Motional stabilization of the elastic manipulator
type: Item
instance of: scholarly article
title: Motional stabilization of the elastic manipulator
zbMATH Open document ID: 0949.93053
author: V. I. Matyukhin
published in: Automation and Remote Control
publication date: 2000-12-05T00:00:00Z
review text: The problem addressed is the joint space trajectory tracking in a manipulation robot having some kind of flexibility. This flexibility is modeled by introducing into the manipulator a suitable number of artificial, non-actuated joints. It is assumed that the elastic forces exerted at these joints depend on the joints' positions and velocities, and are described as \[ M_i=-k_i \psi_i-l_i \dot\psi_i \] \((\psi_i\) denote positions of the non-actuated joints) for some positive gain coefficients \(k_i,l_i\). Under such an assumption the main result of this paper establishes that a control law of the form \[ u_j=-H_j \text{sign}(s_k), \quad s_i=\dot e_j+\lambda_je_j,\;e_j= \varphi_j- \varphi^*_j, \] where \(\varphi_j\) stand for positions of actuated joints, \(\varphi^*_j\) denote desirable actuated joint trajectory, \(\lambda_t>0\), renders the closed loop system exponentially stable provided that the gain coefficients \(l_i\) of non-actuated joints are sufficiently large.
Mathematics Subject Classification ID: 93C85
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 1263131
zbMATH Keywords: elastic joints
zbMATH Keywords: stabilization
zbMATH Keywords: trajectory tracking
zbMATH Keywords: manipulation robot
zbMATH Keywords: flexibility
reviewed by: Krzysztof Tchoń
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1263131