Abstract
Getting inspiration from the constraint forces in the classical mechanics, we presented the nonlinear control method of multiple spacecraft formation flying to accurately keep the desired formation arrays. Considering nonlinearity and perturbation, we changed the question of the formation array control to the Lagrange equations with the holonomic constraints and the differential algebraic equations (DAE), and developed the nonlinear control for design of the follower spacecraft tracking control laws by solving the DAE. Because of using the idea of the constraint forces, this approach can adequately utilize the characteristic of the dynamic equations, i.e., the space natural forces, and accurately keep the arbitrary formation array. Simulation results of the circular formation keeping with the linear and nonlinear dynamical equations were included to illuminate the control performance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Zhang Y L, Zeng G Q, Wang Z K, et al. Theory and Application of the Distributed Satellites (in Chinese). Beijing: Science Press, 2008
Bauer F H, Hartman K, How J P, et al. Enabling spacecraft formation flying through spaceborne GPS and enhanced autonomy technologies. In: ION-GPS Conference. Nashville, TN: ION, 1999. 1493–1508
Sparks A. Satellite formation keeping control in the presence of gravity perturbations. In: Proceedings of the American Control Conference. Chicago: ACC, 2000. 844–848
Vaddi S S, Vadali S R, Alfriend K T. Formation flying: Accommodating nonlinearity and eccentricity perturbations. J Guid Contr Dynam, 2003, 26(2): 214–223
Sengupta P, Vadali S R, Alfriend K T. Modeling and control of satellite formations in high eccentricity orbits. J Astronaut Sci, 2004, 52(1–2): 149–168
Queiroz M S, Kapila V, Yan Q. Adaptive nonlinear control of satellite formation flying. In: AIAA Guidance, Navigation, and Control Conference. Portland: AIAA, 1999. 1596–1604
Queiroz M S, Yan Q, Yang G, et al. Global output feedback tracking control of spacecraft formation flying with parametric uncertainty. In: Proceedings of the IEEE Conference on Decision and Control. Phoenic: IEEE, 1999. 584–589
Massey T E. Satellite Formation Control Using Continuous Sliding Modes. Dissertation of Masteral Degree. Huntsville: The University of Alabama in Huntsville, 2003
Scaub H, Vadali S R, Junkins J L, et al. Spacecraft formation flying control using mean orbit elements. J Astronaut Sci, 2000, 48(1): 60–87
Wang R X. The dynamic equation of relative motion (in Chinese). Phys Eng, 2002, 12(5): 18–20
Pan Z K, Zhao W J, Hong J Z, et al. On numerical algorithms for differential/algebraic equations of motion of multibody systems (in Chinese). Adv Mech, 1996, 26(1): 28–40
Sabol C, Burns R, McLaughlin C A. Satellite formation flying design and evolution. J Spacecraft Rockets, 2001, 38(2): 270–278
Xing J J, Tang G J, Xi X N, et al. Satellite formation design and optimal station keeping considering nonlinearity and eccentricity. AIAA J Guid Contr Dynam, 2007, 30(5): 1523–1528
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by China Postdoctoral Science Foundation (Grant No. 20080440217)
Rights and permissions
About this article
Cite this article
Xing, J., Lei, Y., Cheng, W. et al. Nonlinear control of multiple spacecraft formation flying using the constraint forces in Lagrangian systems. Sci. China Ser. E-Technol. Sci. 52, 2930–2936 (2009). https://doi.org/10.1007/s11431-009-0261-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-009-0261-7