Program/Track C/C.3.1/Construction of dierential equations of a nonholonomic mechanical system and perspectives of motion control using articial intelligence methods

# Construction of dierential equations of a nonholonomic mechanical system and perspectives of motion control using articial intelligence methods

Andrey Borisov, Robert Mukharlyamov, Kaspirovich Ivan

15m

First, a mechanical model of a mechanism with two links of variable length
in space with holonomic constraints is considered. Its mathematical model is
obtained, in the form of Lagrange equations of the second kind. Then we consider
a model similar in structure - the number and design of links with a nonholonomic
constraint in the form of a skier-snowboarder. The mathematical model of a
system of rigid bodies with a nonholonomic constraint is based on the Routh
dierential equations for a nonholonomic system in generalized coordinates
with Lagrange multipliers. A method is developed for constructing dierential
equations for a system containing nonholonomic constraints using Lagrange
equations of the second kind for a model of a similar structure with holonomic
constraints. As an example, the model is applied to the description of a skiersnowboarder
with two variable-length movable links on one ski. Usually, the
control of such systems is implemented on the basis of the method of stabilizing
links, however, this article declares methods for controlling mechanical systems
based on articial intelligence systems and outlines approaches to their use in
models with nonholonomic links.