A Sliding-rod Variable-strain Model for Concentric Tube Robots

Abstract

<div>In this work, the Piecewise Variable-strain (PVS) approach is applied to the case of Concentric Tube Robots (CTRs) and extended to include the tubes’ sliding motion. In particular, the currently accepted continuous Cosserat rod model is discretized onto a finite set of strain basis functions. At the same time, the insertion and rotation motions of the tubes are included as generalized coordinates instead of boundary kinematic conditions. Doing so, we obtain a minimum set of closed-form algebraic equations that can be solved not only for the shape variables but also for the actuation forces and torques for the first time. This new approach opens the way to torque-controlled CTRs, which is poised to enhance elastic stability and improve interaction forces’ control at the end-effector. </div>

Soft Robots Modeling: A Structured Overview

“…In this case, the complex double space integrals required by the strain-based parametrization are automatically performed through the two passes of the continuous computed torque algorithm of [22], whose inputs and outputs are reduced on the strain modes. In [76], the GVS approach is further extended to the modeling of concentric tube robot systems, including the modeling of the tube's insertion motion in quasi-steady conditions. In [77], the same approach is applied to the unsteady case to address the "paradoxical" dynamics of the sliding spaghetti [78].…”

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

“…The recent methods can potentially resolve some concerns about having computationally efficient models. Strain‐based modelling methods, 108–110 Screw theory‐based modelling, 111 and learning‐based approaches 112,113 are of the promising modelling techniques.…”

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

“…Beam or Cosserat rod mechanics and Hooke's material law are utilised for both cases. Other investigated models include [7]: (iii) approximating the robot forward map via Truncated Fourier series [1], (iv) lookup table for the robot kinematics based on precomputing simulation data, (v) direct measurement of the Boundary Conditions (BC) by force sensing at the robot base [8], (vi) finite element modeling based on piecewise constant strain assumption [9], (vii) reduced-order static model based on curvature interpolation [10], and (viii) learning-based methods [11]. Notably, all aforementioned models are quasi-static.…”

“…To address the infinite modeling states within the CTR research domain, Renda et al recently employed a reducedorder kinematic framework based on curvature interpolation to model a CTR in quasi-static motion [10]. The model achieved accuracy comparable to a Cosserat rod-based solution, and benefited from the reduced number of states, ease of considering curve-space constraints and forces (e.g., tube friction, although it is not considered there), and calculation of the deformation virtual energy.…”