Trajectory planning for mechanical systems based on time-reversal symmetry

Stepan Ozana , Tomas Docekal , Aleksandra Kawala-Sterniuk , Jakub Możaryn , Milos Schlegel , Akshaya Raj

Abstract

The generation of feasible trajectories poses an eminent task in the field of control design in mechanical systems. The paper demonstrates innovative approach in trajectory planning for mechanical systems via time-reversal symmetry. It also presents two case studies: mass-spring-damper and inverted pendulum on the cart. As real systems break the time-reversal symmetry, the authors of this work propose a unique method in order to overcome this drawback. It computes a feed-forward reference control signal and state trajectories. The proposed solution enables compensation for the effects of couplings, which break the time-symmetry by a special proposed measure. The method suppresses the overall open-loop accumulated error and produces high-quality favorable control and state trajectories. Furthermore, the existence of the designed control signal and state trajectories is guaranteed if the equations of the motion have a solution in the direct flow of time.

Author Stepan Ozana - Department of Cybernetics and Biomedical Engineering, Faculty of Electrical Engineering and Computer Science [VSB – Technical University of Ostrava]
Stepan Ozana,,
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, Tomas Docekal - Department of Cybernetics and Biomedical Engineering, Faculty of Electrical Engineering and Computer Science [VSB – Technical University of Ostrava]
Tomas Docekal,,
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, Aleksandra Kawala-Sterniuk - Politechnika Opolska
Aleksandra Kawala-Sterniuk,,
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, Jakub Możaryn (FM / IACR)
Jakub Możaryn,,
- The Institute of Automatic Control and Robotics
, Milos Schlegel - Department of Cybernetics, Faculty of Applied Sciences [University of West Bohemia]
Milos Schlegel,,
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, Akshaya Raj - Department of Cybernetics and Biomedical Engineering, Faculty of Electrical Engineering and Computer Science [VSB – Technical University of Ostrava]
Akshaya Raj,,
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Journal seriesSymmetry-Basel, [Symmetry], ISSN 2073-8994
Issue year2020
Vol12
No5
Pages1-19
Publication size in sheets0.9
Article number792
Keywords in Englishtime-reversal symmetry, trajectory planning, inverted pendulum, mass-spring-damper model, two-point BvP
ASJC Classification1601 Chemistry (miscellaneous); 1701 Computer Science (miscellaneous); 2600 General Mathematics; 3101 Physics and Astronomy (miscellaneous)
DOIDOI:10.3390/SYM12050792
URL https://www.mdpi.com/2073-8994/12/5/792
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 09-07-2020, ArticleFromJournal
Publication indicators Scopus Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.64; WoS Impact Factor: 2018 = 2.143 (2) - 2018=2.041 (5)
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