{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T21:56:25Z","timestamp":1747173385306,"version":"3.40.5"},"reference-count":34,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2020,7,16]],"date-time":"2020-07-16T00:00:00Z","timestamp":1594857600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2021,4]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>This paper deals with motion planning and control problems for a class of partially differentially flat systems. They possess a feature that the derivative of the fiber variable can be represented purely by the base variable and its derivatives. Based on this feature, a Beta function-based motion planning algorithm is proposed with less computational cost compared with the optimal control formulation while providing similar system performance. Then, an adaptive controller is constructed through a function approximation technique-based approach. Finally, the feasibility of the proposed motion planning and control algorithms is verified by simulations.<\/jats:p>","DOI":"10.1017\/s0263574720000685","type":"journal-article","created":{"date-parts":[[2020,7,16]],"date-time":"2020-07-16T09:41:25Z","timestamp":1594892485000},"page":"718-734","source":"Crossref","is-referenced-by-count":6,"title":["On Motion Planning and Control for Partially Differentially Flat Systems"],"prefix":"10.1017","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1080-1939","authenticated-orcid":false,"given":"Yang","family":"Bai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2459-2250","authenticated-orcid":false,"given":"Mikhail","family":"Svinin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7316-5664","authenticated-orcid":false,"given":"Evgeni","family":"Magid","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6644-9084","authenticated-orcid":false,"given":"Yujie","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2020,7,16]]},"reference":[{"key":"S0263574720000685_ref20","unstructured":"20. Ramasamy, S. , Wu, G. and Sreenath, K. , \u201cDynamically Feasible Motion Planning Through Partial Differential Flatness,\u201d Proceedings of Robotics: Science and Systems (2014) pp. 125\u2013130."},{"key":"S0263574720000685_ref23","first-page":"133","article-title":"The motion planning problem: Differential flatness and nilpotent approximation","volume":"2","author":"Romero-Melendez","year":"2012","journal-title":"Cybern. Phys."},{"key":"S0263574720000685_ref3","doi-asserted-by":"publisher","DOI":"10.9746\/jcmsi.11.477"},{"key":"S0263574720000685_ref5","doi-asserted-by":"publisher","DOI":"10.1109\/70.954753"},{"volume-title":"Applied Nonlinear Control","year":"1991","author":"Slotine","key":"S0263574720000685_ref27"},{"key":"S0263574720000685_ref28","unstructured":"28. Sofronniou, M. and Knapp, R. , Advanced Numerical Differential Equation Solving in Mathematica (Wolfram Research, Inc., Champaign, IL, 2008)."},{"key":"S0263574720000685_ref1","unstructured":"1. Bai, Y. , Svinin, M. and Yamamoto, M. , \u201cMotion Planning for a Hoop-Pendulum Type of Underactuated Systems,\u201d Proceedings of the IEEE International Conference on Robotics and Automation (2016) pp. 2739\u20132744."},{"key":"S0263574720000685_ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2010.2053732"},{"key":"S0263574720000685_ref29","unstructured":"29. Spong, M. W. , \u201cPartial Feedback Linearization of Underactuated Mechanical Systems,\u201d Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (1994) pp. 314\u2013321."},{"key":"S0263574720000685_ref7","unstructured":"7. Gao, B. , Zhang, X. , Chen, H. and Zhao, J. . \u201cEnergy-Based Control Design of an Underactuated 2-Dimensional Tora System,\u201d Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (2009) pp. 1296\u20131301."},{"key":"S0263574720000685_ref9","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620120607"},{"key":"S0263574720000685_ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2007.893054"},{"key":"S0263574720000685_ref17","unstructured":"17. Olfati-Saber, R. , \u201cTrajectory Tracking for a Flexible One-Link Robot Using a Nonlinear Noncollocated Output,\u201d Proceedings of the 39th IEEE Conference on Decision and Control (2000) pp. 4024\u20134029."},{"key":"S0263574720000685_ref14","unstructured":"14. Nagarajan, U. , Kantor, G. and Hollis, R. L. , \u201cTrajectory Planning and Control of an Underactuated Dynamically Stable Single Spherical Wheeled Mobile Robot,\u201d Proceedings of the IEEE International Conference on Robotics and Automation (2009) pp. 3743\u20133748."},{"key":"S0263574720000685_ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.846598"},{"key":"S0263574720000685_ref34","unstructured":"34. Ladd, A. and Kavraki, L. , \u201cMotion Planning in the Presence of Drift, Underactuation and Discrete System Changes.\u201d Proceedings of Robotics: Science and Systems (RSS2005) (2005) pp. 233\u2013240."},{"key":"S0263574720000685_ref19","unstructured":"19. Qian, D. W. , Yi, J. Q. and Zhao, D. B. , \u201cRobust Control Using Sliding Mode for a Class of Underactuated Systems with Mismatched Uncertainties,\u201d Proceedings of the IEEE International Conference on Robotics and Automation (2007) pp. 1449\u20131454."},{"volume-title":"Control and Nonlinearity","year":"2007","author":"Coron","key":"S0263574720000685_ref21"},{"key":"S0263574720000685_ref26","unstructured":"26. Shiriaev, A. , Ludvigsen, H. , Egeland, O. and Pogromsky, A. , \u201cOn Global Properties of Passivity Based Control of the Inverted Pendulum,\u201d Proceedings of the 38th IEEE Conference on Decision and Control (1999) pp. 2513\u20132518."},{"key":"S0263574720000685_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-0177-2"},{"key":"S0263574720000685_ref13","unstructured":"13. McNinch, L. C. and Ashrafiuon, H. , \u201cPredictive and Sliding Mode Cascade Control for Unmanned Surface Vessels,\u201d Proceedings of the American Control Conference (2011) pp. 184\u2013189."},{"key":"S0263574720000685_ref18","unstructured":"18. Pettersen, K. Y. and Nijmeijer, H. , \u201cTracking Control of an Underactuated Surface Vessel,\u201d Proceedings of the 37th IEEE Conference on Decision and Control (1998) pp. 4561\u20134566."},{"key":"S0263574720000685_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-007-9324-0"},{"key":"S0263574720000685_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2007.10.011"},{"key":"S0263574720000685_ref31","unstructured":"31. Tyan, F. and Lee, S. , \u201cAn Adaptive Control for Rotating Stall and Surge of Jet Engines \u2013 A Function Approximation Approach. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 (2005) pp. 5498\u20135503."},{"key":"S0263574720000685_ref2","unstructured":"2. Bai, Y. , Svinin, M. and Yamamoto, M. , \u201cAdaptive Trajectory Tracking Control for the Ball-Pendulum System with Time-Varying Uncertainties,\u201d Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (2017) pp. 2083\u20132090."},{"key":"S0263574720000685_ref25","unstructured":"25. Shammas, E. , Generalized Motion Planning for Underactuated Mechanical Systems Ph.D. Thesis (Carnegie Mellon University, Pittsburgh, Pennsylvania, 2006)."},{"key":"S0263574720000685_ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2008.2012338"},{"key":"S0263574720000685_ref4","doi-asserted-by":"publisher","DOI":"10.1109\/9.871753"},{"key":"S0263574720000685_ref15","unstructured":"15. Nersesov, S. G. , Ashrafiuon, H. and Ghorbanian, P. , \u201cOn the Stability of Sliding Mode Control for a Class of Underactuated Nonlinear Systems,\u201d Proceedings of the American Control Conference (2010) pp. 3446\u20133451."},{"key":"S0263574720000685_ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.814104"},{"key":"S0263574720000685_ref16","first-page":"223","article-title":"Control of the underactuated mechanical systems using natural motion","volume":"48","author":"Neusser","year":"2012","journal-title":"Kybernetika"},{"key":"S0263574720000685_ref22","doi-asserted-by":"publisher","DOI":"10.1109\/SII46433.2020.9026292"},{"key":"S0263574720000685_ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2007.05.014"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574720000685","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,16]],"date-time":"2021-04-16T16:22:56Z","timestamp":1618590176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574720000685\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,16]]},"references-count":34,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["S0263574720000685"],"URL":"https:\/\/doi.org\/10.1017\/s0263574720000685","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"type":"print","value":"0263-5747"},{"type":"electronic","value":"1469-8668"}],"subject":[],"published":{"date-parts":[[2020,7,16]]}}}