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

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Title: Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz–Galerkin Methods
Authors: Sadati, SMH
Naghibi, SE
Walker, ID
Althoefer, K
Nanayakkara, T
Item Type: Journal Article
Abstract: To address the challenges with real-time accurate modeling of multisegment continuum manipulators in the presence of significant external and body loads, we introduce a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic methods. 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 the nonlinear impedance and configuration control. We showed that by considering the mechanical effects of highly elastic axial deformation, the model accuracy is increased 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 three-dimensional motions. Comparing to five different models in the literature, our approximate solution is shown to be more accurate with the smallest possible number of modeling states and suitable for real-time modeling, observation, and control applications.
Issue Date: 22-Aug-2017
Date of Acceptance: 30-Jul-2017
ISSN: 2377-3766
Publisher: Institute of Electrical and Electronics Engineers
Start Page: 328
End Page: 335
Journal / Book Title: IEEE Robotics and Automation Letters
Volume: 3
Issue: 1
Copyright Statement: © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor/Funder: Engineering & Physical Science Research Council (E
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/R511547/1
Publication Status: Published
Appears in Collections:Faculty of Engineering
Dyson School of Design Engineering

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