{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T10:07:59Z","timestamp":1777716479202,"version":"3.51.4"},"reference-count":28,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2014,2,20]],"date-time":"2014-02-20T00:00:00Z","timestamp":1392854400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2014,5]]},"abstract":"<jats:p>This paper presents a trajectory planning algorithm for linear multi-axis systems. It generates smooth trajectories of any order subject to general initial and final conditions, and constant state and control constraints. The algorithm is recursive, as it constructs a high order trajectory using lower order trajectories. Multi-axis trajectories are computed by synchronizing independent single-axis trajectories to reach their respective targets at the same time.<\/jats:p>\n                  <jats:p>The algorithm\u2019s efficiency and ability to handle general initial and final conditions make it suitable for reactive real-time applications. Its ability to generate high order trajectories makes it suitable for applications requiring high trajectory smoothness. The algorithm is demonstrated in several examples for single- and dual-axis trajectories of orders 2\u20136.<\/jats:p>","DOI":"10.1177\/0278364913517148","type":"journal-article","created":{"date-parts":[[2014,2,20]],"date-time":"2014-02-20T21:45:11Z","timestamp":1392932711000},"page":"898-916","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":49,"title":["Planning high order trajectories with general initial and final conditions and asymmetric bounds"],"prefix":"10.1177","volume":"33","author":[{"given":"Ben","family":"Ezair","sequence":"first","affiliation":[{"name":"The Department of Mathematics and Computer Science, The Open University, Ra\u2019anana, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tamir","family":"Tassa","sequence":"additional","affiliation":[{"name":"The Department of Mathematics and Computer Science, The Open University, Ra\u2019anana, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zvi","family":"Shiller","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering and Mechatronics, Ariel University, Ariel, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2014,2,20]]},"reference":[{"key":"bibr1-0278364913517148","doi-asserted-by":"publisher","DOI":"10.1109\/56.811"},{"key":"bibr2-0278364913517148","doi-asserted-by":"publisher","DOI":"10.1177\/027836498500400301"},{"key":"bibr3-0278364913517148","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2008.4650608"},{"key":"bibr4-0278364913517148","volume-title":"Applied Optimal Control","author":"Bryson A","year":"1969"},{"key":"bibr5-0278364913517148","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-4563(200005)17:5<233::AID-ROB1>3.0.CO;2-Y"},{"key":"bibr6-0278364913517148","unstructured":"Ezair B, Tassa T, Shiller Z (2013) Robot application simulation. 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