{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T22:10:16Z","timestamp":1777932616935,"version":"3.51.4"},"reference-count":10,"publisher":"SAGE Publications","issue":"9-10","license":[{"start":{"date-parts":[[2008,9,1]],"date-time":"2008-09-01T00:00:00Z","timestamp":1220227200000},"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":["Journal of Vibration and Control"],"published-print":{"date-parts":[[2008,9]]},"abstract":"<jats:p>This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Pad\u00e9 and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Pad\u00e9 approximation with a small number of terms, gives the best results.<\/jats:p>","DOI":"10.1177\/1077546307087436","type":"journal-article","created":{"date-parts":[[2008,9,30]],"date-time":"2008-09-30T09:57:52Z","timestamp":1222768672000},"page":"1473-1485","source":"Crossref","is-referenced-by-count":11,"title":["Using Fractional Derivatives in Joint Control of Hexapod Robots"],"prefix":"10.1177","volume":"14","author":[{"given":"Manuel F.","family":"Silva","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 4200 - 072 Porto, Portugal,"}]},{"given":"J.A.","family":"Tenreiro Macahdo","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 4200 - 072 Porto, Portugal"}]},{"given":"Ramiro S.","family":"Barbosa","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 4200 - 072 Porto, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2008,9,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300205"},{"key":"atypb2","volume-title":"Proceedings of the IEEE International Conference on Robotics and Automation","author":"Low, K.H."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2000.844113"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-29461-9_5"},{"key":"atypb5","volume-title":"Proceedings of the 9th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines","author":"Silva, M.F."},{"issue":"10","key":"atypb6","first-page":"2785","volume":"86","author":"Silva, M.F.","year":"2006","journal-title":"Signal Processing, Special Section-Fractional Calculus Applications in Signals and Systems"},{"key":"atypb7","first-page":"33","volume":"5","author":"Silva, M.F.","year":"2003","journal-title":"Machine Intelligence and Robot Control"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574704001195"},{"key":"atypb9","volume-title":"Proceedings of the IEEE International Conference on Robotics and Automation","author":"Yang, A."},{"key":"atypb10","volume-title":"Proceedings of the IEEE International Conference on Robotics and Automation","author":"Zhou, D."}],"container-title":["Journal of Vibration and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307087436","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307087436","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T01:24:59Z","timestamp":1777685099000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1077546307087436"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9]]},"references-count":10,"journal-issue":{"issue":"9-10","published-print":{"date-parts":[[2008,9]]}},"alternative-id":["10.1177\/1077546307087436"],"URL":"https:\/\/doi.org\/10.1177\/1077546307087436","relation":{},"ISSN":["1077-5463","1741-2986"],"issn-type":[{"value":"1077-5463","type":"print"},{"value":"1741-2986","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9]]}}}