Skip to main content
SpringerLink
Log in

Multi-rotor spacecraft attitude control by triggering chaotic modes on strange chaotic attractors

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper discusses chaos in dynamical systems as a positive aspect. It can be used to solve the problem of a spacecraft angular reorientation. Chaos can generate such a phase trajectory that will ensure the transition from the initial zone of a phase space to required one. As objects generating dynamical chaos in the paper strange chaotic attractors are considering. The goal is to initiate chaotic attractors in spacecraft attitude dynamics phase space. It is possible to achieve the target angular position of the spacecraft using the initiated chaotic attractors. An algorithm for chaotic attractors creation in the spacecraft attitude dynamics is developed in the paper, and five new chaotic attractors are discovered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data availability

Enquiries about data availability should be directed to the authors.

References

  1. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130–141 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  2. Henon, M.: A two-dimensional mapping with a strange attractor. Commun. Math. Phys. 50, 69–77 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  3. Rossler, O.E.: An equation for continuous chaos. Phys. Lett. A 57(5), 397–398 (1976)

    Article  ADS  Google Scholar 

  4. Matsumoto, T., Chua, L., Komuro, M.: The double scroll. IEEE Trans. Circ. Syst. 32, 797–818 (1985)

    Article  MathSciNet  Google Scholar 

  5. Chua, L., Komuro, M., Matsumoto, T.: The double scroll family. IEEE Trans. Circ. Syst. 33, 1072–1118 (1986)

    Article  ADS  Google Scholar 

  6. Kuate, P.D.K., Tchendjeu, A.E.T., Fotsin, H.: A modified Rossler prototype-4 system based on Chua’s diode nonlinearity: dynamics, multistability, multiscroll generation and FPGA implementation. Chaos Solitons Fractals 140, 110213 (2020)

    Article  MathSciNet  Google Scholar 

  7. Wang, N., Zhang, G., Kuznetsov, N.V., Bao, H.: Hidden attractors and multistability in a modified Chua’s circuit. Commun. Nonlinear Sci. Numer. Simul. 92, 105494 (2021)

    Article  MathSciNet  Google Scholar 

  8. Wang, Z., Zhang, C., Bi, Q.: Bursting oscillations with bifurcations of chaotic attractors in a modified Chua’s circuit. Chaos Solitons Fractals 165, 112788 (2022)

    Article  MathSciNet  Google Scholar 

  9. Elhadj, Z., Sprott, J.C.: Simplest 3D continuous-time quadratic systems as candidates for generating multiscroll chaotic attractors. Int. J. Bifurc. Chaos 23(7), 1–6 (2013)

    Article  MathSciNet  Google Scholar 

  10. Iñarrea, M.: Chaos and its control in the pitch motion of an asymmetric magnetic spacecraft in polar elliptic orbit. Chaos Solitons Fractals 40(4), 1637–1652 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  11. Iñarrea, M., Lanchares, V., Rothos, V.M., Salas, J.P.: Chaotic rotations of an asymmetric body with timedependent moment of inertia and viscous drag. Int. J. Bifurc. Chaos 13(2), 393–409 (2003)

    Article  Google Scholar 

  12. Liu, J., Chen, L., Cui, N.: Solar sail chaotic pitch dynamics and its control in Earth orbits. Nonlinear Dyn. 90(3), 1755–1770 (2017)

    Article  MathSciNet  Google Scholar 

  13. Aslanov, V.S.: Chaotic attitude dynamics of a LEO satellite with flexible panels. Acta Astronaut. 180, 538–544 (2021)

    Article  ADS  Google Scholar 

  14. Doroshin, A.V.: Homoclinic solutions and motion chaotization in attitude dynamics of a multi-spin spacecraft. Commun. Nonlinear Sci. Numer. Simul. 19(7), 2528–2552 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  15. Doroshin, A.V.: Heteroclinic chaos and its local suppression in attitude dynamics of an asymmetrical dual-spin spacecraft and gyrostat-satellites: the part I-main models and solutions. Commun. Nonlinear Sci. Numer. Simul. 31(1), 151–170 (2016)

    Article  MathSciNet  Google Scholar 

  16. Doroshin, A.V.: Heteroclinic chaos and its local suppression in attitude dynamics of an asymmetrical dual-spin spacecraft and gyrostat-satellites: the Part II: the heteroclinic chaos investigation. Commun. Nonlinear Sci. Numer. Simul. 31(1), 171–196 (2016)

    Article  MathSciNet  Google Scholar 

  17. Doroshin, A.V.: Regimes of regular and chaotic motion of gyrostats in the central gravity field. Commun. Nonlinear Sci. Numer. Simul. 69, 416–431 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  18. Doroshin, A.V., Eremenko, A.V.: Heteroclinic chaos detecting in dissipative mechanical systems: chaotic regimes of compound nanosatellites dynamics. Commun. Nonlinear Sci. Numer. Simul. 127, 107525 (2023)

    Article  MathSciNet  Google Scholar 

  19. Wiggins, S.: Global bifurcations and Chaos: Analytical Methods. Applied Mathematical Sciences. Springer (1988)

    Book  Google Scholar 

  20. Leung, A.Y.T., Kuang, J.L.: Chaotic rotations of a liquid-filled solid. J. Sound Vib. 302(3), 540–563 (2007)

    Article  ADS  Google Scholar 

  21. Kuang, J.L., Meehan, P.A., Leung, A.Y.T.: On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral. Int. J. Non. Linear. Mech. 41(4), 475–490 (2006)

    Article  ADS  Google Scholar 

  22. Zhou, L., Chen, Yu., Chen, F.: Stability and chaos of a damped satellite partially filled with liquid. Acta Astronaut. 65, 1628–1638 (2009)

    Article  ADS  Google Scholar 

  23. Liu, Y., Liu, X., Cai, G., Chen, J.: Attitude evolution of a dual-liquid-filled spacecraft with internal energy dissipation. Nonlinear Dyn. 99, 2251–2263 (2020)

    Article  Google Scholar 

  24. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  25. Shinbrot, T., Ott, E., Grebogi, C., Yorke, J.A.: Using chaos to direct trajectories to targets. Phys. Rev. Lett. 65, 3215–3218 (1990)

    Article  ADS  CAS  PubMed  Google Scholar 

  26. Romeiras, F.J., Grebogi, C., Ott, E., Dayawansa, W.P.: Controlling chaotic dynamical systems. Phys. D 58, 165–192 (1992)

    Article  MathSciNet  Google Scholar 

  27. Grebogi, C., Lai, Y.-C.: Controlling chaotic dynamical systems. Syst. Control Lett. 31(5), 307–312 (1997)

    Article  MathSciNet  Google Scholar 

  28. Macau, E.E.N.: Using chaos to guide a spacecraft to the Moon. Acta Astronaut. 47(12), 871–878 (2000)

    Article  ADS  Google Scholar 

  29. Macau, E.E.N., Grebogi, C.: Control of chaos and its relevancy to spacecraft steering. Phil. Trans. R. Soc. A 364, 2463–2481 (2006)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  30. Zheng, Yu., Pan, B., Tang, S.: A hybrid method based on invariant manifold and chaos control for earth-moon low-energy transfer. Acta Astronaut. 163, 145–156 (2019)

    Article  ADS  Google Scholar 

  31. Belbruno, E.: Ballistic lunar capture transfers using the fuzzy boundary and solar perturbations: a survey. J. Br. Interplanet. Soc. 47, 73–80 (1994)

    ADS  Google Scholar 

  32. Pal, P., Jin, G.G., Bhakta, S., Mukherjee, V.: Adaptive chaos synchronization of an attitude control of satellite: a backstepping based sliding mode approach. Heliyon 8, e11730 (2022)

    Article  PubMed  PubMed Central  Google Scholar 

  33. Alsaade, F.W., Yao, Q., Bekiros, S., Al-zahrani, M.S., Alzahrani, A.S., Jahanshali, H.: Chaotic attitude synchronization and anti-synchronization of master-slave satellites using a robust fixed-time adaptive controller. Chaos Solitons Fract. 165, 112883 (2022)

    Article  MathSciNet  Google Scholar 

  34. Doroshin, A.V.: Initiations of chaotic regimes of attitude dynamics of multi-spin spacecraft and gyrostat-satellites basing on multiscroll strange chaotic attractors. In: SAI intelligent systems conference (IntelliSys), 698–704 (2015)

  35. Doroshin, A.V.: Implementation of regimes with strange attractors in attitude dynamics of multi-rotor spacecraft. In: Proceedings of 2020 international conference on information technology and nanotechnology (ITNT), 1–4 (2020)

  36. Doroshin, A.V.: Chaos as the hub of systems dynamics: the part I: The attitude control of spacecraft by involving in the heteroclinic chaos. Commun. Nonlinear Sci. Numer. Simul. 59, 47–66 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  37. Benettin, G., Galgani, L., Giorgilli, A., Strelcyn, J.-M.: Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: a method for computing all of them. P.I.: Theory P.II: numerical application. Meccanica 15, 9–30 (1980)

    Article  ADS  Google Scholar 

  38. Storn, R., Price, K.: Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the Russian Science Foundation (# 19-19-00085).

Author information

Authors and Affiliations

  1. Research Laboratory of Aircraft Flight Dynamics and Control, Samara National Research University, Moskovskoe Sh. 34, Samara, Russia, 443086

    Anton V. Doroshin & Nikolay A. Elisov

Authors
  1. Anton V. Doroshin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nikolay A. Elisov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anton V. Doroshin.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix A.1. Parameters of the strange attractors

Coefficients of Eq. (38) for considered attractors are presented in Table 

Table 5 Coefficients of Eq. (38)
Full size table

5.

LCEs and Kaplan–Yorke dimension of considered attractors are given in Table 

Table 6 LCEs and Kaplan–Yorke dimension
Full size table

6.

To initiate the chaotic mode with above-mentioned chaotic attractor, the control parameters (31) must have the following values, presented in Table 

Table 7 Control parameters for initialization of chaotic attractor
Full size table

7.

Appendix A.2. Modeling results for new systems with chaotic attractors

2.1 The chaotic attractor #2

The phase portrait and LCE are shown in Fig. 

Fig. 11
figure 11

a Phase portrait and b LCE of the chaotic attractor #2

Full size image

11.

2.2 The chaotic attractor #3

The phase portrait and LCE are shown in Fig. 

Fig. 12
figure 12

a Phase portrait and b LCE of the chaotic attractor #3

Full size image

12.

2.3 The chaotic attractor #4

The phase portrait and LCE are shown in Fig. 

Fig. 13
figure 13

a Phase portrait and b LCE of the chaotic attractor #4

Full size image

13.

2.4 The strange chaotic attractor #5

The phase portrait and LCE are shown in Fig. 

Fig. 14
figure 14

a Phase portrait and b LCE of the chaotic attractor #5

Full size image

14.

Appendix B. Transition from the initial zone to the target one

Figures 

Fig. 15
figure 15

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

15,

Fig. 16
figure 16

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

16,

Fig. 17
figure 17

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

17 shows the numerical results corresponding to attitude reorientation C → A, B → A, and A → C with the help of chaotic attractor #2.

Figures 

Fig. 18
figure 18

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

18,

Fig. 19
figure 19

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

19,

Fig. 20
figure 20

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

20 shows the numerical results corresponding to attitude reorientation C → A, B → A, and A → C with the help of the chaotic attractor #3.

Figures 

Fig. 21
figure 21

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

21,

Fig. 22
figure 22

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

22,

Fig. 23
figure 23

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

23 shows the numerical results corresponded to attitude reorientations C → A, B → A, and A → C with the help of the chaotic attractor #4.

Figures 

Fig. 24
figure 24

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

24,

Fig. 25
figure 25

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

25,

Fig. 26
figure 26

Dependence of (a) nutation, (b) p velocity component, (c) q velocity component, and (d) r velocity component on time

Full size image

26 shows the numerical results corresponding to attitude reorientation C → A, B → A, and A → C with the help of the chaotic attractor #5.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Doroshin, A.V., Elisov, N.A. Multi-rotor spacecraft attitude control by triggering chaotic modes on strange chaotic attractors. Nonlinear Dyn 112, 4617–4649 (2024). https://doi.org/10.1007/s11071-024-09302-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-024-09302-7

Keywords

Search

Navigation