{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:54:57Z","timestamp":1777715697385,"version":"3.51.4"},"reference-count":16,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[1999,9,1]],"date-time":"1999-09-01T00:00:00Z","timestamp":936144000000},"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":[[1999,9]]},"abstract":"<jats:p>An original method called the three-cubic method is proposed to generate online robot                 joint trajectories interpolating given position points with associated velocities.                 The method is based on an acceleration profile composed of three cubic polynomial                 segments, which ensure a zero acceleration at each intermediate point. Velocity and                 acceleration continuity is obtained, and this three-cubics combination allows the                 analytical solution to the minimum time trajectory problem under maximum velocity                 and acceleration constraints. Possible wandering is detected and can be overcome.                 Furthermore, the analytical solution to the minimum time trajectory problem leads to                 an online trajectory computation.<\/jats:p>","DOI":"10.1177\/02783649922066637","type":"journal-article","created":{"date-parts":[[2003,7,19]],"date-time":"2003-07-19T02:59:46Z","timestamp":1058583586000},"page":"893-901","source":"Crossref","is-referenced-by-count":32,"title":["The Three-Cubic Method: An Optimal Online Robot Joint Trajectory Generator                 under Velocity, Acceleration, and Wandering Constraints"],"prefix":"10.1177","volume":"18","author":[{"given":"Bertrand","family":"Tondu","sequence":"first","affiliation":[{"name":"LESIA, Electrical Engineering Department, of INSAT Campus de Rangueil,                         31077, Toulouse Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shafaat Ahmed","family":"Bazaz","sequence":"additional","affiliation":[{"name":"LESIA, Electrical Engineering Department, of INSAT Campus de Rangueil,                         31077, Toulouse Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1999,9]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1109\/56.811","volume":"4","year":"1988","unstructured":"Bobrow, J. 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