Maxwell Points of Dynamical Control Systems Based on Vertical Rolling Disc-Numerical Solutions

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dc.contributor.authorStodola, Marekcs
dc.contributor.authorRajchl, Matejcs
dc.contributor.authorBrablc, Martincs
dc.contributor.authorFrolík, Stanislavcs
dc.contributor.authorKřivánek, Václavcs
dc.coverage.issue3cs
dc.coverage.volume10cs
dc.date.accessioned2021-12-01T11:55:02Z
dc.date.available2021-12-01T11:55:02Z
dc.date.issued2021-07-12cs
dc.description.abstractWe study two nilpotent affine control systems derived from the dynamic and control of a vertical rolling disc that is a simplification of a differential drive wheeled mobile robot. For both systems, their controllable Lie algebras are calculated and optimal control problems are formulated, and their Hamiltonian systems of ODEs are derived using the Pontryagin maximum principle. These optimal control problems completely determine the energetically optimal trajectories between two states. Then, a novel numerical algorithm based on optimisation for finding the Maxwell points is presented and tested on these control systems. The results show that the use of such numerical methods can be beneficial in cases where common analytical approaches fail or are impractical.en
dc.formattextcs
dc.format.extent1-19cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationRobotics. 2021, vol. 10, issue 3, p. 1-19.en
dc.identifier.doi10.3390/robotics10030088cs
dc.identifier.issn2218-6581cs
dc.identifier.other173085cs
dc.identifier.urihttp://hdl.handle.net/11012/203030
dc.language.isoencs
dc.publisherMDPIcs
dc.relation.ispartofRoboticscs
dc.relation.urihttps://www.mdpi.com/2218-6581/10/3/88cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/2218-6581/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectdifferential drive wheeled mobile roboten
dc.subjectgeometric control theoryen
dc.subjectLie algebraen
dc.subjectnon-holonomics mechanicsen
dc.subjectnilpotent approximationen
dc.subjectoptimal controlen
dc.subjectMaxwell pointsen
dc.subjectnonlinear optimisationen
dc.subjectnumerical solveren
dc.titleMaxwell Points of Dynamical Control Systems Based on Vertical Rolling Disc-Numerical Solutionsen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-173085en
sync.item.dbtypeVAVen
sync.item.insts2021.12.01 12:55:02en
sync.item.modts2021.12.01 12:15:19en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav mechaniky těles, mechatroniky a biomechanikycs
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
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