Constrained geometric attitude control on SO(3)

  • Shankar KulumaniEmail author
  • Taeyoung Lee
Regular Papers Robot and Applications


This paper presents a new geometric adaptive control system with state inequality constraints for the attitude dynamics of a rigid body. The control system is designed such that the desired attitude is asymptotically stabilized, while the controlled attitude trajectory avoids undesired regions defined by an inequality constraint. In addition, we develop an adaptive update law that enables attitude stabilization in the presence of unknown disturbances. The attitude dynamics and the proposed control systems are developed on the special orthogonal group such that singularities and ambiguities of other attitude parameterizations, such as Euler angles and quaternions are completely avoided. The effectiveness of the proposed control system is demonstrated through numerical simulations and experimental results.


Adaptive control attitude control constraint obstacle special orthogonal group 


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  1. [1]
    P. Hughes, Spacecraft Attitude Dynamics, Dover Publications, 2004.Google Scholar
  2. [2]
    J. R. Wertz, Spacecraft Attitude Determination and Control, Springer, vol. 73, 1978.Google Scholar
  3. [3]
    S. P. Bhat and D. S. Bernstein, “A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon,” Systems & Control Letters, 2000.Google Scholar
  4. [4]
    M. D. Shuster, “A survey of attitude representations,” Journal of the Astronautical Sciences, vol. 41, no. 8, pp. 439–517, Oct. 1993.MathSciNetGoogle Scholar
  5. [5]
    N. Chaturvedi, A. K. Sanyal, N. H. McClamroch, et al., “Rigid–body attitude control,” IEEE Control Systems, vol. 31, no. 3, pp. 30–51, 2011. [click]MathSciNetCrossRefGoogle Scholar
  6. [6]
    F. Bullo and A. D. Lewis, Geometric Control of Mechanical Systems, ser. Texts in Applied Mathematics, New York–Heidelberg–Berlin: Springer Verlag, vol. 49, 2004.Google Scholar
  7. [7]
    C. Mayhew and A. Teel, “Synergistic potential functions for hybrid control of rigid–body attitude,” Proceedings of the American Control Conference, pp. 875–880, 2011.Google Scholar
  8. [8]
    T. Lee, “Global exponential attitude tracking controls on SO(3),” IEEE Transactions on Automatic Control, vol. 60, no. 10, pp. 2837–2842, 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    H. B. Hablani, “Attitude commands avoiding bright objects and maintaining communication with ground station,” Journal of Guidance, Control, and Dynamics, vol. 22, no. 6, pp. 759–767, 2015/09/19 1999. [Online]. Available: Scholar
  10. [10]
    E. Frazzoli, M. Dahleh, E. Feron, and R. Kornfeld, “A randomized attitude slew planning algorithm for autonomous spacecraft,” AIAA Guidance, Navigation, and Control Conference and Exhibit, Montreal, Canada, 2001.Google Scholar
  11. [11]
    A. Guiggiani, I. Kolmanovsky, P. Patrinos, and A. Bemporad, “Fixed–point constrained model predictive control of spacecraft attitude,” arXiv:1411.0479, 2014. [Online]. Available: Scholar
  12. [12]
    U. Kalabic, R. Gupta, S. Di Cairano, A. Bloch, and I. Kolmanovsky, “Constrained spacecraft attitude control on SO(3) using fast nonlinear model predictive control using reference governors and nonlinear model predictive control,” American Control Conference (ACC), pp. 5586–5593, June 2014. [click]Google Scholar
  13. [13]
    R. Gupta, U. Kalabic, S. Di Cairano, A. Bloch, and I. Kolmanovsky, “Constrained spacecraft attitude control on SO(3) using fast nonlinear model predictive control,” American Control Conference (ACC), 2015, pp. 2980–2986, July 2015. [click]CrossRefGoogle Scholar
  14. [14]
    E. Rimon and D. E. Koditschek, “Exact robot navigation using artificial potential functions,” Robotics and Automation, IEEE Transactions on, vol. 8, no. 5, pp. 501–518, 1992. [click]CrossRefGoogle Scholar
  15. [15]
    U. Lee and M. Mesbahi, “Spacecraft Reorientation in Presence of Attitude Constraints via Logarithmic Barrier Potentials,” Proceedings of the American Control Conference, pp. 450–455, 2011.Google Scholar
  16. [16]
    C. R. McInnes, “Large angle slew maneuvers with autonomous sun vector avoidance,” Journal of Guidance, Control, and Dynamics, vol. 17, no. 4, pp. 875–877, 2015/07/10 1994. [Online]. Available: Scholar
  17. [17]
    T. Lee, “Robust adaptive tracking on SO(3) with an application to the attitude dynamics of a quadrotor UAV,” IEEE Transactions on Control Systems Technology, vol. 21, no. 5, pp. 1924–1930, September 2013. [click]CrossRefGoogle Scholar
  18. [18]
    N. S. Nise, Control Systems Engineering, 4th ed., JohnWiley & Sons, 2004.zbMATHGoogle Scholar
  19. [19]
    D. A. Vallado, Fundamentals of Astrodynamics and Applications, 3rd ed. Microcosm Press, 2007.zbMATHGoogle Scholar
  20. [20]
    P. A. Ioannou and J. Sun, Robust Adaptive Control, Courier Corporation, 2012.zbMATHGoogle Scholar
  21. [21]
    E. Kaufman, K. Caldwell, D. Lee, and T. Lee, “Design and development of a free–floating hexrotor UAV for 6–dof maneuvers,” Proceedings of the IEEE Aerospace Conference, 2014.Google Scholar
  22. [22]
    H. K. Khalil, Nonlinear Systems, 3rd ed., Prentice Hall New Jersey, 2002.zbMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringGeorge Washington UniversityWashington DCUSA

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