Address: Faculty of Physics, University of Warsaw, L. Pasteura 5, 02-093 Warsaw, Poland and Center for Theoretical Physics Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
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Abstract: We study the geometry associated with the kinematics of a planar robot known as the three-segment snake, whose velocity distribution belongs to a class of $(2,3,5)$ distributions. We discover that, under certain assumptions on its construction parameters, the snake may be endowed with a CR structure of CR dimension 1 and real codimension 3. We solve the associated Cartan equivalence problem and find the invariants of the snake’s CR structure.
AMSclassification: primary 53A17; secondary 32V05, 53A55, 58A15.
Keywords: snake robot, CR structure, Cartan equivalence method.
DOI: 10.5817/AM2025-3-93