{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T16:26:17Z","timestamp":1778948777923,"version":"3.51.4"},"reference-count":33,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[1997,10,1]],"date-time":"1997-10-01T00:00:00Z","timestamp":875664000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[1997,10]]},"abstract":"<jats:p>One of the simplest position controllers for robot manipula tors is the PD control with desired gravity compensation. The objective of this article is to review important aspects of this control scheme that are reported in the literature. We begin by showing the boundedness of solutions for the closed-loop system, and conditions for equilibrium uniqueness. The global asymptotic stability analysis provided by Takegaki and Arimoto (1981) is discussed in detail, as well as an alternative method that uses a strict Lyapunov function. The stability robustness of the control system against parametric uncertainties is also ad dressed. We show that interesting phenomena such as equilibria bifurcation can appear if the design procedure is violated. To overcome parametric uncertainties, we review an adaptive ver sion of the PD control with desired gravity compensation, and finally, we revise an extension of the controller to handle robots with elastic joints.<\/jats:p>","DOI":"10.1177\/027836499701600505","type":"journal-article","created":{"date-parts":[[2007,3,4]],"date-time":"2007-03-04T20:24:06Z","timestamp":1173039846000},"page":"660-672","source":"Crossref","is-referenced-by-count":112,"title":["PD Control with Desired Gravity Compensation of Robotic Manipulators"],"prefix":"10.1177","volume":"16","author":[{"given":"Rafael","family":"Kelly","sequence":"first","affiliation":[{"name":"Divisi\u00f3n de Fisica Aplicada CICESE Carretera Tijuana-Ensenada Km. 107 Ensenada, Baja California, 22800, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1997,10,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(93)90076-I"},{"key":"atypb2","unstructured":"Arimoto, S., and Miyazaki, F. 1984. Stability and robustness of PID feedback control for robot manipulators of sensory capability. In Brady, M., and Paul, R. P. (eds.): Robotics Research: First International Symposium. Cambridge, MA: MIT Press, pp. 783-799."},{"key":"atypb3","unstructured":"Arimoto, S., and Miyazaki, F. 1986. Stability and robustness of PD feedback control with gravity compensation for robot manipulators. In Paul, F. W. and Youcef-Toumi, D. (eds.): Robotics: Theory and Applications\u2014DSC, vol. 3. American Society of Mechanical Engineers , pp. 67-72."},{"key":"atypb4","volume-title":"Proceedings of the American Control Conference","author":"Arimoto, S."},{"key":"atypb5","volume-title":"Proceedings of the First ASCC (Asian Control Conference","author":"Arimoto, S."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(93)90071-D"},{"key":"atypb7","volume-title":"Introduction to Robotics","author":"Craig, J.J.","year":"1989","edition":"2"},{"key":"atypb8","volume-title":"Feedback Systems: Input-Output Properties","author":"Desoer, C.A.","year":"1975"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1177\/027836499301200508"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4426-4"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620110606"},{"key":"atypb12","volume-title":"Perspectives of Nonlinear Dynamics","author":"Jackson, A.E.","year":"1991"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/70.210803"},{"key":"atypb14","volume-title":"Proceedings of the 12th IFAC World Congress","author":"Kelly, R."},{"key":"atypb15","volume-title":"Bifurcation in PD feedback regulation of a single pendulum. 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