Real-Time Dynamics of Concentric Tube Robots With Reduced-Order Kinematics Based on Shape Interpolation

Sadati, S. M. Hadi; Mitros, Zisos; Henry, Ross; Zeng, Lingyun; Cruz, Lyndon da; Bergeles, Christos

doi:10.1109/lra.2022.3151399

Cited by 11 publications

(19 citation statements)

References 26 publications

(32 reference statements)

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“…Example of such continuum mechanics models are Cosserat, Kirchhoff, and Euler-Bernoulli rod/beam theories. [100][101][102][103][104] Modal techniques (reduced-order model-ROM): which provide a shape function based on the approximation of the robot backbone strain, [105][106][107][108][109][110] shape, [111][112][113][114][115] or cross-section geometry deformation [116,117] via a shape-fitting technique (e.g., cubic spline, Bezier) or a weighted sum of differentiable shape functions (known as system modes). As a result, a differentiable finite state-space system is formed to benefit from conventional rigidbody robot modeling and control techniques.…”

Section: Modelingmentioning

confidence: 99%

“…Both PCS and ANCF can employ a modal (shape function) representation, such as constant curvature or a cubic polynomial curve, to represent the individual element kinematics. -Variable curvature (Cosserat) [100][101][102][103][104] -Modal (fitting, reduced order): *Shape fitting [111][112][113][114][115] *Strain fitting, piecewise variable strain (PVS) [105][106][107][108][109][110] -Relative states: *Pseudo rigid Body chain [16,119] *Piecewise constant strain (PCS) or curvature (PCC) [98,119,120] -Absolute states: *Absolute nodal coordinate formulation (ANCF) [96][97][98] Mechanics:…”

Section: Modelingmentioning

confidence: 99%

“…-Cosserat rod [100][101][102][103]116,117] -Euler-Bernoulli beam [131,132] -Principle of virtual work [97,116] -TMT [98,111,112] -Lagrangian dynamics: *Continuous [104,106,133] *Lumped mass [118,134,135] -Recursive computation [99,133] -Hooke's law [100,133] -Finite strain (hyperelasticity):…”

Section: Modelingmentioning

confidence: 99%

“…The alternative TMT method, owing its acronym to the

T^{normalT} M T

formulation of the projected inertial term M onto the state space using the space transformation Jacobian T , derives system dynamics in a vector formalism based on PVW with fewer derivation steps compared to the Lagrangian method. [ 98,111,112 ] The resulting finite‐state system is computationally lighter than Cosserat rod dynamics, and compatible with rigid‐body nonlinear control design techniques. However, the EoM are less accurate due to the underlying approximated kinematics, time stepping issues, and complex derivations prone to numerical instabilities.…”

Section: Modelingmentioning

confidence: 99%

See 3 more Smart Citations

Continuum Robots: An Overview

Russo

Sadati

Dong

et al. 2023

Advanced Intelligent Systems

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When thinking of robots, the image that immediately springs to mind is either an android, designed to resemble human beings and mimic their behavior, or an industrial manipulator, for example, a large machine of rigid steel working in an assembly line. However, robotic systems of multiple forms have been developed to carry out the most diverse tasks, with designs that evolved from readily available structures, such as vehicles, or inspired by nature. In the last decade, more and more bioinspired designs have been enabled by advances in computer science, materials, and manufacturing. Among them, continuum robots, inspired by snakes, trunks, and tendrils, are characterized by a compliant backbone capable of continuous bending, whose shape (configuration, i.e., position and orientation along the backbone curve) is controlled by applying loads through onboard "intrinsic" actuators (e.g., pneumatics or hydraulics) or transmission elements (e.g., tendons, rods, or compliant tubes) that are pushed/pulled from an extremity of the backbone ("extrinsic actuation"). These robots have flexible bodies with a high length to cross-section diameter ratio and are uniquely suited to tasks that require the deployment of tools or sensors with a long reach into tortuous and narrow paths. [1] Continuum robots were first developed in the 1960s [2] and rose to prominence in the late 1990s, [3] when they were often called elephant trunk, [4] tentacle/tendril, [5] or flexible [6] manipulators. Whereas other robots were characterized by intrinsic actuation and larger sizes, research on continuum robots first focused on miniaturization for medical applications, [7,8] leading to extrinsic actuation to enable leaner designs. Recently, continuum robots have been developed for a wider range of applications, including manufacturing, aerospace, search and rescue, and nuclear. In such scenarios, the infinite degrees of freedom (DoFs) of these slender robots enable inspection and intervention in areas that cannot be accessed by conventional robots (e.g., tunnels [9] and gas turbines [10] ).An exhaustive literature search (see Appendix) outlines a surging interest in continuum robots, with a 19.6% average annual growth in publications between 2012 and 2021 (continuum robot search on Web of Science). Three main topics can be observed in recent literature surveys, listed in Table 1. DesignTendon-driven and concentric tube robots are predominant in surveys, but they are not the only design solutions. [18] This richer literature can be attributed to intense research effort toward medical and other small-scale applications when compared to larger-scale tasks (e.g., manipulation) where intrinsic actuation is advantageous.

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Section: Modelingmentioning

confidence: 99%

Section: Modelingmentioning

confidence: 99%

Section: Modelingmentioning

confidence: 99%

“…The alternative TMT method, owing its acronym to the

T^{normalT} M T

Section: Modelingmentioning

confidence: 99%

See 2 more Smart Citations

Continuum Robots: An Overview

Russo

Sadati

Dong

et al. 2023

Advanced Intelligent Systems

Self Cite

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show abstract

“…The shape of a CR is described by a continuous curve, which belongs to a subset of an infinite-dimensional functional space. Although the shape can be approximated by functional basis interpolation to generate a finite-dimensional configuration space [19], [20], it is non-trivial to check whether a configuration is achievable under environmental contact. Due to the above reasons, applying existing robot planning methods to CRs with contact is not straightforward and remains understudied.…”

Section: Introductionmentioning

confidence: 99%

Kinetostatic Modeling of Continuum Delta Robot With Variable Curvature Continuum Joints

Wang

Ding

Zeng

et al. 2023

Journal of Mechanisms and Robotics

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Continuum robots have attracted lots of attention due to their structural compliance, manipulation dexterity, and design compactness. To extend the application scenarios, a slender continuum robot, the CurviPicker, was developed for low-load medium-speed pick-and-place tasks in a previous study. To improve the payload capacity and positioning accuracy of the CurviPicker, a novel Continuum Delta Robot (CDR) was then proposed with three dual-continuum-joint translators in a preliminary investigation. However, the initial version of the CDR did not fully utilize the bending ranges of its continuum joints. What's more, while being modeled using the constant curvature assumption for the continuum joints, the CDR shows lowered positioning accuracy for heavier objects, as the CDR's continuum joints diverge from the assumed constant curvature shapes. In this paper, the design of the CDR was re-optimized to enable wider bending ranges of the continuum joints (> 90 °) to generate enlarged workspace, taking into considerations several possible structural interferences. Furthermore, a kinetostatic model is derived based on the Cosserat rod theory to reduce the positioning errors caused by the external loads. The experimental result showed that the workspace is enlarged to approximately 9.47 × 107 mm3 compared with the volume of 6.57 × 107 mm3 of the initial version. Within this enlarged workspace, the average positioning error with a 1000-gram load was reduced to 1.93 mm, compared with 4.43 mm obtained by the previous constant curvature assumption.

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Quasi-static Path Planning for Continuum Robots By Sampling on Implicit Manifold

Wang,

Chen

2024

2024 IEEE International Conference on Robotics and Automation (ICRA)

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Real-Time Dynamics of Concentric Tube Robots With Reduced-Order Kinematics Based on Shape Interpolation

Cited by 11 publications

References 26 publications

Continuum Robots: An Overview

Continuum Robots: An Overview

Kinetostatic Modeling of Continuum Delta Robot With Variable Curvature Continuum Joints

Quasi-static Path Planning for Continuum Robots By Sampling on Implicit Manifold

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