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

Research output: Contribution to journalArticle

S.M.Hadi Sadati, S. Elnaz Naghibi, Ian D. Walker, Kaspar Althoefer, Thrishantha Nanayakkara

Original languageEnglish
JournalIEEE Robotics and Automation Letters
Early online date22 Aug 2017
StateE-pub ahead of print - 22 Aug 2017


  • Control Space Reduction_SADATI_Publishedonline22August2017_GREEN AAM

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    Accepted author manuscript


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King's Authors


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 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 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.

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