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

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 p...

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Bibliographic Details
Published in:IEEE robotics and automation letters 2018-01, Vol.3 (1), p.328-335
Main Authors: Sadati, S. M. Hadi, Naghibi, S. Elnaz, Walker, Ian D., Althoefer, Kaspar, Nanayakkara, Thrishantha
Format: Article
Language:English
Subjects:
Deformable models
Deformation effects
Dynamics
Elastic deformation
flexible robots
force control
Galerkin method
Kinematics
Load modeling
Manipulator dynamics
Manipulators
Mathematical analysis
Model accuracy
Modelling
motion control
Nonlinear control
Polynomials
Real time
Ritz method
soft material robotics
Solid modeling
Three dimensional models
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Summary: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.
ISSN:2377-3766
2377-3766
DOI:10.1109/LRA.2017.2743100