Article 2220

Title of the article

RESEARCH OF SYNTHESIZED OPTIMAL CONTROL FOR A GROUP OF ROBOTS IN THE PRESENCE OF UNCERTAINTIES 

Authors

Diveev Askhat Ibragimovich, doctor of technical sciences, professor, chief researcher, head of the department of robotics control, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (42/2 Vavilova street, Moscow, Russia), E-mail: aidiveev@mail.ru
Shmalko Elizaveta Yurievna, candidate of technical sciences, senior researcher, department of robotics control, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (42/2 Vavilova street, Moscow, Russia), E-mail: e.shmalko@gmail.com 

Index UDK

51-74, 519.6 

DOI

10.21685/2307-4205-2020-2-2 

Abstract

Background. The paper considers the problem of optimal control for a group of robots with phase constraints. The problem is characterized by the presence of two types of constraints: static and dynamic, which greatly complicates the formulation of the problem and makes it practically impossible to apply the fundamental Pontryagin’s maximum principle in view of colossal computational complexity. There is a need to apply numerical approaches.
Matherials and methods. The article considers two alternative numerical approaches to solving the optimal control problem with phase constraints. A new method of synthesized optimal control is compared with one of the direct approaches based on finitedimensional optimization using the example of solving the problem of controlling a group of mobile robots in a complex environment with phase constraints. The method of synthesized optimal control is based on multi-point stabilization with respect to several optimally located points in the state space. It is assumed that this approach, which includes an additional stage of the synthesis of the stabilization system, will increase the reliability of the system even in the presence of noise or other small disturbances.
Results. A numerical implementation of the considered methods is presented. The obtained solutions are investigated in the presence of noise and uncertainties in the model and initial conditions. Addition of a random component in the form of noise into the model of the object showed that the method of synthesized optimal control turned out to be less sensitive to model inaccuracies and random noise in the initial conditions.
Conclusions. A peculiarity of the synthesized optimal control method consists in solving at the initial stage the problem of numerical synthesis of a feedback control system, which makes it possible to stabilize the control object at some point in the state space. This allows for further practical implementation of the optimal control obtained in the second stage to level out small disturbances or inaccuracies in the model of the control object. In view of the fact that the model of the control object is never known exactly, such an approach seems more reliable and expedient than direct methods from the point of view of applied applications. 

Key words

model, optimal control with phase constraints, Pontryagin maximum principle, finite-dimensional optimization, state space, feedback control 

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Дата создания: 17.07.2020 11:10
Дата обновления: 17.07.2020 11:38