Geometrically Exact Finite Element Formulation for Tendon-Driven Continuum Robots

Li, Xin; Yu, Wenkai; Baghaee, Mehdi; Cao, Changyong; Chen, Dunyu; Ju, Liu; Yuan, Hongyan

doi:10.1007/s10338-022-00311-w

Cited by 9 publications

(3 citation statements)

References 33 publications

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“…Modeling continuum robots is a multifaceted and multi-dimensional challenge. From the perspective of handling the unit structural form, continuum robot modeling can be primarily categorized into several approaches: Cosserat rod theory [ 89 , 90 , 91 , 92 ] for micropolar bodies, piecewise constant curvature (PCC) models [ 23 ], arc segment models [ 93 ], geometrically finite element methods [ 94 ], and modal methods [ 95 , 96 ]. Micropolar and finite element approaches are more suited for describing complex nonlinear deformations in continuum robots.…”

Section: Continuum Robotsmentioning

confidence: 99%

Continuum Robots and Magnetic Soft Robots: From Models to Interdisciplinary Challenges for Medical Applications

Wang,

Mao,

2024

Micromachines

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This article explores the challenges of continuum and magnetic soft robotics for medical applications, extending from model development to an interdisciplinary perspective. First, we established a unified model framework based on algebra and geometry. The research progress and challenges in principle models, data-driven, and hybrid modeling were then analyzed in depth. Simultaneously, a numerical analysis framework for the principle model was constructed. Furthermore, we expanded the model framework to encompass interdisciplinary research and conducted a comprehensive analysis, including an in-depth case study. Current challenges and the need to address meta-problems were identified through discussion. Overall, this review provides a novel perspective on understanding the challenges and complexities of continuum and magnetic soft robotics in medical applications, paving the way for interdisciplinary researchers to assimilate knowledge in this domain rapidly.

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Section: Continuum Robotsmentioning

confidence: 99%

Continuum Robots and Magnetic Soft Robots: From Models to Interdisciplinary Challenges for Medical Applications

Wang,

Mao,

2024

Micromachines

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“…In the past decades, a few analytical models have been developed for the kinematic modeling of tendondriven robots, such as the constant curvature model [39] and the geometrically exact beam theory [40]. The constant curvature model is the most adopted The initial configuration and the deformed configuration with the free body diagram of the SCR are shown in figures 3(a) and (b).…”

Section: Improved Constant Curvature Model Involving Axial Contractionmentioning

confidence: 99%

A minimally designed soft crawling robot for robust locomotion in unstructured pipes

Yu¹,

Li²,

Chen³

et al. 2022

Bioinspir. Biomim.

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Soft robots have attracted increasing attention due to their excellent versatility and broad applications. In this article, we present a minimally-designed soft crawling robot capable of robust locomotion in unstructured pipes with various geometric/material properties and surface topology. In particular, the soft crawling robot can squeeze through narrow pipes smaller than its cross-section and propel robustly in spiked pipes. The gait pattern and locomotion mechanism of this robot are experimentally investigated and analyzed by the finite element analysis, revealing that the resultant forward frictional force is generated due to the asymmetric mechanical properties along the length direction of the robot. The proposed simple yet working soft crawling robot could inspire novel designs and applications of soft robots in unstructured narrow canals such as large intestines or industrial pipelines.

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“…The node values are then solved to satisfy the BCs following the relation between elements as defined by the PDEs. For complex geometries, the elements can be locally refined or relaxed to capture sensitive changes or expedite computations [92,93]. These models provide the most accurate predictions of dynamic soft materials but are also the most computationally expensive.…”

Section: Femmentioning

confidence: 99%

Geometric Recursive Dynamic Modelling and Simulation of Soft Robotic Systems

Samei

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This thesis studies the dynamics of soft robotic systems modelled as rigid-flexible multi-body systems. A numerical framework is developed to capture finite deformations including extension, shear, bending and torsion of a dynamic 1-Dimensional (1D) flexible body on the Special Euclidean group SE(3) based on Cosserat rod theory. The governing parameterization-free equations are expressed as a set of Partial Differential Equations (PDEs) on the SE(3). An implicit differentiation method semidiscretizes the time derivatives on the Lie algebra of SE(3) to convert the PDEs to a set of Ordinary Differential Equations (ODEs) in the arc-length of the continuum. The novelty of this work is the implementation of a finite difference solution on SE(3) along with a higher-order Runge-Kutta-Munthe-Kaas geometric integrator employed to spatially propagate the configuration of the rod. The resulting solution is a dynamic model of the flexible body that is parameterization-free, computationally inexpensive and can be used in real-time applications.A recursive parameterization-free formulation for the forward and inverse dynamics of multi-body systems is expressed on the SE(3), using the previously developed model for flexible bodies. The system is composed of bodies serially connected with single degree of freedom actuated joints from a fixed base. The Newton-Euler equation of motion for a rigid body and a set of PDEs for a dynamic Cosserat rod are coupled to recursively formulate the dynamics of multi-body systems. The joint kinematics is captured through the exponential map of the SE(3). The inverse dynamics algorithm recursively determines the system response and the joint torques needed to follow a given joint space trajectory, while the forward dynamics algorithm determines the system's motion given joint torques. A shooting-method-based Boundary Condition (BC) solver is developed to solve for the BCs in the set of PDEs and implement a finite difference solution. This study can be implemented to develop joint-space computed-torque control strategies.Recent geometric methods for rigid-flexible multi-body dynamics often use shape This thesis is submitted under only my name but the hardest part of this endeavor, keeping me motivated, was done by everyone but me. Any progress that I have made, and more that I will, is from the guidance of my professors with a special gratitude for Prof. Chhabra, Benavides, Gerrick and Hill. As with solving any problem, running into challenges was inevitable; and in such times working on this thesis, I have relied on my friends Dana, Paige, Wissam, Marana, Harry and Zach to remind me what it means to love learning. More often than not, I have sustained an unhealthy fixation on my studies. So I am grateful to my colleagues Reza, Vaughn, Aman, Ini, Kamala and Sara for taking better care of me than I did of myself and my homies Elias, Hassan and Arafain for telling me when it's time to go home. But no night could end nor sleep subsist without my ma or sisters wishing me goodnight. With the support f...

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Geometrically Exact Finite Element Formulation for Tendon-Driven Continuum Robots

Cited by 9 publications

References 33 publications

Continuum Robots and Magnetic Soft Robots: From Models to Interdisciplinary Challenges for Medical Applications

Continuum Robots and Magnetic Soft Robots: From Models to Interdisciplinary Challenges for Medical Applications

A minimally designed soft crawling robot for robust locomotion in unstructured pipes

Geometric Recursive Dynamic Modelling and Simulation of Soft Robotic Systems

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