A model of relative translation and rotation in leader-follower spacecraft formations

“A model of relative translation and rotation in leader-follower spacecraft formations”

Authors: Raymond Kristiansen, Esten I. Grøtli, Per J. Nicklasson and Jan T. Gravdahl,
Affiliation: Narvik University College and NTNU, Department of Engineering Cybernetics
Reference: 2007, Vol 28, No 1, pp. 3-14.

Keywords: Spacecraft formation, relative motion, 3D general orbits, orbital perturbations

Abstract: In this paper, a model of a leader-follower spacecraft formation in six degrees of freedom is derived and presented. The nonlinear model describes the relative translational and rotationalmotion of the spacecraft, and extends previous work by providing a more complete factorization, together with detailed information about the matrices in the model. The resulting model shows many similarities with models for systems such as robot manipulators and marine vehicles. In addition, mathematical models of orbital perturbations due to gravitational variations, atmospheric drag, solar radiation and third-body effects are presented for completeness. Results from simulations are presented to visualize the properties of the model and to show the impact of the different orbital perturbations on the flight path.

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DOI forward links to this article:

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References:
[1] Battin, R. H. (1999). An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition, AIAA Education Series. American Institute of Aeronautics and Astronautics, Reston, VA.
[2] Clohessy, W. H. Wiltshire, R. S. (1960). Terminal guidance system for satellite rendezvous, Journal of Aerospace Sciences, 2.9:653 - 658.
[3] Egeland, O. Gravdahl, J. T. (2002). Modeling and Simulation for Automatic Control, Marine Cybernetics, Trondheim, Norway.
[4] Fjellstad, O.-E. (1994). Control of Unmanned Underwater Vehicles in Six Degrees of Freedom, Ph.D. thesis, Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway.
[5] Fossen, T. I. (2002). Marine Control Systems: Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles, Marine Cybernetics, Trondheim, Norway.
[6] Golikov, A. (2003). Evolution of formation flying satellite relative motion: analysis based on the theona satellite theory, In Proceedings of the 17th International Symposium on Space Flight Dynamics. Moscow, Russia.
[7] Hill, G. W. (1878). Researches in the lunar theory, American Journal of Mathematics, .1:5-26 doi:10.2307/2369430
[8] Kristiansen, R., Grøtli, E. I., Nicklasson, P. J., Gravdahl, J. T. (2005). A 6DOF model of a leader-follower spacecraft formation, In Proceedings of the Conference on Simulation and Modeling. Trondheim, Norway.
[9] Lawden, D. (1954). Fundamentals of space navigation, Journal of the British Interplanetary Society, 1.2:87-101.
[10] Manikonda, V., Arambel, P. O., Gopinathan, M., Mehra, R. K., Hadaegh, F. Y. (1999). A model predictive control based approach for spacecraft formation keeping and attitude control, In Proceedings of the American Control Conference. San Diego, CA.
[11] McInnes, C. R. (1995). Autonomous ring formation for a planar constellation of satellites, AIAA Journal of Guidance, Control and Dynamics, 1.5:1215 - 1217 doi:10.2514/3.21531
[12] Montenbruck, O. Gill, E. (2001). Satellite Orbits, Models, methods, applications. Springer-Verlag, Berlin, Germany, First edition, corrected second printing.
[13] Naasz, B., Berry, M. M., Kim, H.-Y., Hall, C. D. (2003). Integrated orbit and attitude control for a nanosatellite with power constraints, In Proceedings of the AAS/AIAA Space Flight Mechanics Conference. Ponce, Puerto Rico.
[14] Ortega, R., Loria, A., Nicklasson, P. J., Sira-Ramirez, H. (1998). Passivity-based Control of Euler-Lagrange Systems, Springer-Verlag, London.
[15] Pan, H. Kapila, V. (2001). Adaptive nonlinear control for spacecraft formation flying with coupled translational and attitude dynamics, In Proceedings of the Conference on Decision and Control. Orlando, FL.
[16] Ploen, S. R., Hadaegh, F. Y., Scharf, D. P. (2004). Rigid body equations of motion for modeling and control of spacecraft formations - part 1: Absolute equations of motion, In Proceedings of the American Control Conference. Boston, MA.
[17] Roy, A. E. (2005). Orbital motion, Fourth edition, Institute of Physics Publishing Ltd, Bristol, UK.
[18] Schaub, H. (2004). Relative orbit geometry through classical orbit element differences, AIAA Journal of Guidance, Control and Dynamics, 2.5:839-848 doi:10.2514/1.12595
[19] Schaub, H. Junkins, J. L. (2003). Analytical Mechanics of Space Systems, AIAA Education Series. American Institute of Aeronautics and Astronautics, Reston, VA.
[20] Schaub, H., Vadali, S. R., Junkins, J. L., Alfriend, K. T. (1999). Spacecraft formation control using mean orbit elements, Journal of the Astronautical Sciences, 4.1:69-87.
[21] Schaub, H., Vadali, S. R., Junkins, J. L., Alfriend, K. T. (2000). Spacecraft formation flying control using mean orbit elements, Journal of the Astronautical Sciences, 4.1:69-87.
[22] Sidi, M. J. (1997). Spacecraft Dynamics and Control, Cambridge University Press, New York.
[23] Tschauner, J. (1967). Elliptic orbit rendezvous, AIAA Journal, .6:1110-1113 doi:10.2514/3.4145
[24] Wang, P. K. C. Hadaegh, F. Y. (1996). Coordination and control of multiple microspacecraft moving in formation, Journal of the Astronautical Sciences, 4.3:315-355.
[25] Wertz, J. R., editor. (1978). Spacecraft Attitude Determination and Control, Kluwer Academic Publishers, London.
[26] Yan, Q., Yang, G., Kapila, V., de Queiroz, M. (2000). Nonlinear dynamics and adaptive control of multiple spacecraft in periodic relative orbits, In Proceedings of the AAS Guidance and Control Conference. Breckenridge, CO.

BibTeX:
@article{MIC-2007-1-1,
  title={{A model of relative translation and rotation in leader-follower spacecraft formations}},
  author={Kristiansen, Raymond and Grøtli, Esten I. and Nicklasson, Per J. and Gravdahl, Jan T.},
  journal={Modeling, Identification and Control},
  volume={28},
  number={1},
  pages={3--14},
  year={2007},
  doi={10.4173/mic.2007.1.1},
  publisher={Norwegian Society of Automatic Control}
};

Article

“A model of relative translation and rotation in leader-follower spacecraft formations”