Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods
Article
Sadati, S. M. H., Naghibi, S. E., Walker, I. D., Althoefer, K. and Nanayakkara, T. 2017. Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods. IEEE Robotics and Automation Letters. 3 (1), pp. 328 - 335. https://doi.org/10.1109/LRA.2017.2743100
Authors | Sadati, S. M. H., Naghibi, S. E., Walker, I. D., Althoefer, K. and Nanayakkara, T. |
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Abstract | To address the challenges with real-time accurate modeling of multi-segment 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 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 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 3D 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. |
Keywords | Flexible Robots; Soft Material Robotics; Dynamics; Motion Control; Force Control |
Journal | IEEE Robotics and Automation Letters |
Journal citation | 3 (1), pp. 328 - 335 |
ISSN | 2377-3766 |
Year | 2017 |
Publisher | IEEE |
Accepted author manuscript | License File Access Level Anyone |
Digital Object Identifier (DOI) | https://doi.org/10.1109/LRA.2017.2743100 |
Publication dates | |
Online | 22 Aug 2017 |
Publication process dates | |
Deposited | 05 Jun 2023 |
Funder | Engineering and Physical Sciences Research Council (EPSRC) |
European Union H2020 | |
Copyright information | © 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. |
https://repository.uel.ac.uk/item/8w165
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Accepted author manuscript
FinalAcceptedbeforeprrofreadcorrections.pdf | ||
License: All rights reserved | ||
File access level: Anyone |
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