{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:47Z","timestamp":1740134567902,"version":"3.37.3"},"reference-count":17,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61075083","13A120204","2012CXRC14","2012BS043"],"award-info":[{"award-number":["61075083","13A120204","2012CXRC14","2012BS043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Henan Education Department","award":["61075083","13A120204","2012CXRC14","2012BS043"],"award-info":[{"award-number":["61075083","13A120204","2012CXRC14","2012BS043"]}]},{"name":"Technology Innovation Talents Plan of Henan University of Technology","award":["61075083","13A120204","2012CXRC14","2012BS043"],"award-info":[{"award-number":["61075083","13A120204","2012CXRC14","2012BS043"]}]},{"DOI":"10.13039\/501100003172","name":"Science Foundation of Henan University of Technology","doi-asserted-by":"crossref","award":["61075083","13A120204","2012CXRC14","2012BS043"],"award-info":[{"award-number":["61075083","13A120204","2012CXRC14","2012BS043"]}],"id":[{"id":"10.13039\/501100003172","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>The mathematic description of the trajectory of robot manipulators with the optimal trajectory tracking problem is formulated as an optimal control problem, and a parametric approach is proposed for the optimal trajectory tracking control problem. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, a practical method is presented to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results of 2-link robot manipulator are presented to show the effectiveness of the proposed method.<\/jats:p>","DOI":"10.1155\/2013\/958597","type":"journal-article","created":{"date-parts":[[2013,10,31]],"date-time":"2013-10-31T23:11:26Z","timestamp":1383261086000},"page":"1-6","source":"Crossref","is-referenced-by-count":1,"title":["Parametric Approach to Trajectory Tracking Control of Robot Manipulators"],"prefix":"10.1155","volume":"2013","author":[{"given":"Shijie","family":"Zhang","sequence":"first","affiliation":[{"name":"Research Institute of Robotics, Henan University of Technology, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Ning","sequence":"additional","affiliation":[{"name":"Research Institute of Robotics, Henan University of Technology, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"2","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2012.2191969"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2007.912235"},{"key":"5","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1109\/TNNLS.2012.2228230","volume":"24","year":"2013","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.2514\/3.25412"},{"key":"7","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1002\/(SICI)1097-4563(200005)17:5<233::AID-ROB1>3.0.CO;2-Y","volume":"17","year":"2000","journal-title":"Journal of Robotic Systems"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574700002770"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1002\/rob.20045"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1109\/70.313107"},{"issue":"7","key":"13","first-page":"1579","volume":"5","year":"2006","journal-title":"WSEAS Transactions on Systems"},{"key":"14","first-page":"2991","volume":"3","year":"2004","journal-title":"WSEAS Transactions on Systems"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1109\/41.836358"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1109\/5326.827451"},{"key":"18","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1109\/72.485674","volume":"7","year":"1996","journal-title":"IEEE Transactions on Neural Networks"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1017\/S0334270000010936"},{"year":"1991","key":"20"},{"year":"1996","key":"22"},{"issue":"2","key":"23","first-page":"157","volume":"4","year":"1996","journal-title":"Neural, Parallel & Scientific Computations"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/958597.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/958597.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/958597.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T21:14:07Z","timestamp":1498079647000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/958597\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":17,"alternative-id":["958597","958597"],"URL":"https:\/\/doi.org\/10.1155\/2013\/958597","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}