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Almost periodic motion planning and control for double rotary pendulum with experimental validation
Beijing Institute of Control Engineering, Beijing, China.
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.ORCID iD: 0000-0003-0730-9441
Beijing Institute of Control Engineering, Beijing, China.
2020 (English)In: Asian Journal of Control, ISSN 1561-8625, E-ISSN 1934-6093, Vol. 22, no 6, p. 2434-2443Article in journal (Refereed) Published
Abstract [en]

The aim is to develop a systematic procedure for planning feasible motions for a double rotary pendulum. This pendulum has one directly actuated horizontal link and two passive links, moving in a rotating vertical plane. We plan a nontrivial oscillatory motion for the passive links that is consistent with the horizontal link rotating at a given average speed and also design a stabilizing controller to approximately induce such a motion. For the motion planning, a numerical optimization procedure is proposed in the form of a sequence of three simpler problems to systematically derive initial guesses for the final optimization search. For the controller design, firstly the system is linearized along a nominal trajectory, and then a parametrized family of candidate stabilizing controllers is designed. For each set of parameters, a necessary and sufficient stability condition can be checked for the derived linear time varying periodic system. Therefore, a numerical optimization procedure is used to find the controller gain for the linear system based on the stability condition. The performance of the closed-loop system is illustrated via numerical simulations and verified via experiments with an educational platform produced by PendCon, demonstrating achieving oscillations with required characteristics. However, the formal proofs for convergence and even for existence of almost periodic solutions are left for future studies.

Place, publisher, year, edition, pages
John Wiley & Sons, 2020. Vol. 22, no 6, p. 2434-2443
Keywords [en]
double rotary pendulum, periodic motion planning, underactuated mechanical systems, virtual lonomic constraints
National Category
Control Engineering Physical Sciences
Identifiers
URN: urn:nbn:se:umu:diva-162005DOI: 10.1002/asjc.2154ISI: 000476849300001Scopus ID: 2-s2.0-85068439850OAI: oai:DiVA.org:umu-162005DiVA, id: diva2:1342186
Available from: 2019-08-13 Created: 2019-08-13 Last updated: 2024-02-28Bibliographically approved

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Freidovich, Leonid B.

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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
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More languages
Output format
  • html
  • text
  • asciidoc
  • rtf