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Periodic Motion Planning and Control for Double Rotary Pendulum via Virtual Holonomic Constraints
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.ORCID iD: 0000-0003-0730-9441
2019 (English)In: IEEE/CAA Journal of Automatica Sinica, ISSN 2329-9266, Vol. 6, no 1, p. 291-298Article in journal (Refereed) Published
Abstract [en]

Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning. We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint (VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2019. Vol. 6, no 1, p. 291-298
Keywords [en]
Double rotary pendulum, periodic motion planning, under-actuated mechanical systems, virtual holonomic constraint (VHC)
National Category
Control Engineering Robotics
Identifiers
URN: urn:nbn:se:umu:diva-155967DOI: 10.1109/JAS.2017.7510712ISI: 000455705900027OAI: oai:DiVA.org:umu-155967DiVA, id: diva2:1286776
Available from: 2019-02-07 Created: 2019-02-07 Last updated: 2019-02-07Bibliographically approved

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Freidovich, Leonid B.

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CiteExportLink to record
Permanent link

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