Singular perturbation model of robots with elastic joints and elastic links constrained by rigid environment
type: Item
instance of: scholarly article
title: Singular perturbation model of robots with elastic joints and elastic links constrained by rigid environment
zbMATH Open document ID: 0914.93042
DOI: 10.1023/A:1007980617248
author: Paolo Rocco
published in: Journal of Intelligent \& Robotic Systems
publication date: 1998-11-26T00:00:00Z
review text: The contribution of this paper lies in the modelling methodology of robotic manipulators with flexible joints and links, subject to a contact with a stiff environment. The model of the dynamics of such a manipulator is provided in terms of a finite number of rigid and flexible coordinates describing the link dynamics, while the joint flexibility is accounted for classically according to Spong's simplified model. Eventually, the following model is derived: \[ M(q_r,q_f)\left[\begin{matrix} \ddot q_r\\ \ddot q_f\end{matrix}\right]+ \left[\begin{matrix} h_r(q_r, \dot q_r, q_f, \dot q_f)\\ h_f(q_r, \dot q_r, q_f,\dot q_f)\end{matrix}\right]+ \left[\begin{matrix} g_r(q_r, q_f)\\ g_f(q_r, q_f)\end{matrix}\right]+ \left[\begin{matrix} K_J(q_m- q_r)\\ K_f q_f\end{matrix}\right]= \left[\begin{matrix} A^T_r(q_r, q_f)\\ A^T_f(q_r, q_f)\end{matrix}\right] \lambda, \] \[ J_m\ddot q_m- K_J(q_m- q_r)= u, \] where \(q_r\), \(q_f\), \(q_m\) denote, respectively, the rigid, the flexible, and the actuator coordinates, and the matrices \(A^T_r\), \(A^T_f\) contain suitable partial derivatives of the constraint equation \(\Phi(q_r, q_f)= 0\). Under the assumption that the constraint equation can be solved with respect to a part of the rigid vector, the model is further reduced resulting in the elimination of the Lagrange multipliers \(\lambda\). Finally, a singularly perturbed version of the dynamics model is introduced. A model corresponding to the general singularly perturbed model with specific cases of rigid joints and flexible links as well as of elastic joints and rigid links is obtained.
Mathematics Subject Classification ID: 93C85
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 70B15
zbMATH DE Number: 1204422
zbMATH Keywords: flexible links
zbMATH Keywords: singular perturbation
zbMATH Keywords: modelling
zbMATH Keywords: robotic manipulators
zbMATH Keywords: flexible joints
zbMATH Keywords: contact
zbMATH Keywords: stiff environment
reviewed by: Krzysztof Tchoń
MaRDI profile type: Publication
full work available at URL: a:1007980617248
OpenAlex ID: W1555610325
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description: scientific article; zbMATH DE number 1204422