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

Published online by Cambridge University Press:  19 April 2012

Ryo Kikuuwe
Ryo Kikuuwe*
Affiliation:
Department of Mechanical Engineering, Kyushu University, Fukuoka, Japan
*
*Corresponding author. E-mail: kikuuwe@mech.kyushu-u.ac.jp
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Summary

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.

Keywords

Robot dynamicsControl of robotic systemsPID controlStability analysisPassivity
Type
Articles
Information
Robotica , Volume 31 , Issue 1 , January 2013 , pp. 113 - 122
Copyright
Copyright © Cambridge University Press 2012

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