Compliant control of a two-link flexible manipulator by constraint Hamiltonian system
type: Item
instance of: scholarly article
title: Compliant control of a two-link flexible manipulator by constraint Hamiltonian system
zbMATH Open document ID: 0980.93054
DOI: 10.1016/S0094-114X(97)00041-4
author: Seung-Bok Choi
author: Hyuc-Bum Lee
author: Brian S. Thompson
published in: Mechanism and Machine Theory
publication date: 1999-09-06T00:00:00Z
review text: The paper attempts to describe the control of a two-link flexible manipulator. But unfortunately a lot of confusion takes place. For example Hamiltonian equations are valid for holonomic systems, so the constraints do not depend on impulses. The first group of equations \(\dot q={\partial H\over\partial p_S}\) give the definition of the impulses and another group give the result of the transformation of a general dynamical equation. And only in the next group of equations the generalized forces: \(\dot q= -{\partial H\over\partial q_S}- Q_S\) are used. But here the generalized forces are entered in both groups of equations. The D'Alembert principle has another signification, namely: The dynamical equations may be rewritten in the form of static equations if one adds the inertia forces to the applied forces. The investigation of stability by the Lyapunov method is incorrect because, for example, the derivative of one term of the Lyapunov function \({\partial\over\partial t}(e^2_1)=2e_1\cdot\dot e_1\), where \(e_1= \theta_1- \theta^*_1\) is of variable sign. So it is impossible to guarantee the negative definiteness of the derivative of the Lyapunov function and the statement about stability makes no sense. Finally, it is relevant to remember that the description on how to account for the flexibility of deformable bodies is contained in the book of \textit{A. I. Lur'e} [Analytic Mechanics (Russisan), Moscow: FizMatLit (1961; Zbl 0103.39803)].
reviewed by: Yuri N. Sankin
Mathematics Subject Classification ID: 93C85
Mathematics Subject Classification ID: 70B15
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 1331544
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: robotic manipulator
zbMATH Keywords: end-effector
zbMATH Keywords: two-link flexible manipulator
zbMATH Keywords: holonomic systems
zbMATH Keywords: constraints
zbMATH Keywords: stability
zbMATH Keywords: flexibility
zbMATH Keywords: deformable bodies
MaRDI profile type: Publication
full work available at URL: s0094-114x(97)00041-4
OpenAlex ID: W1972607966
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description: scientific article; zbMATH DE number 1331544