New Approach to Satellite Formation-Keeping: Exact Solution to the Full Nonlinear Problem

[en] This paper presents a new, simple, and exact solution to the formation keeping of satellites when the relative distance between the satellites is so large that the linearized relative equations of motion no longer hold. We employ a recently proposed approach, the Udwadia-Kalaba approach, which makes it possible to explicitly obtain the desired control function without making any approximations related to the nonlinearities in the underlying dynamics. We use an inertial frame of reference to describe the motion of a satellite and since no approximations are made, the results obtained apply to situations even when the distance between the satellites is arbitrarily large. The paper deals with a projected circular formation, but the methodology in this paper can be applied to any desired configuration or orbital requirements. Numerical simulations confirm the brevity and the accuracy of the analytical solution to the dynamical control problem developed herein.

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Cho, Hancheol ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Yu, Adam; Northrop Grumman Co., Ltd. > F-35 JSF Program Section

Language :

English

Title :

New Approach to Satellite Formation-Keeping: Exact Solution to the Full Nonlinear Problem

Publication date :

2009

Journal title :

Journal of Aerospace Engineering

ISSN :

0893-1321

Publisher :

American Society of Civil Engineers

Volume :

Issue :

Pages :

445-455

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 18 February 2016

Statistics

Number of views

44 (0 by ULiège)

Number of downloads

396 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Armellin, R., Massari, M., and Finzi, A. E. (2004). " Optimal formation flying reconfiguration and station keeping maneuvers using low thrust propulsion.." Proc., 18th Int. Symp. on Space Flight Dynamics (ESA SP-548), ESA Publication Division, Noordwijk, 429-434.
Clohessy, W. H., and Wiltshire, R. S. (1960). " Terminal guidance system for satellite rendezvous.." J. Aerosp. Sci. 0095-9820, 27 (9), 653-658, 674.
Hill, G. W. (1878). " Researches in the lunar theory.." Am. J. Math. 0002-9327, 1 (1), 5-26. 10.2307/2369430
Kalaba, R. E., and Udwadia, F. E. (1993). " Equations of motion for nonholonomic, constrained dynamical systems via Gauss's principle.." J. Appl. Mech. 0021-8936, 60 (3), 662-668. 10.1115/1.2900855
Karlgaard, C. D., and Lutze, F. H. (2003). " Second-order relative motion equations.." J. Guid. Control Dyn. 0731-5090, 26 (1), 41-49. 10.2514/2.5013
Kasdin, N. J., Gurfil, P., and Kolemen, E. (2005). " Canonical modelling of relative spacecraft motion via epicyclic orbital elements.." Celest. Mech. Dyn. Astron. 0923-2958, 92 (4), 337-370. 10.1007/s10569-004-6441-7 (Pubitemid 41650494)
Peters, J., Mistry, M., Udwadia, F. E., and Schaal, S. (2005). " A new methodology for robot controller design.." Proc., 5th ASME Int. Design Engineering Technical Conf. and Computers and Information in Engineering Conf. (DETC 2005-95166, Vol. 5, ASME, 1-10.
Prussing, J. E., and Conway, B. A. (1993). Orbital mechanics, Oxford University Press, New York.
Qingsong, M., Pengji, W., and Di, Y. (2004). " Low-thrust fuzzy formation keeping for multiple spacecraft flying.." Acta Astronaut. 0094-5765, 55 (11), 895-901.
Richardson, D. L., and Mitchell, J. W. (2003). " A third-order analytical solution for relative motion with a circular reference orbit.." J. Astronaut. Sci. 0021-9142, 51 (1), 1-12.
Sabol, C., Burns, R., and McLaughlin, C. A. (2001). " Satellite formation flying design and evolution.." J. Spacecr. Rockets 0022-4650, 38 (2), 270-278. 10.2514/2.3681
Schutte, A. D., and Dooley, B. A. (2005). " Constrained motion of tethered satellites.." J. Aerosp. Eng. 0893-1321, 18 (4), 242-250. 10.1061/(ASCE)0893-1321(2005)18:4(242) (Pubitemid 41441331)
Sparks, A. (2000). " Satellite formation keeping control in the presence of gravity perturbations.." Proc., American Control Conf., Vol. 2, Institute of Electrical and Electronics Engineering, 844-848.
Udwadia, F. E. (2000). " Nonideal constraints and Lagrangian dynamics.." J. Aerosp. Eng. 0893-1321, 13 (1), 17-22. 10.1061/(ASCE)0893- 1321(2000)13:1(17) (Pubitemid 30885721)
Udwadia, F. E. (2002). " Equations of motion for mechanical systems: A unified approach.." Int. J. Nonlinear Mech., 69, 951-958. 0020-7462
Udwadia, F. E. (2003). " A new perspective on the tracking control of nonlinear structural and mechanical systems.." Proc. R. Soc. London, Ser. A 0950-1207, 459, 1783-1800. 10.1098/rspa.2002.1062 (Pubitemid 38333361)
Udwadia, F. E. (2005). " Equations of motion for constrained multibody systems and their control.." J. Optim. Theory Appl. 0022-3239, 127 (3), 627-638.
Udwadia, F. E. (2008). " Optimal tracking control of nonlinear dynamical systems.." Proc. R. Soc. London, Ser. A 0950-1207, 464, 2341-2363. 10.1098/rspa.2008.0040
Udwadia, F. E., and Kalaba, R. E. (1992). " A new perspective on constrained motion.." Proc. R. Soc. London, Ser. A 0950-1207, 439, 407-410. 10.1098/rspa.1992.0158
Udwadia, F. E., and Kalaba, R. E. (1999). " A unified approach for the recursive determination of generalized inverses.." Comput. Math. Appl. 0898-1221, 37 (1), 125-130. 10.1016/S0898-1221(98)00247-8
Udwadia, F. E., and Kalaba, R. E. (2002). " What is the general form of the explicit equations of motion for constrained mechanical systems.." J. Appl. Mech. 0021-8936, 69, 335-339. 10.1115/1.1459071 (Pubitemid 35202544)
Udwadia, F. E., and Kalaba, R. E. (2008). Analytical dynamics: A new approach, Cambridge University Press, New York.
Underwood, C. I., Richardson, G., and Savignol, J. (2003). " In-orbit results from the SNAP-1 nano-satellite and its future potential.." Philos. Trans. R. Soc. London, Ser. A 0962-8428, 361, 199-203. 10.1098/rsta.2002.1123 (Pubitemid 37256166)
Vaddi, S. S., Vadali, S. R., and Alfriend, K. T. (2003). " Formation flying: Accommodating nonlinearity and eccentricity perturbations.." J. Guid. Control Dyn. 0731-5090, 26 (2), 214-223. 10.2514/2.5054
Yan, Q., Kapila, V., and Sparks, A. G. (2000). " Pulse-based periodic control for spacecraft formation flying.." Proc., American Control Conf., Vol 1, Institute of Electrical and Electronics Engineering, 374-378.