This paper discusses coupled orbital and attitude control in spacecraft rendezvous and soft docking. The target spacecraft orbit can be either circular or elliptic. The high-fidelity model for this problem is intrinsically a nonlinear system but can be viewed as a linear time-varying system. Therefore, a model predictive control-based design is proposed to deal with the time-varying feature of the problem. A robust pole assignment method is used in the model predictive control-based design because of the following merits and/or considerations: (a) no oscillation crossing the horizontal line for the relative position and relative attitude (between the target and the chaser spacecraft) to achieve soft docking by placing all closed-loop poles in the negative real axis of the complex plan, which will avoid collision between the target and the chaser in the docking stage, (b) fast online computation, (c) measurement and control error tolerance, and (d) disturbance rejection. This paper will discuss these considerations and merits and use some design examples to demonstrate that the desired performance is indeed achieved.
LuoYZhangJTangG. Survey of orbital dynamics and control of space rendezvous. Chin J Aeronaut2014; 27: 1–11.
2.
HillGW. Researches in lunar theory. Am J Math1878; 1: 5–26.
3.
ClohessyWHWiltshireRS. Terminal guidance system for satellite rendezvous. J Aerosp Sci1960; 27: 653–658.
4.
WangPKCHadaeghFY. Coordination and control of multiple microspacecraft moving in formation. J Astronaut Sci1996; 44: 315355–315355.
5.
Pan H. and Kapila V. Adaptive nonlinear control for spacecraft formation flying with coupled translational and attitude dynamics. In: Proceedings of the conference on decision and control, Orlando, FL, 4–7 December 2001.
6.
KristiansenRGrotliEINicklassoPJet al.A model of relative translation and rotation in leader-follower spacecraft formations. Model Identif Control2007; 28: 3–13.
7.
ZagarisCRomanoM. Reachability analysis of planar spacecraft docking with rotating body in close proximity. J Guid Control Dyn2018; 41: 1416–1422.
8.
SinglaPSubbaraoKJunkinsJL. Adaptive output feedback control for spacecraft rendezvous and docking under measurement uncertainty. J Guid Control Dyn2006; 29: 892–902.
9.
GaoHYangXShiP. Multi-objective robust control of spacecraft rendezvous. IEEE Trans Control Syst Technol2009; 17: 794–802.
10.
ZhouBLinZDuanG. Lyapunov differential equation approach to elliptical orbital rendezvous with constrained controls. J Guid Control Dyn2011; 34: 892–902.
11.
ZhouBWangQLinZet al.Gain scheduled control of linear systems subject to actuator saturation with application to spacecraft rendezvous. IEEE Trans Control Syst Technol2014; 22: 2031–2038.
12.
SunLHuoW. 6-DOF integrated adaptive backstepping control for spacecraft proximity operations. IEEE Trans Aerosp Electron Syst2015; 51: 2433–2443.
13.
ZhangFDuanG. Integrated relative position and attitude control of spacecraft in proximity operation missions. Int J Autom Comput2012; 9: 342–351.
14.
KristiansenaRNicklassonaPJGravdahlbJT. Spacecraft coordination control in 6DOF: integrator backstepping vs passivity-based control. Automatica2008; 44: 2896–2901.
15.
SunHLiaSFeiS. A composite control scheme for 6DOF spacecraft formation control. Acta Astronautica2011; 69: 595–611.
16.
Xu R, Ji H, Li K, et al. Relative position and attitude coupled control with finite-time convergence for spacecraft rendezvous and docking. In: 2015 IEEE 54th annual conference on decision and control (CDC), Osaka, Japan, 15–18 December 2015.
17.
MassariMZamaroM. Application of SDRE technique to orbital and attitude control of spacecraft formation flying. Acta Astronautica2014; 94: 409–420.
18.
SunLHuoWJiaoZ. Adaptive backstepping control of spacecraft rendezvous and proximity operations with input saturation and full-state constraint. IEEE Trans Ind Electron2017; 64: 480–492.
19.
SunLHuoWJiaoZ. Robust nonlinear adaptive relative pose control for cooperative spacecraft during rendezvous and proximity operations. IEEE Trans Control Syst Technol2016; 25: 1840–1847.
20.
SunLZhengZ. Adaptive relative pose control of spacecraft with model couplings and uncertainties. Acta Astronautica2018; 143: 29–36.
21.
Malladi BP, Sanfelice RG, Butcher E, et al. Robust hybrid supervisory control for rendezvous and docking of a spacecraft. In: 2016 IEEE 55th conference on decision and control, Las Vegas, NV, 12–14 December 2016.
22.
LiQYuanJZhangBet al.Model predictive control for autonomous rendezvous and docking with a tumbling target. Aerosp Sci Technol2017; 69: 700–711.
23.
Roscoea CWT, Westphal JJ and Mosleh E. Overview and GNC design of the CubeSat Proximity Operations Demonstration (CPOD) mission. Acta Astronautica 2018; 153: 410–421. DOI:10.1016/j.actaastro.2018.03.033.
24.
YangY. Quaternion based model for momentum biased nadir pointing spacecraft. Aerosp Sci Technol2010; 14: 199–202.
25.
YangY. Quaternion based LQR spacecraft control design is a robust pole assignment design. J Aerosp Eng2014; 27: 168–176.
26.
RughWJShammaJS. Research on gain scheduling. Automatica2000; 36: 1401–1425.
27.
AstromKJWittenmarkB. Computer-controlled systems: theory and design, Mineola, NY: Dover Publications, Inc, 2013.
28.
YangY. Singularity-free model predictive spacecraft attitude regulation using a variable-speed control moment gyroscope model. IEEE Trans Aerosp Electron Syst. 2016; 54: 1511–1518. DOI: 10.1109/TAES.2018.2796878.
29.
DorfRCHishopRH. Modern control systems, 11th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2008.
30.
Pandey A, Schmid R, Nguyen T, et al. Tits, performance survey of robust pole placement methods. In: The 53rd IEEE conference on decision and control, Los Angeles, CA, 15–17 December 2014.
31.
TitsALYangY. Globally convergent algorithms for robust pole assignment by state feedback. IEEE Trans Automat Contr1996; 41: 1432–1452.
32.
OpromollaRFasanoGRufinoGet al.A review of cooperative and uncooperative spacecraft pose determination techniques for close-proximity operations. Progr Aerosp Sci2017; 93: 53–72.
33.
YangY. Spacecraft attitude determination and control: quaternion based method. Annu Rev Control2012; 36: 198–219.
34.
SidiMJ. Spacecraft dynamics and control: a practical engineering approach, Cambridge, UK: Cambridge University Press, 1997.
35.
WieB. Space vehicle dynamics and control, Reston, VA: AIAA, 1998.
36.
Xu Y, Tatsch A and Fitz-Coy NG. Chattering free sliding mode control for a 6 DOF formation flying mission. In: Proceedings of AIAA guidance, navigation, and control conference and exhibit, San Francisco, CA, 15–18 August 2005. Reston, VA: AIAA, pp.2005–6464.
37.
CurtiFRomanoMBevilacquaR. Lyapunov-based thrusters selection for spacecraft control: analysis and experimentation. J Guid Control Dyn2010; 33: 198–219.
38.
YangY. Attitude control in spacecraft orbit-raising using a reduced quaternion model. Adv Aircr Spacecr Sci2014; 1: 427–441.
39.
RughWJ. Linear system theory, Englewood Cliffs, NJ: Prentice-Hall, Inc, 1993, pp. 117–119.
40.
Yang Y and Tits AL. On robust pole assignment by state feedback. In: Proceedings of the American control conference, San Francisco, CA, 2–4 June 1993. pp.2765–2766. Piscataway, NJ: IEEE.
41.
WertzJR. Spacecraft attitude determination and control, Dordrecht: Kluwer, 1978.
