On port-Hamiltonian modeling and control of quaternion systems

Authors

Kenji Fujimoto, Tomoya Takeuchi, Yuki Matsumoto

Abstract

A quaternion representation is often used to describe the attitude of a rigid body type spacecraft since it does not have any singular point whereas the conventional Euler angle description intrinsically has one. However, the dynamical equation with quaternions become more complicated than those described by Euler angles. The scope of this paper is to provide a basis of modeling and control of those systems using port-Hamiltonian system formulation to remove some of those difficulties in control of those systems. A stabilization procedure based on passivity based control is proposed and a sufficient condition for artificial potential energy are derived for a class of simple systems with quaternions.

Keywords

Passivity based control; quaternions; aerospace systems

Citation

• Journal: IFAC-PapersOnLine
• Year: 2015
• Volume: 48
• Issue: 13
• Pages: 39–44
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2015.10.211
• Note: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2015- Lyon, France, 4–7 July 2015

BibTeX

@article{Fujimoto_2015,
  title={{On port-Hamiltonian modeling and control of quaternion systems}},
  volume={48},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2015.10.211},
  number={13},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Fujimoto, Kenji and Takeuchi, Tomoya and Matsumoto, Yuki},
  year={2015},
  pages={39--44}
}

Download the bib file

References

• Arimoto, S. (1996). Control Theory of Non-linear Me-chanical Systems: Passivity-based and Circuit-theoretic Approach. Clarendon Press, Oxford.
• Dirksz, D.A. and Scherpen, J.M.A. (2010). Adaptive tracking control of fully actuated port-Hamiltonian me- chanical systems. In Proc. IEEE Conf. on Control Applications, 1678-1683.
• Duindam, V. & Stramigioli, S. Port-Based Asymptotic Curve Tracking for Mechanical Systems. European Journal of Control vol. 10 411–420 (2004) – 10.3166/ejc.10.411-420
• Fujimoto, K. & Nishiyama, T. On trajectory tracking control of port-Hamiltonian systems with quaternions. 53rd IEEE Conference on Decision and Control 4820–4825 (2014) doi:10.1109/cdc.2014.7040141 – 10.1109/cdc.2014.7040141
• Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica vol. 39 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
• Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory Tracking Control of Nonholonomic Hamiltonian Systems via Generalized Canonical Transformations. European Journal of Control vol. 10 421–431 (2004) – 10.3166/ejc.10.421-431
• Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters vol. 42 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
• Golo, G., Talasila, V., van der Schaft, A.J., and Maschke, B.M. (2005). Hamiltonian discretization of boundary control systems. Automatica, 40(7), 757-771.
• Hughes, P.C. (1986). Spacecraft Atitude Dynamics. Wiley, New York.
• Multidomain modeling of nonlinear networks and systems. IEEE Control Systems vol. 29 28–59 (2009) – 10.1109/mcs.2009.932927
• Joshi, S. M., Kelkar, A. G. & Wen, J. T.-Y. Robust attitude stabilization of spacecraft using nonlinear quaternion feedback. IEEE Transactions on Automatic Control vol. 40 1800–1803 (1995) – 10.1109/9.467669
• Kuipers, J.B. (2002). Quaternions and Rotation Sequence: A Primer with Application to Orbits, Aerospace, and Virtual Relity. Princeton University Press, Princeton.
• Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Taniguchi, M. & Fujimoto, K. Time-varying path following control for port-Hamiltonian systems. Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference 3323–3328 (2009) doi:10.1109/cdc.2009.5400011 – 10.1109/cdc.2009.5400011
• van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
• Wie, B. Space Vehicle Dynamics and Control, Second Edition. (2008) doi:10.2514/4.860119 – 10.2514/4.860119
• Wie, B. & Barba, P. M. Quaternion feedback for spacecraft large angle maneuvers. Journal of Guidance, Control, and Dynamics vol. 8 360–365 (1985) – 10.2514/3.19988
• Zenkov, D. V., Bloch, A. M. & Marsden, J. E. Controlled lagrangian methods and tracking of accelerated motions. 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) vol. 1 533–538 – 10.1109/cdc.2003.1272618