{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T01:33:47Z","timestamp":1791077627982,"version":"4.1.0"},"reference-count":16,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[1994,2,1]],"date-time":"1994-02-01T00:00:00Z","timestamp":760060800000},"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":[[1994,2]]},"abstract":"<jats:p>There has been significant interest in the periodic behavior, generally referred to as repeatability, exhibited by a kine matically redundant manipulator while performing a cyclic end-effector motion. Much of the early work in this area has been restricted to planar manipulators whose configuration is described in terms of absolute joint angles to simplify the problem. Unfortunately, this has resulted in the observation of certain phenomena that are unique to this special case and that do not describe the behavior of more complicated ma nipulators. The goal of this work is to clarify some possible misconceptions concerning the limiting behavior of a redun dant manipulator under nonconservative control strategies, with particular emphasis on pseudoinverse control. In particular, stable surfaces are shown to be extremely rare, and a weaker property, referred to as repeatable trajectories, is responsible for the repeatable behavior observed in previous work. It is also shown that the Lie bracket condition need not be satisfied for this type of repeatable behavior to occur and that such trajectories need not have zero torsion, as has been previously suggested.<\/jats:p>","DOI":"10.1177\/027836499401300105","type":"journal-article","created":{"date-parts":[[2007,3,4]],"date-time":"2007-03-04T20:24:06Z","timestamp":1173039846000},"page":"70-81","source":"Crossref","is-referenced-by-count":28,"title":["Singularities, Stable Surfaces, and the Repeatable Behavior of Kinematically Redundant Manipulators"],"prefix":"10.1177","volume":"13","author":[{"given":"Rodney G.","family":"Roberts","sequence":"first","affiliation":[{"name":"Armstrong Laboratory\/CFBS Wright Patterson Air Force Base Dayton, Ohio 45433"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony A.","family":"Maciejewski","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering Purdue University West Lafayette, Indiana 47907"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[1994,2,1]]},"reference":[{"key":"atypb1","unstructured":"Angeles, J., and Mathur, S. 1989. Resolved-rate control of redundant manipulators with elimination of nonconservative effects. In Miura, H., and Arimoto, S. (eds.): Robotics Research: The Fifth International Symposium. Cambridge, MA: MIT Press, pp. 209-216."},{"key":"atypb2","volume-title":"Proc. 1985 IEEE Int. Conf. Robotics Automat","author":"Baillieul, J."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1177\/027836499201100103"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/JRA.1987.1087118"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1983.6313123"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1109\/70.88043"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1109\/21.156584"},{"key":"atypb8","first-page":"209","author":"Maciejewski, A.A.","year":"1990","journal-title":"Proc. Am. Contr. 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