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Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

Published online by Cambridge University Press:  12 April 2024

Ali Ahmadi N Open the ORCID record for Ali Ahmadi N [Opens in a new window] ,
Ali Kamali Eigoli  and
Afshin Taghvaeipour
Ali Ahmadi N
Affiliation:
Vibration and Control Laboratory, Department of Mechanical Engineering, Amirkabir University of Technology – ISME Node, Tehran, Iran
Ali Kamali Eigoli*
Affiliation:
Vibration and Control Laboratory, Department of Mechanical Engineering, Amirkabir University of Technology – ISME Node, Tehran, Iran
Afshin Taghvaeipour
Affiliation:
Multibody Systems Research Laboratory, Department of Mechanical Engineering, Amirkabir University of Technology – ISME Node, Tehran, Iran
*
Corresponding author: Ali Kamali Eigoli; Email: alikamalie@aut.ac.ir
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Abstract

This research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.

Keywords

screw theoryankle rehabilitationspherical parallel robotsself-tuning controllerexplicit dynamic modeling
Type
Research Article
Information
Robotica , Volume 42 , Issue 5 , May 2024 , pp. 1568 - 1596
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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