Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm

Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm

A numerical method based on the Pontryagin maximum principle for solving an optimal control problem with static and dynamic phase constraints for a group of objects is considered. Dynamic phase constraints are introduced to avoid collisions between objects. Phase constraints are included in the func...

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Main Authors: Askhat Diveev, Elena Sofronova, Ivan Zelinka
Format: Article
Language:English
Published: MDPI AG 2020-11-01
Series:Mathematics
Subjects:
optimal control problem
evolutionary computation
robotics applications
Online Access:https://www.mdpi.com/2227-7390/8/12/2105
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spelling doaj-5d17177d19ce43b2967d9adbe029565e2020-11-27T08:02:31ZengMDPI AGMathematics2227-73902020-11-0182105210510.3390/math8122105Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary AlgorithmAskhat Diveev0Elena Sofronova1Ivan Zelinka2Department of Robotics Control, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, RussiaDepartment of Robotics Control, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, RussiaFaculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, VietnamA numerical method based on the Pontryagin maximum principle for solving an optimal control problem with static and dynamic phase constraints for a group of objects is considered. Dynamic phase constraints are introduced to avoid collisions between objects. Phase constraints are included in the functional in the form of smooth penalty functions. Additional parameters for special control modes and the terminal time of the control process were introduced. The search for additional parameters and the initial conditions for the conjugate variables was performed by the modified self-organizing migrating algorithm. An example of using this approach to solve the optimal control problem for the oncoming movement of two mobile robots is given. Simulation and comparison with direct approach showed that the problem is multimodal, and it approves application of the evolutionary algorithm for its solution.https://www.mdpi.com/2227-7390/8/12/2105optimal control problemevolutionary computationrobotics applications
collection DOAJ
language English
format Article
sources DOAJ
author Askhat Diveev
Elena Sofronova
Ivan Zelinka
spellingShingle Askhat Diveev
Elena Sofronova
Ivan Zelinka
Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm
Mathematics
optimal control problem
evolutionary computation
robotics applications
author_facet Askhat Diveev
Elena Sofronova
Ivan Zelinka
author_sort Askhat Diveev
title Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm
title_short Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm
title_full Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm
title_fullStr Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm
title_full_unstemmed Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm
title_sort optimal control problem solution with phase constraints for group of robots by pontryagin maximum principle and evolutionary algorithm
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-11-01
description A numerical method based on the Pontryagin maximum principle for solving an optimal control problem with static and dynamic phase constraints for a group of objects is considered. Dynamic phase constraints are introduced to avoid collisions between objects. Phase constraints are included in the functional in the form of smooth penalty functions. Additional parameters for special control modes and the terminal time of the control process were introduced. The search for additional parameters and the initial conditions for the conjugate variables was performed by the modified self-organizing migrating algorithm. An example of using this approach to solve the optimal control problem for the oncoming movement of two mobile robots is given. Simulation and comparison with direct approach showed that the problem is multimodal, and it approves application of the evolutionary algorithm for its solution.
topic optimal control problem
evolutionary computation
robotics applications
url https://www.mdpi.com/2227-7390/8/12/2105
work_keys_str_mv AT askhatdiveev optimalcontrolproblemsolutionwithphaseconstraintsforgroupofrobotsbypontryaginmaximumprincipleandevolutionaryalgorithm
AT elenasofronova optimalcontrolproblemsolutionwithphaseconstraintsforgroupofrobotsbypontryaginmaximumprincipleandevolutionaryalgorithm
AT ivanzelinka optimalcontrolproblemsolutionwithphaseconstraintsforgroupofrobotsbypontryaginmaximumprincipleandevolutionaryalgorithm
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