{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,23]],"date-time":"2024-04-23T13:40:12Z","timestamp":1713879612019},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2012,4,19]],"date-time":"2012-04-19T00:00:00Z","timestamp":1334793600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1017\/s0263574712000136","type":"journal-article","created":{"date-parts":[[2012,4,19]],"date-time":"2012-04-19T12:00:00Z","timestamp":1334836800000},"page":"113-122","source":"Crossref","is-referenced-by-count":5,"title":["Alternative proofs of four stability properties of rigid-link manipulators under PID position control"],"prefix":"10.1017","volume":"31","author":[{"given":"Ryo","family":"Kikuuwe","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2012,4,19]]},"reference":[{"key":"S0263574712000136_ref13","first-page":"187","article-title":"An estimate of the domain of attraction for the PID regulator of manipulators","volume":"22","author":"Meza","year":"2007","journal-title":"Int. J. Robot. Autom."},{"key":"S0263574712000136_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(00)00077-3"},{"key":"S0263574712000136_ref17","first-page":"228","article-title":"Robust PID control of robots","volume":"6","author":"Qu","year":"1991","journal-title":"Int. J. Robot. Autom."},{"key":"S0263574712000136_ref15","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008321920742"},{"key":"S0263574712000136_ref11","volume-title":"Nonlinear Systems","author":"Khalil","year":"2002"},{"key":"S0263574712000136_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/b10906"},{"key":"S0263574712000136_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574700017641"},{"key":"S0263574712000136_ref18","doi-asserted-by":"publisher","DOI":"10.1109\/70.508444"},{"key":"S0263574712000136_ref19","unstructured":"J. T. Wen and S. H. Murphy , \u201cPID control for robot manipulators,\u201d CIRSSE Document #54, Rensselaer Polytechnic Institute (1990). 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