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Keywords:
non-integrable distribution; infinitesimal symmetry; solvable Lie group; snake robot
non-integrable distribution; infinitesimal symmetry; solvable Lie group; snake robot
Summary:
In this paper, we study a 5 dimensional configuration space of a 3-link snake robot model moving in a plane. We will derive two vector fields generating a distribution which represents a space of the robot’s allowable movement directions. An arbitrary choice of such generators generates the entire tangent space of the configuration space, i.e. the distribution is bracket-generating, but our choice additionally generates a finite dimensional Lie algebra over real numbers. This allows us to extend our model to a model with local Lie group structure, which may have interesting consequences for our original model.
References:
[1] Anderson, I., Kruglikov, B.: Rank 2 distributions of monge equations: symmetries, equivalences, extensions. Adv. Math. 228 (3) (2011), 1435–1465. DOI 10.1016/j.aim.2011.06.019 | MR 2824560
[2] Cartan, É.: Les systèmes de pfaff, à cinq variables et les équations aux dérivées partielles du second ordre. Ann. Sci. Éc. Norm. Supér. (4) 27 (1910), 109–192. DOI 10.24033/asens.618 | MR 1509120
[3] Hrdina, J., Návrat, A., Vašík, P.: Control of 3-link robotic snake based on conformal geometric algebra. Adv. Appl. Clifford Algebr. 26 (2016), 1069–1080. DOI 10.1007/s00006-015-0621-2 | MR 3541137
[4] Montgomery, R.: A tour of subriemannian geometries, their geodesics and applications. Amer. Math. Soc., 2002. MR 1867362 | Zbl 1044.53022
[5] Olver, P.J.: Equivalence, Invariants and Symmetry. London Mathematical Society Lecture Note, Cambridge University Press, 1995. MR 1337276 | Zbl 0837.58001
[6] The, D.: Exceptionally simple PDE [Presentation]. Pure Math. Colloquium, University of Waterloo, Canada, 2018, January 5, 2018, available online (as of 2024-04-05): https://math.uit.no/ansatte/dennis/talks/ExcSimpPDE-Waterloo2018.pdf
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