Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods. Sadati, S. M. H., Naghibi, S. E., Walker, I. D., Althoefer, K., & Nanayakkara, T. IEEE Robotics and Automation Letters, 3(1):328–335, January, 2018. doi abstract bibtex 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.
@article{sadati_control_2018,
title = {Control {Space} {Reduction} and {Real}-{Time} {Accurate} {Modeling} of {Continuum} {Manipulators} {Using} {Ritz} and {Ritz}-{Galerkin} {Methods}},
volume = {3},
doi = {10.1109/LRA.2017.2743100},
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.},
number = {1},
journal = {IEEE Robotics and Automation Letters},
author = {Sadati, S. M. H. and Naghibi, S. E. and Walker, I. D. and Althoefer, K. and Nanayakkara, T.},
month = jan,
year = {2018},
keywords = {Deformable models, Dynamics, Galerkin method, Kinematics, Lagrangian dynamic methods, Load modeling, Manipulator dynamics, Ritz-Galerkin methods, Solid modeling, continuum manipulators, control space reduction, elastic axial deformation, elastic deformation, flexible robots, force control, manipulator dynamics, mechanical effects, motion control, real-time accurate modeling, soft material robotics, variable-curvature Cosserat rod static},
pages = {328--335}
}
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