Alternative proofs of four stability properties of rigid-link manipulators under PID position control

Ryo Kikuuwe

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper presents new proofs of four stability properties (semiglobal strict passivity, semiglobal asymptotic stability, semiglobal input-to-state stability, and semiglobal uniform ultimate boundedness with an arbitrarily reducible ultimate bound) of a rigid-link manipulator under proportional- integral-derivative (PID) position control. The proofs employ a strict Lyapunov function and a novel parameterization to provide four inequality conditions for the stability properties. In those inequalities, arithmetic operations on physical quantities are physically consistent if the joints are all revolute or all prismatic. A gain selection procedure is presented by which the ultimate bounds of velocity error, position error, and its integral can be independently designed.

Original languageEnglish
Pages (from-to)113-122
Number of pages10
JournalRobotica
Volume31
Issue number1
DOIs
Publication statusPublished - Jan 1 2013

Fingerprint

Position Control
Position control
Manipulator
Manipulators
Directly proportional
Derivatives
Ultimate Boundedness
Derivative
Uniform Boundedness
Passivity
Alternatives
Selection Procedures
Asymptotic Stability
Parameterization
Lyapunov Function
Lyapunov functions
Asymptotic stability

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Mathematics(all)
  • Computer Science Applications

Cite this

Alternative proofs of four stability properties of rigid-link manipulators under PID position control. / Kikuuwe, Ryo.

In: Robotica, Vol. 31, No. 1, 01.01.2013, p. 113-122.

Research output: Contribution to journalArticle

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