{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,6]],"date-time":"2025-06-06T14:48:47Z","timestamp":1749221327463,"version":"3.37.0"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,3,9]],"date-time":"2009-03-09T00:00:00Z","timestamp":1236556800000},"content-version":"unspecified","delay-in-days":5365,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[1994,7]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>A new approach to generating smooth piecewise local trajectories for mobile robots is proposed in this paper. Given the configurations (position and direction) of two points, we search for the trajectory that minimizes the integral of acceleration (tangential and normal). The resulting trajectory should not only be smooth but also safe in order to be applicable in real-life situations. Therefore, we investigate two different obstacle-avoidance constraints that satisfy the minimization problem. Unfortunately, in this case the problem becomes more complex and not suitable for real time implementations. Therefore, we introduce two simple solutions, based on the idea of polynomial fitting, to generate safe trajectories once a collision is detected with the original smooth trajectory. Simulation results of the different algorithms are presented.<\/jats:p>","DOI":"10.1017\/s026357470001732x","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T13:14:01Z","timestamp":1236690841000},"page":"299-307","source":"Crossref","is-referenced-by-count":3,"title":["Piecewise smooth and safe trajectory planning"],"prefix":"10.1017","volume":"12","author":[{"given":"Ashraf","family":"Elnagar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anup","family":"Basu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"volume-title":"Geometric Principles and Procedures for Computing Graphic Applications","year":"1978","author":"Chasen","key":"S026357470001732X_ref014"},{"volume-title":"Two-point Boundary Value Problems: Shooting Methods","year":"1972","author":"Roberts","key":"S026357470001732X_ref012"},{"key":"S026357470001732X_ref003","unstructured":"3. Jacobs P. and Canny C. , \u201cRobust motion planning for mobile robots\u201d Proceedings of the IEEE International Conference on Robotics and Automation (1990) pp. 2\u20137."},{"key":"S026357470001732X_ref005","doi-asserted-by":"publisher","DOI":"10.1145\/356056.356061"},{"key":"S026357470001732X_ref002","unstructured":"2. Laumond J. , \u201cFinding collision-free smooth trajectories for a nen-holonomic mobile robot\u201d Proceedings of the Tenth International Joint Conference on Artificial Intelligence (1987) pp. 1120\u20131123."},{"key":"S026357470001732X_ref004","unstructured":"4. Donald D. and Xavier P. , \u201cA provably good approximation algorithm for optimal time trajectory planning\u201d Proceedings of the IEEE International Conference on Robotics and Automation (1989) pp. 958\u2013963."},{"key":"S026357470001732X_ref009","doi-asserted-by":"crossref","unstructured":"9. Elnagar A. and Basu A. , \u201cHeuristics for local path planning\u201d Proceedings of the IEEE International Conference of Robotics and Automation (05, 1992) pp. 2481\u20132486.","DOI":"10.1109\/ROBOT.1992.220093"},{"volume-title":"Numerical Methods for Two-point Boundary-Value Problems","year":"1968","author":"Keller","key":"S026357470001732X_ref011"},{"key":"S026357470001732X_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0734-189X(90)90105-5"},{"key":"S026357470001732X_ref008","unstructured":"8. Kanayama Y. and Hartman B. \u201cSmooth local path planning for autonomous vehicles\u201d Proceedings of the IEEE International Conference on Robotics and Automation (1980) pp. 1265\u20131270."},{"key":"S026357470001732X_ref006","doi-asserted-by":"publisher","DOI":"10.1145\/7921.7924"},{"key":"S026357470001732X_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/2372560"},{"volume-title":"Calculus of Variation","year":"1961","author":"Elsgolc","key":"S026357470001732X_ref010"},{"key":"S026357470001732X_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6333-3"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S026357470001732X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T04:54:23Z","timestamp":1738990463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S026357470001732X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,7]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1994,7]]}},"alternative-id":["S026357470001732X"],"URL":"https:\/\/doi.org\/10.1017\/s026357470001732x","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"type":"print","value":"0263-5747"},{"type":"electronic","value":"1469-8668"}],"subject":[],"published":{"date-parts":[[1994,7]]}}}