{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T02:59:07Z","timestamp":1771037947250,"version":"3.50.1"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"12","license":[{"start":{"date-parts":[[2017,4,3]],"date-time":"2017-04-03T00:00:00Z","timestamp":1491177600000},"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":[[2017,12]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>This paper focuses on the problem of robust time-optimal trajectory planning of robotic manipulators to track a given path under a probabilistic limited actuation, that is, the probability for the actuation to be limited is no less than a given bound \u03ba. We give a general and practical method to reduce the probabilistic constraints to a set of deterministic constraints and show that the deterministic constraints are equivalent to a set of linear constraints under certain conditions. As a result, the original problem is reduced to a linear optimal control problem which can be solved with linear programming in polynomial time. In the case of \u03ba = 1, the original problem is proved to be equivalent to the linear optimal control problem. Overall, a very general, practical, and efficient algorithm is given to solve the above problem and numerical simulation results are used to show the effectiveness of the method.<\/jats:p>","DOI":"10.1017\/s026357471700011x","type":"journal-article","created":{"date-parts":[[2017,4,3]],"date-time":"2017-04-03T11:44:23Z","timestamp":1491219863000},"page":"2400-2417","source":"Crossref","is-referenced-by-count":10,"title":["An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation"],"prefix":"10.1017","volume":"35","author":[{"given":"Ming-Yong","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Shan","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2017,4,3]]},"reference":[{"key":"S026357471700011X_ref003","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1985.1104009"},{"key":"S026357471700011X_ref006","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2009.2028959"},{"key":"S026357471700011X_ref018","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-013-3180-4"},{"key":"S026357471700011X_ref021","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2004.04.002"},{"key":"S026357471700011X_ref013","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2014.2323934"},{"key":"S026357471700011X_ref014","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2014.2344507"},{"key":"S026357471700011X_ref015","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1076\/mcmd.8.1.75.8343","article-title":"Robust optimal trajectory planning for robots by stochastic optimization","volume":"8","author":"Marti","year":"2002","journal-title":"Math. 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