 publications

References 25 publications

Mechanics of Continuum Manipulators, a Comparative Study of Five Methods with Experiments

Mechanics of Continuum Manipulators, a Comparative Study of Five Methods with Experiments

Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz–Galerkin Methods

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

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