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A remark on Controlled Lagrangian approach
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics. Department of Engineering Cybernetics, Norwegian University of Science & Technology, Trondheim, Norway.
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics. (Robotics and Control Lab)ORCID iD: 0000-0003-0730-9441
2013 (English)In: European Journal of Control, ISSN 0947-3580, E-ISSN 1435-5671, Vol. 19, no 6, 438-444 p.Article in journal (Refereed) Published
Abstract [en]

A new approach to trajectory planning for underactuated mechanical systems is presented and discussed based on analysis of feasible behaviors of a standard 2-DOF benchmark example - the cart-pendulum system. Following the Controlled Lagrangians approach of Bloch et al. (2000) [7], we present and re-establish known conditions and forms of feedback control laws for this example, which are leading to an equivalent completely integrable closed-loop Euler-Lagrange system; and then extend them. As shown, full integrability and, in particular, the presence of a linear in velocities first integral of dynamics plays the key role in an elegant new procedure for trajectory planning.

Place, publisher, year, edition, pages
Lavoisier , 2013. Vol. 19, no 6, 438-444 p.
Keyword [en]
Underactuated mechanical systems, Cart-pendulum system, Controlled Lagrangians, Virtual holonomic constraints, Motion and trajectory planning, Feedback equivalence
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:umu:diva-85801DOI: 10.1016/j.ejcon.2013.09.004ISI: 000329274500002OAI: oai:DiVA.org:umu-85801DiVA: diva2:695907
Available from: 2014-02-12 Created: 2014-02-10 Last updated: 2017-12-06Bibliographically approved

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Shiriaev, Anton S.Freidovich, Leonid
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