Spacecraft formation flying in the port-Hamiltonian framework
The problem of controlling the relative position and velocity in multi-spacecraft formation flying in the planetary orbits is an enabling technology for current and future research. This paper proposes a family of tracking controllers for different dynamics of Spacecraft Formation Flying (SFF) in the framework of port-Hamiltonian (pH) systems through application of timed Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC). The leader–multi-follower architecture is used to address this problem. In this regard, first we model the spacecraft motion in the pH framework in the Earth Centered Inertial frame and then transform it to the Hill frame which is a special local coordinate system. By this technique, we may present a unified structure which encompasses linear/nonlinear dynamics, with/without perturbation. Then, using the timed IDA-PBC method and the contraction analysis, a new method for controlling a family of SFF dynamics is developed. The numerical simulations show the efficiency of the approach in two different cases of missions.
KeywordsSpacecraft formation flying Port-Hamiltonian systems Trajectory tracking Timed IDA-PBC technique
The authors would like to thank members of ACSL (Advanced Control Systems Laboratory) of University of Tehran, Mohammad Javanmardi and Maziar Sharbafi for the fruitful discussion on the subject.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest concerning the publication of this manuscript.
- 1.Alfriend, K., Gurfil, P.: Spacecraft Formation Flying: Dynamics, Control and Navigation, ser. Astrodynamics Series. Elsevier, Amsterdam (2010)Google Scholar
- 4.Curtis, H.: Orbital Mechanics: For Engineering Students, ser. Aerospace Engineering. Elsevier, Amsterdam (2015)Google Scholar
- 9.Eyer, J.K.: A dynamics and control algorithm for low earth orbit precision formation flying satellites. Ph.D. dissertation, University of Toronto (2009)Google Scholar
- 12.Jian, M.: Formation flying of spacecrafts for monitoring and inspection. Master’s thesis, Lulea University of Technology (2009)Google Scholar
- 13.Lanczos, C.: The Variational Principles of Mechanics, ser. Dover Books on Physics. Dover Publications, New York (1986)Google Scholar
- 19.Reyes-Báez, R., van der Schaft, A., Jayawardhana, B., Donaire, A., Pérez, T.: Tracking control of marine craft in the port-hamiltonian framework: a virtual differential passivity approach. In: 2019 18th European Control Conference (ECC), pp. 1636–1641. IEEE, 2019Google Scholar
- 21.Sherrill, R.: Dynamics and control of satellite relative motion in elliptic orbits using Lyapunov-Floquet theory. Ph.D. dissertation (2013)Google Scholar
- 25.Wang, D., Wu, B., Poh, E.K.: Satellite Formation Flying: Relative Dynamics, Formation Design, Fuel Optimal Maneuvers and Formation Maintenance, vol. 87. Springer, Berlin (2016)Google Scholar