Aerotecnica Missili & Spazio

, Volume 96, Issue 3, pp 111–123 | Cite as

Inverse-Dynamics Particle Swarm Optimization for Spacecraft Minimum-Time Slew Maneuvers with Constraints

  • D. SpillerEmail author
  • F. Curti
  • L. Ansalone


The problem of planning spacecraft minimum time reorientation maneuvers under boundaries and path constraints is addressed. Keep-out constraints for an optical sensor are considered and end-point constraints are imposed to obtain a rest-to-rest maneuver. The recently developed Inverse-dynamics Particle Swarm Optimization is improved and employed to solve the transcribed parameters problem. The numerical optimization technique is based on a differential flatness formulation of the dynamical system and the application of swarm intelligence to search for the solution. The flat outputs are chosen as the Modified Rodriguez Parameters which are approximated with B-spline curves. State and control are expressed as nonlinear functions of the flat outputs. It is established that the computation of minimum time maneuvers with the proposed technique leads to near optimal solutions, which fully satisfy all the boundaries and path constraints.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K.D. Bilimoria and B. Wie. Time-optimal threeaxis reorientation of rigid spacecraft. Journal of Guidance, Control, and Dynamics, 16(3):446–452, 1993. DOI: 10.2514/3.21030.CrossRefGoogle Scholar
  2. 2.
    F. Li and P. M. Bainum. Numerical approach for solving rigid spacecraft minimum time attitude maneuvers. Journal of Guidance, Control, Dynamics, 13(1):38–45, 1990. DOI: 10.2514/3.20515.MathSciNetCrossRefGoogle Scholar
  3. 3.
    J. Li. Time-optimal three-axis reorientation of asymmetric rigid spacecraft via homotopic approach. Advances in space research, 57(10):2204–2217, 2016. DOI: 10.1016/j.asr.2016.02.016.CrossRefGoogle Scholar
  4. 4.
    J. Li and X.-N. Xi. Time-optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach. Optimal Control Applications and Methods, 36(6):889–918, 2015. DOI: 10.1002/oca.2145.MathSciNetCrossRefGoogle Scholar
  5. 5.
    X. Bai and J. L. Junkins. New results for time-optimal three-axis reorientation of a rigid spacecraft. Journal of Guidance, Control, and Dynamics, 32(4):1071–1076, 2009. DOI: 10.2514/1.43097.CrossRefGoogle Scholar
  6. 6.
    C. R. McInnes. Large angle slew maneuvers with autonomous sun vector avoidance. Journal of Guidance, Control, and Dynamics, 17(4):875–877, 1994. DOI: 10.2514/3.21283.CrossRefGoogle Scholar
  7. 7.
    H. B. Hablani. Attitude commands avoiding bright objects and maintaining communication with ground station. Journal of Guidance, Control, and Dynamics, 22 (6):759–767, 1999. DOI: 10.2514/2.4469.CrossRefGoogle Scholar
  8. 8.
    E. Frazzoli, M.A. Dahleh, E. Feron, and R. Kornfeld. A randomized attitude slew planning algorithm for autonomous spacecraft. In AIAA Guidance, Navigation, and Control Conference and Exhibit, Montreal, Canada, Montreal, Quebec, Canada, 2001.Google Scholar
  9. 9.
    U. Lee and M. Mesbahi. Spacecraft reorientation in presence of attitude constraints via logarithmic barrier potentials. Proceedings of the American Control Conference, pages 450–455, 2011. DOI: 10.1109/ACC.2011.5991284.Google Scholar
  10. 10.
    T. Lee, M. Leok, and N. H. McClamroch. Time optimal attitude control for a rigid body. In American Control Conference, 2008, pages 5210–5215. IEEE, 2008. DOI: 10.1109/ACC.2008.4587322.CrossRefGoogle Scholar
  11. 11.
    X. S. Yang. Engineering Optimization - An Introduction with Metaheuristic Applications. John Wiley & Sons, New Jersey, 2010. ISBN: 978-0-470-58246-6.CrossRefGoogle Scholar
  12. 12.
    P. Cui, W. Zhong, and H. Cui. Onboard spacecraft slew-planning by heuristic state-space search and optimization. Proceedings of the 2007 International Conference on Mechatronics and Automation, pages 2115–2119, 2007. DOI: 10.1109/ICMA.2007.4303878.CrossRefGoogle Scholar
  13. 13.
    L.-C. Lai, C.-C. Yang, and C.-J. Wu. Timeoptimal maneuvering control of a rigid spacecraft. Acta Astronautica, 60(10):791–800, 2007. DOI: 10.1016/j.actaastro.2006.09.039.CrossRefGoogle Scholar
  14. 14.
    R. G. Melton. Hybrid methods for determining time-optimal, constrained spacecraft reorientation maneuvers. Acta Astronautica, 94:294-301, 2014. DOI: 10.1016/j.actaastro.2013.05.007.CrossRefGoogle Scholar
  15. 15.
    R. Kornfeld. On-board autonomous attitude maneuver planning for planetary spacecraft using genetic algorithms. AIAA Guidance, Navigation, and Control Conference and Exhibit, Guidance, Navigation, and Control and Co-located Conferences. DOI: 10.2514/6.2003-5784.Google Scholar
  16. 16.
    Y. S. X. Shijie. Spacecraft attitude maneuver planning based on particle swarm optimization. Journal of Beijing University of Aeronautics and Astronautics, 1:013, 2010.Google Scholar
  17. 17.
    D. J. Showalter and J. T. Black. Responsive theater maneuvers via particle swarm optimization. Journal of Spacecraft and Rockets, 51(6):1976–1985, 2014. DOI: 10.2514/1.A32989.CrossRefGoogle Scholar
  18. 18.
    P. Huang, G. Liu, J. Yuan, and Y. Xu. Multiobjective optimal trajectory planning of space robot using particle swarm optimization. Advances in Neural Networks-ISNN 2008, pages 171–179, 2008. DOI: 10.1007/978-3-540-87734-9-20.CrossRefGoogle Scholar
  19. 19.
    N. Xia, D. Han, G. Zhang, J. Jiang, and K. Vu. Aerotecnica Study on attitude determination based on discrete particle swarm optimization. Science China Technological Sciences, 53(12):3397–3403, 2010. DOI: 10.1007/s11431-010-4148-4.CrossRefGoogle Scholar
  20. 20.
    D. Spiller, L. Ansalone, and F. Curti. Particle swarm optimization for time-optimal spacecraft reorientation with keep-out cones. Journal of Guidance, Control, and Dynamics, 39(2):312–325, 2016. DOI: 10.2514/1.G001228.CrossRefGoogle Scholar
  21. 21.
    M. Fliess, J. Lévine, P. Martin, and P. Rouchon. Flatness and defect of non-linear systems: introductory theory and examples. International Journal of Control, 61:1327–1361, 2007. DOI: 10.1080/00207179508921959.MathSciNetCrossRefGoogle Scholar
  22. 22.
    C. Louembet. Design of algorithms for satellite slew manoeuver by flatness and collocation. Proceedings of the 26th American Control Conference, pages 3168–3173, 2007. DOI: 10.1109/ACC.2007.4282459.Google Scholar
  23. 23.
    M. A. Patterson and A. V. Rao. GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming. ACM Transactions on Mathematical Software, 41(1):1–37, 2014. DOI: 10.1145/2558904.MathSciNetCrossRefGoogle Scholar
  24. 24.
    F. Boldrini, D. Procopio, S. P. Airy, and L. Giulicchi. Miniaturised star tracker (aa-str) ready to fly. Proceedings of the 4S Symposium: Small Satellites, Systems and Services (ESA SP-571), 2004.Google Scholar
  25. 25.
    U. Schmidt, T. Fiksel, A. Kwiatkowski, B. Steinbach, I. abd Pradarutti, K. Michel, and E. Benzi. Autonomous star sensor astro aps: flight experience on alphasat. CEAS Space Journal, pages 1–10, 2015. DOI: 10.1007/s12567-014-0071-z.Google Scholar
  26. 26.
    L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko. The Mathematical Theory of Optimal Processes. Interscience Publishers, John Wiley & Sons, 1965.Google Scholar
  27. 27.
    J. Kennedy and R. Eberhart. Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks, 4:1942–1948, 1995. DOI: 10.1109/ICNN.1995.488968.CrossRefGoogle Scholar
  28. 28.
    M. Clerc. Particle Swarm Optimization. ISTE. Wiley, 2013. ISBN: 9781118613979.zbMATHGoogle Scholar
  29. 29.
    K. E. Parsopoulos and M. N. Vrahatis. Parameter selection and adaptation in unified particle swarm optimization. Mathematical and Computer Modelling, 46:198-213, 2007. DOI: 10.1016/j.mcm.2006.12.019.MathSciNetCrossRefGoogle Scholar
  30. 30.
    R. Eberhart and J. Kennedy. A new optimizer using particle swarm theory. In Micro Machine and Human Science, 1995. MHS’95., Proceedings of the Sixth International Symposium on, pages 39–43. IEEE, 1995. DOI: 10.1109/MHS.1995.494215.CrossRefGoogle Scholar
  31. 31.
    C. De Boor. On calculating with b-splines. Journal of Approximation Theory, 6:50–62, 1972. DOI: 10.1016/0021-9045(72)90080-9.MathSciNetCrossRefGoogle Scholar
  32. 32.
    C. De Boor. Splines as linear combinations of bsplines. a survey. Journal of Approximation Theory, 1986. DOI: Scholar
  33. 33.
    M. G. Cox. Practical spline approximation. In Topics in Numerical Analysis, pages 79–112. Springer, 1982. DOI: 10.1007/BFb0063201.CrossRefGoogle Scholar
  34. 34.
    A. Saxena and B. Sahay. Computer Aided Engineering Design. Springer Netherlands, 2007. ISBN: 9781402038716.Google Scholar
  35. 35.
    S.S. Rao. Engineering Optimization: Theory and Practice. Wiley, 2009. ISBN: 9780470183526.CrossRefGoogle Scholar
  36. 36.
    M. D. Shuster. A survey of attitude representations. The Journal of the Astronautical Sciences, 41(4):439–517, 1993.MathSciNetGoogle Scholar

Copyright information

© AIDAA Associazione Italiana di Aeronautica e Astronautica 2017

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace Engineering“Sapienza” - University of RomeRomeItaly
  2. 2.School of Aerospace Engineering“Sapienza” - University of RomeRomeItaly
  3. 3.Italian Space AgencyRomeItaly

Personalised recommendations