This investigation deals with the problem of spacecraft relative motion control, which is typically associated with the spacecraft rendezvous and proximity maneuvers. Relative position and linear velocity are considered. A distinguishing attribute of the presented approach is consideration of definitely larger relative distance between the satellites than it is commonly addressed in the literature. The presented control method is applicable in the case where the chief satellite moves in a known, highly elliptical orbit. A quasi-optimal control is found by a model predictive control algorithm, where the nonlinear optimization problem is reduced to quadratic optimization by preliminary estimation of the future control trajectory. Significance of the method has been verified using a computer simulation.
Di CairanoDSParkHKolmanovskyIV. Model predictive control approach for guidance of spacecraft rendezvous and proximity maneuvering. Int J Robust Nonlinear Control2012; 22: 1398–1427.
2.
YangXBYuJYGaoHJ. An impulse control approach to spacecraft autonomous rendezvous based on genetic algorithms. Neurocomputing2012; 77: 189–196.
3.
GaoHJYangXBShiP. Multi-objective robust control of spacecraft rendezvous. IEEE Trans Control Syst Technol2009; 17: 794–802.
HartleyENTroddenPARichardsAG, et al.Maciejowski. Model predictive control system design and implementation for spacecraft rendezvous. Control Eng Pract2012; 20: 695–713.
6.
KimS-GCrassidisJLChengY, et al.Kalman filtering for relative spacecraft attitude and position estimation. J Guid Control Dyn2007; 30: 133–143.
7.
Weiss A, Kolmanovsky I, Baldwin M, et al. Model predictive control of three dimensional spacecraft relative motion. In: Proceedings of the American control conference 2012, 2012, pp.173–178. USA: IEEE.
8.
LuPLiuX. Autonomous trajectory planning for rendezvous and proximity operations by conic optimization. J Guid Control Dyn2013; 36: 375–389.
9.
HillGW. Researches in the lunar theory. Am J Math1878; 1: 5–26.
10.
ClohessyWHWiltshirePS. Terminal guidance system for satellite rendezvous. J Aerosp Sci1960; 27: 653–658.
11.
KechichianJA. Techniques of accurate analytic terminal rendezvous in near-circular orbit. Acta Astronaut1992; 26: 377–394.
12.
TschaunerJHempelP. Rendezvous with an orbiting target in an elliptical orbit (in German). Acta Astronaut1965; 11: 104–109.
13.
YamanakaKAnkersenF. New state transition matrix for relative motion on an arbitrary elliptical orbit. J Guid Control Dyn2002; 25: 60–66.
14.
AlfriendKTYanH. Evaluation and comparison of relative motion theories. J Guid Control Dyn2005; 28: 254–261.
15.
OkashaMNewmanB. Modeling, dynamics and control of spacecraft relative motion in a perturbed Keplerian orbit. Int J Aeronaut Space Sci2015; 16: 77–88.
16.
LuoYZhangJTangG. Survey of orbital dynamics and control of space rendezvous. Chin J Aeronaut2014; 27: 1–11.
17.
QinSJBadgwellTA. A survey of industrial model predictive control technology. Control Eng Pract2003; 11: 733–764.
18.
WangL. Model predictive control system design and implementation using MATLAB®, London: Advances in Industrial Control. Springer, 2009.
19.
BordonsCCamachoEF. Model predictive control. Advanced Textbooks in Control and Signal Processing, London: Springer, 2004.
20.
MayneDQRawlingsJBRaoCV, et al.Constrained model predictive control: stability and optimality. Automatica2000; 36: 789–814.
21.
XiY-GLiD-WLinS. Model predictive control – status and challenges. Acta Autom Sin2013; 39: 222–236.
22.
Felisiak PA. Control of spacecraft for rendezvous maneuver in an elliptical orbit. PhD Thesis, Wrocław University of Technology, Wrocław, Poland, 2016.
23.
SchaubHJunkinsJL. Analytical mechanics of space systems, Reston, VA: AIAA, 2003.
24.
Sherrill RE. Dynamics and control of satellite relative motion in elliptic orbits using Lyapunov–Floquet theory. PhD Thesis, Auburn University, Auburn, Alabama, US, May 2013.
25.
MeshcherskyIV. Dynamics of a point of variable mass (in Russian), St. Petersburg, Russia: Printing House of the Imperial Academy of Sciences, 1897.
