Address: Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic
E-mail: 408740@mail.muni.cz
Abstract: 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.
AMSclassification: primary 70Q05; secondary 22E60, 37J60.
Keywords: non-integrable distribution, infinitesimal symmetry, solvable Lie group, snake robot.
DOI: 10.5817/AM2024-4-221