New Class of Attitude Controllers Guaranteed to Converge within Specified Finite-Time

  • Marcelino M. de AlmeidaEmail author
  • Maruthi R. Akella


This paper introduces a new class of finite-time feedback controllers for rigid-body attitude dynamics subject to full actuation. The control structure is Lyapunov-based and is designed to regulate the configuration from an arbitrary initial state to any prescribed final state within user-specified finite transfer-time. A salient feature here is that the synthesis of the control structure is explicit, i.e., given the transfer-time time, the feedback-gains are explicitly stated to satisfy the convergence specifications. A major contrast between this work and others in the literature is that instead of resorting to feedback-linearization (to get to the so-called normal form), our approach efficiently marries the process of designing time-varying feedback gains with the logarithmic Lyapunov function for attitude kinematics based on the Modified Rodrigues Parameters representation. Saliently, this finite-time solution extends nicely for accommodating trajectory tracking objectives and possesses robustness with respect to bounded external disturbance torques. Numerical simulations are performed to test and validate the performance and robustness features of the new control designs.


Attitude tracking Finite-time control Disturbance rejection Modified Rodrigues parameters 



  1. 1.
    Athans, M., Falb, P.L.: Optimal Control: An Introduction to the Theory and its Applications. Courier Corporation (2013)Google Scholar
  2. 2.
    Slotine, J.-J.E., Li, W., et al.: Applied Nonlinear Control, vol. 199. Prentice Hall, Englewood Cliffs (1991)Google Scholar
  3. 3.
    Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control. Optim. 38(3), 751–766 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Song, Y., Wang, Y., Holloway, J., Krstic, M.: Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time. Automatica 83, 243–251 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bryson, A., Ho, Y.-C.: Applied Optimal Control: Optimization, Estimation, and Control (Revised Edition). Taylor & Francis, Levittown (1975)Google Scholar
  6. 6.
    Tsiotras, P.: New Control Laws for the Attitude Stabilization of Rigid Bodies. Automatic Control in Aerospace 1994 (Aerospace Control’94), pp. 321–326. Elsevier (1995)Google Scholar
  7. 7.
    Junkins, J.L., Akella, M.R., Robinett, R.D.: Nonlinear adaptive control of spacecraft maneuvers. J. Guid. Control Dyn. 20(6), 1104–1110 (1997)CrossRefzbMATHGoogle Scholar
  8. 8.
    Shuster, M.D.: A survey of attitude representations. Navigation 8(9), 439–517 (1993)MathSciNetGoogle Scholar
  9. 9.
    Khalil, H.K.: Nonlinear Systems. New Jewsey, Prentice Hall (2002)zbMATHGoogle Scholar
  10. 10.
    Wen, J.-Y., Kreutz-Delgado, K.: The attitude control problem. IEEE Trans. Autom. control 36(10), 1148–1162 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Chatuverdi, N., Sanyal, A.K., McClamroch, N.H.: Rigid-body attitude control using rotation matrices for continuous, singularity-free control laws. IEEE Control. Syst. Mag. 31(8), 30–51 (2011)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Cemenska, J.: Sensor Modelling and Kalman Filtering Applied to Satellite Attitude Determination. University of California at Berkeley, PhD thesis (2004)Google Scholar

Copyright information

© American Astronautical Society 2019

Authors and Affiliations

  1. 1.Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at AustinAustinUSA

Personalised recommendations