This paper presents a non-linear adaptive controller for the multiple spacecraft formation flying problem. The formulation allows for gravitational field models of arbitrary order, and a broad class of linearly parameterized external disturbance force models. This paper builds upon previous results using feedback of the filtered error. Making use of Barbalat's lemma, a broad class of controllers feeding back the filtered error is obtained, which encompasses the linear feedback that is typically used in the literature. In particular, conditions are presented under which the linear feedback is asymptotically stable under actuator saturation. The resulting controller performance is demonstrated with a numerical simulation for a relative orbit under J2 perturbations.
D'AmicoS.ArdaensJ.-S.De FlorioS.MontenbruckO.‘Autonomous formation flying - TanDEM-X, PRISMA and beyond.’ 5th International Workshop onSatellite constellations and formation flying, Evpatoria, Crimea, 2-4 July, 2008
2.
YoshiharaK.van MierloM.NgA.KumarShankar B.de RuiterA.KomatsuY.HoriguchiH.HashimotoH. ‘JC2Sat-FF: an international collaboration nano-sat project - overview of the system analyses and design.’ The 4S Symposium, Rhodes, Greece, 26-30 May, 2008
3.
EyerJ.DamarenC. J.‘The stability analysis of a discrete-time control algorithm for the Canadian advanced nanospace eXperiment - 4 & 5 formation flying nanosatellites.’Proc. IMechE, Part G: J. Aerospace Engineering223 (G4) (2009): 441-452 DOI: 10.1243/09544100JAER0470
4.
VassarR. H.SherwoodR. B.‘Formationkeeping for a pair of satellites in a circular orbit.’J. Guidance, Control and Dynamics8 (2) (1985): 235–242
5.
VadaliS. R.VaddiS. S.AlfriendK. T.‘An intelligent control concept for formation flying satellites.’Int. J. Robust and Nonlinear Control12 (2-3) (2002): 97–115
6.
CarpenterJ. R.‘Decentralized control of satellite formations.’Int. J. Robust and Nonlinear Control12 (2-3) (2002): 141–161
7.
KangW.SparksA.BandaS.‘Coordinated control of multisatellite systems.’J. Guidance, Control and Dynamics24 (2) (2001): 360–368
8.
WangP. K. C.HadaeghF. Y.LauK.‘Synchronized formation rotaiton and attitude control of multiple free-flying spacecraft.’J. Guidance, Control and Dynamics22 (1) (1999): 28–35
9.
LiuH. T.ShanJ.SunD.‘Adaptive synchronization control of multiple spacecraft formation flying.’ASME J. Dynamic Systems, Measmt Control129 (3) (2007): 337–342
10.
de QueirozM. S.KapilaV.YanQ.‘Adaptive nonlinear control of spacecraft formation flying.’J. Guidance, Control and Dynamics23 (3) (2000): 385–390
11.
ShanJ.LinH.‘Non-linear filter-based adaptive output feedback control for spacecraft formation flying.’Proc. IMechE, Part I: J. Systems and Control Engineering223 (I5) (2009): 683-691 DOI: 10.1243/09596518JSCE752
12.
GurfilP.IshanM.KasdinN. J.‘Adaptive neural control of deep-space formation flying.’AIAA J. Guidance, Control and Dynamics26 (3) (2003): 491–501
13.
SlotineJ.-J. E.LiW.‘Adaptive manipulator control: A case study.’IEEE Trans. Autom. Control33 (11) (1988): 995–1003
14.
SlotineJ.-J. E.Di BenedettoM. D.‘Hamiltonian adaptive control of spacecraft.’IEEE Trans. Autom. Control35 (7) (1990): 848–852
15.
FossenT. I.‘Comments on ‘Hamiltonian adaptive control of spacecraft’.’IEEE Trans. Autom. Control38 (4) (1993): 671–672
16.
OrtegaR.SpongM. W.‘Adaptive motion control of rigid robots: A tutorial.’Automatica25 (6) (1989): 877–888
17.
DawsonD. M.HuJ.LauK.Nonlinear control of electric machinery (Marcel Dekker, New York1998)
18.
KhalilH. K.Nonlinear systems, second edition (Prentice Hall, Upper Saddle River NJ1996)
