Alexander Andreev
Publications:
Andreev A. S., Peregudova O. A.
On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass
2020, Vol. 16, no. 1, pp. 115131
Abstract
This paper addresses the trajectory tracking control design of an omnidirectional mobile
robot with a center of mass displaced from the geometrical center of the robot platform. Due
to the high maneuverability provided by omniwheels, such robots are widely used in industry
to transport loads in narrow spaces. As a rule, the center of mass of the load does not coincide
with the geometric center of the robot platform. This makes the trajectory tracking control
problem of a robot with a displaced center of mass relevant. In this paper, two controllers
are constructed that solve the problem of global trajectory tracking control of the robot. The
controllers are designed based on the Lyapunov function method. The main difficulty in applying
the Lyapunov function method for the trajectory tracking control problem of the robot is that
the time derivative of the Lyapunov function is not definite negative, but only semidefinite
negative. Moreover, the LaSalle invariance principle is not applicable in this case since the
closedloop system is a nonautonomous system of differential equations. In this paper, it is
shown that the quasiinvariance principle for nonautonomous systems of differential equations
is much convenient for the asymptotic stability analysis of the closedloop system. Firstly,
we construct an unbounded state feedback controller such as proportionalderivative term plus
feedforward. As a result, the global uniform asymptotic stability property of the origin of
the closedloop system has been proved. Secondly, we find that, if the damping forces of the
robot are large enough, then the saturated position output feedback controller solves the global
trajectory tracking control problem without velocity measurements. The effectiveness of the
proposed controllers has been verified through simulation tests. Namely, a comparative analysis
of the bounded controller obtained and the wellknown “PD+” like control scheme is carried
out. It is shown that the approach proposed in this paper saves energy for control inputs.
Besides, a comparative analysis of the bounded controller and its analogue constructed earlier
in a cylindrical phase space is carried out. It is shown that the controller provides lower values
for the root mean square error of the position and velocity of the closedloop system.

Andreev A. S., Peregudova O. A.
On the Stability and Stabilization Problems of Volterra IntegroDifferential Equations
2018, Vol. 14, no. 3, pp. 387407
Abstract
In this paper, the stability and stabilization problems for nonlinear Volterra integrodifferential
equations with unlimited delay are considered. The development of the direct Lyapunov
method in the study of the limiting properties of the solutions of these equations is carried
out by using Lyapunov functionals with a semidefinite time derivative. The topological dynamics
of these equations has been constructed revealing the limiting properties of their solutions.
The assumption of the existence of a Lyapunov functional with a semidefinite time derivative
gives a more complete solution to the positive limit set localization problem. On this basis new
theorems on sufficient conditions for the asymptotic stability and instability of the zero solution
of nonlinear Volterra integrodifferential equations are proved. These theorems are applied to the
problem of the equilibrium position stability of the hereditary mechanical systems as well as the
regulation problem of the controlled mechanical systems using a proportionalintegrodifferential
controller. As an example, the regulation problem of a mobile robot with three omnidirectional
wheels and a displaced mass center is solved using the nonlinear integral controllers without
velocity measurements.

Andreev A. S., Peregudova O. A.
On control for doublelink manipulator with elastic joints
2015, Vol. 11, No. 2, pp. 267277
Abstract
In the paper the problem on stabilization of program motion for twolink manipulator with elastic joints is solved. Absolutely rigid manipulator links are connected by elastic cylindrical joint and via the same one the first link is fixed to the base. Thus, the manipulator can perform motion in a vertical plane. Motions of the manipulator are described by the system of Lagrange equations of the second kind. The problem on synthesis of motion control of such a system consists in the construction of the laws of change of control moments that allow the manipulator to carry out a given program motion in real conditions of external and internal disturbances, inaccuracy of the model itself. In this paper the mathematical model of controlled motion of the manipulator is constructed for the case of the control actions in the form of continuous functions. Using vector Lyapunov functions and comparison systems on the base of the cascade decomposition of the system we justified the application of these control laws in the problem of stabilization of the program motion of the manipulator. The novelty of the results is to solve the problem of stabilization of nonstationary and nonlinear formulation, without going to the linearized model. The graphs for the coordinates and velocities of the manipulator links confirm the theoretical results.
