{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T06:05:17Z","timestamp":1778306717434,"version":"3.51.4"},"reference-count":24,"publisher":"Emerald","issue":"1","license":[{"start":{"date-parts":[[2018,1,15]],"date-time":"2018-01-15T00:00:00Z","timestamp":1515974400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IR"],"published-print":{"date-parts":[[2018,1,15]]},"abstract":"<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>This paper aims to present a method for improving the state estimation of a robot in the presence of noise measurement, which can improve the performance of the robot controller.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>In this work, a novel nonlinear tracking differentiator (NTD) was formulated to solve the problems of phase lag, low stability and amplitude attenuation faced by traditional tracking differentiators, which can be used for the state estimation of a robot. Based on the user-defined function stu() with linear and nonlinear characteristics, the authors establish a new acceleration function of NTD and confirm its global asymptotic stability by using the Lyapunov method and the system equivalence method. Phase plane analysis shows that the origin is its stable nodal point or focus point and uncovers the basic constraint conditions for parameter regulation. In addition, the convergence property and robustness performance against noises are studied by describing function method.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>Comparative simulations, robot state estimation experiments and joint trajectory tracking experiments have indicated that NTD proposed integrates tracking rapidness, accuracy and transitional stability and has high approximation and filtering effects on generalized derivatives of the signal, which contribute to an excellent performance of robot controller in stability and response speed in practice.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>The main contribution of this paper lies in the design of a novel NTD, which successfully improves the state estimation of a robot joint in noisy surroundings, the tracking performance of robot controller and the stability of the system.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/ir-08-2017-0149","type":"journal-article","created":{"date-parts":[[2017,12,13]],"date-time":"2017-12-13T09:10:04Z","timestamp":1513156204000},"page":"11-22","source":"Crossref","is-referenced-by-count":4,"title":["State estimation of a robot joint by a novel nonlinear tracking differentiator"],"prefix":"10.1108","volume":"45","author":[{"given":"Xiao","family":"Tu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunfei","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pu","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Cheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","reference":[{"issue":"4","key":"key2020093023520098300_ref001","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1108\/01439910710749618","article-title":"An introduction to computational intelligence techniques for robot control","volume":"34","year":"2007","journal-title":"Industrial Robot: An International Journal"},{"issue":"4","key":"key2020093023520098300_ref002","first-page":"533","article-title":"Design and phase plane analysis of an arctangent-based tracking differentiator","volume":"27","year":"2010","journal-title":"Control Theory & Applications"},{"issue":"4","key":"key2020093023520098300_ref003","first-page":"487","article-title":"Nonlinear PID controller","volume":"20","year":"1994","journal-title":"Acta Automatica Sinica"},{"issue":"2","key":"key2020093023520098300_ref004","first-page":"177","article-title":"Nonlinear tracking-differentiator","volume":"14","year":"1994","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"key":"key2020093023520098300_ref005","first-page":"2","article-title":"The discrete form of tracking-differentiator","volume":"3","year":"1999","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"issue":"10","key":"key2020093023520098300_ref006","first-page":"234","article-title":"On the improved nonlinear tracking differentiator based nonlinear PID controller design","volume":"7","year":"2016","journal-title":"International Journal of Advanced Computer Science and Applications"},{"issue":"6","key":"key2020093023520098300_ref007","first-page":"729","article-title":"A new discrete-time form of optimal tracking differentiator","volume":"42","year":"2013","journal-title":"Information and Control"},{"issue":"7","key":"key2020093023520098300_ref008","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1016\/j.mechatronics.2004.03.002","article-title":"Precise slow motion control of a direct-drive robot arm with velocity estimation and friction compensation","volume":"14","year":"2004","journal-title":"Mechatronics"},{"key":"key2020093023520098300_ref009","first-page":"182","article-title":"Qualitative methods and bifurcation for ordinary differential equations","year":"2002"},{"issue":"1","key":"key2020093023520098300_ref010","first-page":"312","article-title":"From PID to nonlinear state error feedback controller","volume":"8","year":"2017","journal-title":"International Journal of Advanced Computer Science and Applications"},{"issue":"11","key":"key2020093023520098300_ref011","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1002\/rnc.3643","article-title":"Robust output-control for uncertain linear systems: homogeneous differentiator-based observer approach","volume":"27","year":"2017","journal-title":"International Journal of Robust and Nonlinear Control"},{"issue":"8","key":"key2020093023520098300_ref012","first-page":"1116","article-title":"Nonlinear tracking differentiator based on improved sigmoid function","volume":"31","year":"2014","journal-title":"International Journal of Control Theory and Applications"},{"issue":"9","key":"key2020093023520098300_ref013","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1016\/j.jfranklin.2016.03.007","article-title":"Back-stepping robust trajectory linearization control for hypersonic reentry vehicle via novel tracking differentiator","volume":"353","year":"2016","journal-title":"Journal of the Franklin Institute"},{"key":"key2020093023520098300_ref014","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.ymssp.2016.12.034","article-title":"Augmented nonlinear differentiator design","volume":"90","year":"2017","journal-title":"Mechanical Systems and Signal Processing"},{"key":"key2020093023520098300_ref015","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.isatra.2016.11.011","article-title":"Augmented nonlinear differentiator design and application to nonlinear uncertain systems","volume":"67","year":"2017","journal-title":"ISA Transactions"},{"issue":"4","key":"key2020093023520098300_ref016","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/JSTSP.2009.2024591","article-title":"Nonlinear tracking-differentiator for velocity determination using carrier phase measurements","volume":"3","year":"2009","journal-title":"IEEE Journal of Selected Topics in Signal Processing"},{"issue":"7","key":"key2020093023520098300_ref017","doi-asserted-by":"crossref","first-page":"3736","DOI":"10.1109\/TIE.2013.2262754","article-title":"Improving the rapidity of nonlinear tracking differentiator via feedforward","volume":"61","year":"2014","journal-title":"IEEE Transactions on Industrial Electronics"},{"key":"key2020093023520098300_ref018","volume-title":"Nonlinear Systems Analysis","year":"2002"},{"issue":"6","key":"key2020093023520098300_ref019","first-page":"875","article-title":"Nonlinear tracking-differentiator with high speed in whole course","volume":"20","year":"2003","journal-title":"Control Theory & Applications"},{"issue":"9","key":"key2020093023520098300_ref020","doi-asserted-by":"crossref","first-page":"1731","DOI":"10.1109\/TAC.2007.904290","article-title":"Finite-time-convergent differentiator based on singular perturbation technique","volume":"52","year":"2007","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"2","key":"key2020093023520098300_ref021","first-page":"127","article-title":"A high-speed nonlinear discrete tracking-differentiator with high precision","volume":"26","year":"2009","journal-title":"Control Theory & Applications"},{"issue":"13","key":"key2020093023520098300_ref022","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1002\/rnc.606","article-title":"Robust and non-linear control of marine system","volume":"11","year":"2001","journal-title":"International Journal of Robust and Nonlinear Control"},{"issue":"6","key":"key2020093023520098300_ref023","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1108\/IR-09-2012-406","article-title":"A novel PID tuning method for robot control","volume":"40","year":"2013","journal-title":"Industrial Robot: An International Journal"},{"issue":"45","key":"key2020093023520098300_ref024","first-page":"43","article-title":"Design of nonlinear-linear tracking differentiator with high stability and high speed","volume":"8","year":"2011","journal-title":"Journal of Xi\u2019an Jiaotong University"}],"container-title":["Industrial Robot: An International Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/IR-08-2017-0149\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/IR-08-2017-0149\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T21:39:41Z","timestamp":1753393181000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/ir\/article\/45\/1\/11-22\/175432"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,15]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1,15]]}},"alternative-id":["10.1108\/IR-08-2017-0149"],"URL":"https:\/\/doi.org\/10.1108\/ir-08-2017-0149","relation":{},"ISSN":["0143-991X"],"issn-type":[{"value":"0143-991X","type":"print"}],"subject":[],"published":{"date-parts":[[2018,1,15]]}}}