| Title:
|
Lie algebra structure in the model of 3-link snake robot (English) |
| Author:
|
Doležal, Martin |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2024 |
| Pages:
|
221-229 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
non-integrable distribution |
| Keyword:
|
infinitesimal symmetry |
| Keyword:
|
solvable Lie group |
| Keyword:
|
snake robot |
| MSC:
|
22E60 |
| MSC:
|
37J60 |
| MSC:
|
70Q05 |
| DOI:
|
10.5817/AM2024-4-221 |
| . |
| Date available:
|
2024-11-27T08:34:22Z |
| Last updated:
|
2024-11-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152641 |
| . |
| Reference:
|
[1] Anderson, I., Kruglikov, B.: Rank 2 distributions of monge equations: symmetries, equivalences, extensions.Adv. Math. 228 (3) (2011), 1435–1465. MR 2824560, 10.1016/j.aim.2011.06.019 |
| Reference:
|
[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. MR 1509120, 10.24033/asens.618 |
| Reference:
|
[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. MR 3541137, 10.1007/s00006-015-0621-2 |
| Reference:
|
[4] Montgomery, R.: A tour of subriemannian geometries, their geodesics and applications.Amer. Math. Soc., 2002. Zbl 1044.53022, MR 1867362 |
| Reference:
|
[5] Olver, P.J.: Equivalence, Invariants and Symmetry.London Mathematical Society Lecture Note, Cambridge University Press, 1995. Zbl 0837.58001, MR 1337276 |
| Reference:
|
[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. |
| . |
