Geodesic
Lie algebra structure in the model of 3-link snake robot
Archivum mathematicum, Tome 60 (2024) no. 4, pp. 221-229 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2024-4-221
Classification : 22E60, 37J60, 70Q05
Keywords: non-integrable distribution; infinitesimal symmetry; solvable Lie group; snake robot 
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Doležal, Martin. Lie algebra structure in the model of 3-link snake robot. Archivum mathematicum, Tome 60 (2024) no. 4, pp. 221-229. doi: 10.5817/AM2024-4-221

[1] Anderson, I., Kruglikov, B.: Rank 2 distributions of monge equations: symmetries, equivalences, extensions. Adv. Math. 228 (3) (2011), 1435–1465. | DOI | MR

[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 | MR

[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 | MR

[4] Montgomery, R.: A tour of subriemannian geometries, their geodesics and applications. Amer. Math. Soc., 2002. | MR | Zbl

[5] Olver, P.J.: Equivalence, Invariants and Symmetry. London Mathematical Society Lecture Note, Cambridge University Press, 1995. | MR | Zbl

[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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