The Optimal Quaternion Equilibrium Point - Using an Energy Function to Choose the Optimal Quaternion Equilibrium Point

Margrete Djupaa, Rune Schlanbusch

2013

Abstract

By parameterizing the attitude of a rotating rigid body in a closed-loop system with unit quaternions, the existence of dual equilibria leads to new challenges. In order to optimize the energy consumption due to control effort, the choice of the cheapest equilibria, that is, the one which requires least energy to reach, is essential. A new predicting solution of choosing the optimal equilibrium point for rotational maneuvers of a rigid body is presented in this article. This new solution consists of an energy function which base its prediction on the initial attitude on the rotational sphere, taking account for both potential and kinetic energy of the rigid body. The equilibrium energy function is developed through a previously presented statistical analysis for the system behaviour of a rigid body in closed loop attitude control.

References

  1. Table 3: Average Energy Difference.
  2. EnergyDiff Hit 0.169 0.060 3.366
  3. EnergyDiff Non-Hit 0.016 0.004 0.178
  4. Bhat, S. P. and Bernstein, D. S. (2000). A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon. Systems & Control Letters, 39(1):63-70.
  5. Egeland, O. and Gravdahl, J. T. (2002). Modeling and Simulation for Automatic Control. Marine Cybernetics AS. ISBN: 82-92356-01-0.
  6. Fjellstad, O.-E. (1994). Control of Unmanned Underwater Vehicles on Six Degrees of Freedom. A Quaternion Feedback Approach. NTNU, Dep of Engineering Cybernetics. Dr.ing thesis Report 94-92-W.
  7. Hahn, W. (1967). Stability of Motion. Springer-Verlag. ISBN: 9783540038290.
  8. Khalil, H. K. (2002). Nonlinear Systems. Prentice Hall. ISBN: 978-01-306-7389-3.
  9. Kristiansen, R. (2008). Dynamic Synchronization of Spacecraft. Modeling and Coordinated Control of LeaderFollower Spacecraft Formations. NTNU, Dep of Engineering Cybernetics. Dr.ing thesis 2008:115 ISBN: 978-82-471-8317-5.
  10. Mayhew, C. G., Sanfelice, R. G., and Teel, A. R. (2009). Robust global asymptotic attitude stabilization of a rigid body by quaternion-based hybrid feedback. In Proceedings of the 48th IEEE Conference on Decision and Control, held jointly with the 28th Chinese Control Conference, pages 2522-2527, Shanghai, P. R. China.
  11. Paden, B. and Panja, R. (1988). Globally asymptotically stable 'PD+78 controller for robot manipulators. International Journal of Control, 47(6):1697-1712.
  12. Schlanbusch, R. (2012). Control of Rigid Bodies with applications to leader-follower spacecraft formations. NTNU, Dep of Engineering Cybernetics. Dr.ing thesis 2012:49 ISBN: 978-82-471-3365-1.
  13. Sidi, M. J. (1997). Spacecraft Dynamics & Control. A practical engineering approach. Cambridge University Press. ISBN: 0-521-78780-7.
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Paper Citation


in Harvard Style

Djupaa M. and Schlanbusch R. (2013). The Optimal Quaternion Equilibrium Point - Using an Energy Function to Choose the Optimal Quaternion Equilibrium Point . In Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-8565-69-3, pages 345-352. DOI: 10.5220/0004422903450352


in Bibtex Style

@conference{simultech13,
author={Margrete Djupaa and Rune Schlanbusch},
title={The Optimal Quaternion Equilibrium Point - Using an Energy Function to Choose the Optimal Quaternion Equilibrium Point},
booktitle={Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2013},
pages={345-352},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004422903450352},
isbn={978-989-8565-69-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - The Optimal Quaternion Equilibrium Point - Using an Energy Function to Choose the Optimal Quaternion Equilibrium Point
SN - 978-989-8565-69-3
AU - Djupaa M.
AU - Schlanbusch R.
PY - 2013
SP - 345
EP - 352
DO - 10.5220/0004422903450352