Evgeniya Mikishanina
Publications:
Mikishanina E. A.
Control of a Spherical Robot with a Nonholonomic Omniwheel Hinge Inside
2024, Vol. 20, no. 1, pp. 179193
Abstract
This study investigates the rolling along the horizontal plane of two coupled rigid bodies:
a spherical shell and a dynamically asymmetric rigid body which rotates around the geometric
center of the shell. The inner body is in contact with the shell by means of omniwheels.
A complete system of equations of motion for an arbitrary number of omniwheels is constructed.
The possibility of controlling the motion of this mechanical system along a given trajectory by
controlling the angular velocities of omniwheels is investigated. The cases of two omniwheels
and three omniwheels are studied in detail. It is shown that two omniwheels are not enough to
control along any given curve. It is necessary to have three or more omniwheels. The quaternion
approach is used to study the dynamics of the system.

Mikishanina E. A.
Motion Control of a Spherical Robot with a Pendulum Actuator for Pursuing a Target
2022, Vol. 18, no. 5, pp. 899913
Abstract
The problem of controlling the rolling of a spherical robot with a pendulum actuator pursuing
a moving target by the pursuit method, but with a minimal control, is considered. The mathematical
model assumes the presence of a number of holonomic and nonholonomic constraints, as
well as the presence of two servoconstraints containing a control function. The control function
is defined in accordance with the features of the simulated scenario. Servoconstraints set the
motion program. To implement the motion program, the pendulum actuator generates a control
torque which is obtained from the joint solution of the equations of motion and derivatives of
servoconstraints. The first and second components of the control torque vector are determined
in a unique way, and the third component is determined from the condition of minimizing the
square of the control torque. The system of equations of motion after reduction for a given
control function is reduced to a nonautonomous system of six equations. A rigorous proof of
the boundedness of the distance function between a spherical robot and a target moving at
a bounded velocity is given. The cases where objects move in a straight line and along a curved
trajectory are considered. Based on numerical integration, solutions are obtained, graphs of the
desired mechanical parameters are plotted, and the trajectory of the target and the trajectory
of the spherical robot are constructed.

Mikishanina E. A.
Qualitative Analysis of the Dynamics of a Trailed Wheeled Vehicle with Periodic Excitation
2021, Vol. 17, no. 4, pp. 437451
Abstract
This article examines the dynamics of the movement of a wheeled vehicle consisting of two
links (trolleys). The trolleys are articulated by a frame. One wheel pair is fixed on each link.
Periodic excitation is created in the system due to the movement of a pair of masses along the
axis of the first trolley. The center of mass of the second link coincides with the geometric center
of the wheelset. The center of mass of the first link can be shifted along the axis relative to the
geometric center of the wheelset. The movement of point masses does not change the center of
mass of the trolley itself. Based on the joint solution of the Lagrange equations of motion with
undetermined multipliers and time derivatives of nonholonomic coupling equations, a reduced
system of differential equations is obtained, which is generally nonautonomous. A qualitative
analysis of the dynamics of the system is carried out in the absence of periodic excitation and
in the presence of periodic excitation. The article proves the boundedness of the solutions of
the system under study, which gives the boundedness of the linear and angular velocities of
the driving link of the articulated wheeled vehicle. Based on the numerical solution of the
equations of motion, graphs of the desired mechanical parameters and the trajectory of motion
are constructed. In the case of an unbiased center of mass, the solutions of the system can be
periodic, quasiperiodic and asymptotic. In the case of a displaced center of mass, the system
has asymptotic dynamics and the mobile transport system goes into rectilinear uniform motion.

Mikishanina E. A.
Dynamics of a Controlled Articulated $n$trailer Wheeled Vehicle
2021, Vol. 17, no. 1, pp. 3948
Abstract
This article is devoted to the study of the dynamics of movement of an articulated ntrailer
wheeled vehicle with a controlled leading car. Each link of the vehicle can rotate relative to its
point of fixation. It is shown that, in the case of a controlled leading car, only nonholonomic
constraint equations are sufficient to describe the dynamics of the system, which in turn form
a closed system of differential equations. For a detailed analysis of the dynamics of the system,
the cases of movement of a wheeled vehicle consisting of three symmetric links are considered,
and the leading link (leading car) moves both uniformly along a circle and with a modulo variable
velocity along a certain curved trajectory. The angular velocity remains constant in both cases.
In the first case, the system is integrable and analytical solutions are obtained. In the second
case, when the linear velocity is a periodic function, the solutions of the problem are also periodic.
In numerical experiments with a large number of trailers, similar dynamics are observed.

Borisov A. V., Mikishanina E. A.
Dynamics of the Chaplygin Ball with Variable Parameters
2020, Vol. 16, no. 3, pp. 453462
Abstract
This work is devoted to the study of the dynamics of the Chaplygin ball with variable
moments of inertia, which occur due to the motion of pairs of internal material points, and
internal rotors. The components of the inertia tensor and the gyrostatic momentum are periodic
functions. In general, the problem is nonintegrable. In a special case, the relationship of the
problem under consideration with the Liouville problem with changing parameters is shown.
The case of the Chaplygin ball moving from rest is considered separately. Poincaré maps are
constructed, strange attractors are found, and the stages of the origin of strange attractors are
shown. Also, the trajectories of contact points are constructed to confirm the chaotic dynamics
of the ball. A chart of dynamical regimes is constructed in a separate case for analyzing the
nature of strange attractors.

Vetchanin E. V., Mikishanina E. A.
Vibrational Stability of Periodic Solutions of the Liouville Equations
2019, Vol. 15, no. 3, pp. 351363
Abstract
The dynamics of a body with a fixed point, variable moments of inertia and internal rotors
are considered. A stability analysis of permanent rotations and periodic solutions of the system is
carried out. In some simplest cases the stability analysis is reduced to investigating the stability
of the zero solution of Hill’s equation. It is shown that by periodically changing the moments of
inertia it is possible to stabilize unstable permanent rotations of the system. In addition, stable
dynamical regimes can lose stability due to a parametric resonance. It is shown that, as the
oscillation frequency of the moments of inertia increases, the dynamics of the system becomes
close to an integrable one.

Mikishanina E. A.
Abstract
