The impact of symmetry violations on determining optimal control trajectories for complex robotic systems

The impact of symmetry violations on determining optimal control trajectories for complex robotic systems

Andrey A. Kurnosov
PhD in Technical Sciences, JSC United Shipbuilding Corporation, JSC United Shipbuilding Corporation, JSC «Saint Petersburg Marin Design Bureau «Malachite», Head of Armament Research, 18, Frunze ul., Saint Petersburg,196135, Russia,  This email address is being protected from spambots. You need JavaScript enabled to view it.

Received October 7, 2022

Abstract
Complex robotic systems, their properties, features and interactions are considered, the article offers the definition of a complex system on the basis of 5 properties: openness, non-morphic variability of three types (structural, spatial and information), Double-code, event aggregation and violation of physical symmetries. The influence of violations of physical symmetries on the determination of optimal control trajectories is reflected in the paradigm approach to the study of complex robotic systems that are not formalized as mathematical objects. The basic concepts, postulates and hypotheses are formulated. Ideal designs of variability of complex systems; energy causal sets; energies; events, causes, effects and evolution; spacetime, quanta and vacuum; interaction of individuals; operators of physical interactions, aggregated events, text and attachments of words. Three basic models for the study of complex systems - the model of physical interactions, the neurolinguistic model and the model of control at incomplete compatibility are proposed and briefly described. The structure of the kernel of the platform of physical simulation modeling for the researches of complex systems is resulted. Three types of space-time quantum modeling - minimal, semantic and evolutionary - are described. The article provides an illustration of results of application of the proposed approach to the study of actions of complex systems. It is noted that the resulting mathematical structure exhibits fractal properties. Typical trajectories of evolution - «homeostat»; «attenuation of actions»; «invariant»; «accident»; «window of possibilities» have been allocated. The article provides a number of principles of research of complex methodological and methodical systems. Recommendations were made on the scope of the proposed approach.

Key words
System, complexity, complex system, interaction, symmetries, variability, energy causal set, hypergraph, evolution, unergodicity, possible individual, event, unpredictability, neurolinguistics, activity, aggregation, word embedding, text, concordance, fractal.

DOI
10.31776/RTCJ.11108

Bibliographic description
Kurnosov, A.A. (2023). The impact of symmetry violations on determining optimal control trajectories for complex robotic systems. Robotics and Technical Cybernetics, 11(1), pp.60-72.

UDC identifier:
681.51:007.52

References

  1. Nikolis, G. and Prigozhin, I. (1979). Samoorganizatsiya V Neravnovesnykh Sistemakh. Ot Dissipativnykh Struktur K Uporyadochennosti Cherez Fluktuatsii [Self-Organization In Non-Equilibrium Systems. From Dissipative Structures To Orderliness Through Fluctuations], Mir, Moscow, Russia.
  2. Burkov, V.N. and Novikov, D.A. (1999). Teoriya Aktivnykh Sistem: Sostoyaniye I Perspektivy [Theory of Active Systems: Status And Prospects], Sinteg, Moscow. (in Russian).
  3. Barbour, J. and Smolin, L. (1992). Extremal Variety As the Foundation of a Cosmological Quantum Theory, [online]. Available at: https://arxiv.org/abs/hep-th/9203041 (Accessed 14 November 2022).
  4. Berg, A.I., Kitov, A.I. and Lyapunov A.A. (1961). Kibernetika v voyennom dele [Cybernetics in military affairs]. Voyennaya Mysl [Military Thought]. (in Russian).
  5. Perrow, Ch. (1984). Normal Accidents. Living With High-Risk Technologies, Basic Books, USA.
  6. Smolin, L. (2018). The dynamics of difference. Foundations of Physics, vol. 48, pp.121-134.
  7. Wolfram, S. (2019). A Class of Models with the Potential to Represent Fundamental Physics. Wolfram Research. Available at: https://www.wolframphysics.org/technical-introduction/inc/Wolfram-ModelsForPhysics.pdf (Accessed 14 November 2022).
  8. Husserl, E. (1928). Fenomenologiya Vnutrennego Soznaniya Vremeni [Vorlesungen Zur Phänomenologie Des Inneren Zeitbewusstseins], Translated by Molchanov, V.I., Gnosis, Moscow, Russia.
  9. Pavlov, D.G. (2004). Khronometriya trekhmernogo vremeni [Chronometry of three-dimensional time]. Giperkompleksnyye Chisla V Geometrii i Fizike [Hypercomplex Numbers In Geometry And Physics], MSTU im. N.E. Bauman, 1.
  10. Kurnosov, A. (2021). Predictive Temporal Analytics Method in Situational Modeling of the Evolution of Complex Systems. Journal of Physics: Conference Series / Intelligent Information Technology and Mathematical Modeling 2021, 2131 (3):032026, DOI:10.1088/1742-6596/2131/3/032026.
  11. (2023). ISO 15926-2:2003. Industrial automation systems and integration - Integration of life-cycle data for process plants including oil and gas production facilities - Part 2: Data model: Publication date: 2003-12, Technical Committee: ISO/TC 184/SC 4 Industrial data, p.225.
  12. Alexeev, A.V. et al. (2008). Monitor gidroakusticheskikh poley i signalov [Monitor of hydroacoustic fields and signals]. Patent no. 2008611164, RU.
  13. Pospelov, D.A. (1986). Situatsionnoye Upravleniye. Teoriya I Praktika [Situational Management. Theory And Practice], Nauka, Main editorial office nat.-mat. Lit, Moscow, Russia.
  14. Mikolov, T., Corrado, G., Chen, K., and Dean, J. (2013). Efficient Estimation of Word Representations in Vector Space. In: Proceedings of the International Conference on Learning Representations (ICLR 2013).
  15. Pshenichnikov, S.B. (2022). Algebra Teksta [Text Algebra], Izdatel'skiye Resheniya, Moscow, Russia.
  16. Kurnosov, A.A. (2020). Podkhod k sozdaniyu yedinoy platformy fizicheskogo imitatsionnogo modelirovaniya mno-gosrednogo informatsionnogo vzaimodeystviya slozhnykh sistem [An approach to creating a unified platform for physical simulation of multi-media information interaction of complex systems]. In: Vserossiyskiy Festival' Nauki «Nauka 0+»: Sbornik Dokladov [All-Russian Festival Of Science «Nauka 0+»: Collection Of Reports], vol. 2, no. 1, pp.616-630.
  17. Kripke Saul, (1997) Speaker’s Reference and Semantic Reference, Midwest Studies in Philosophy, 2, pp.25-276.