Suboptimal Nonlinear Model Predictive Control Strategies for Tracking Near Rectilinear Halo Orbits

Near Rectilinear Halo Orbits (NRHOs), a subclass of halo orbits around the L1 and L2 Lagrange points, are promising candidates for future lunar gateways in cis-lunar space and as staging orbits for lunar missions. Closed-loop control is beneficial to compensate orbital perturbations and potential instabilities while maintaining spacecraft on NRHOs and performing relative motion maneuvers. This paper investigates the use of nonlinear model predictive control (NMPC) coupled with low-thrust actuators for station-keeping on NRHOs. It is demonstrated through numerical simulations that NMPC is able to stabilize a spacecraft to a reference orbit and handle control constraints. Further, it is shown that the computational burden of NMPC can be managed using specialized optimization routines and suboptimal approaches without jeopardizing closed-loop performance.

[1]  Ilya Kolmanovsky,et al.  Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction , 2020, Autom..

[2]  John V. Breakwell,et al.  Station-keeping for a translunar communication station , 1974 .

[3]  G. Martin,et al.  Nonlinear model predictive control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[4]  R. Broucke,et al.  Stability of periodic orbits in the elliptic restricted three-body problem. , 1969 .

[5]  Jaume Llibre,et al.  On the optimal station keeping control of halo orbits , 1986 .

[6]  J. McMahon,et al.  Landing Trajectories to Moons from the Unstable Invariant Manifolds of Periodic Libration Point Orbits , 2020 .

[7]  Ilya Kolmanovsky,et al.  Design Environment for Nonlinear Model Predictive Control , 2016 .

[8]  Amanda F. Haapala,et al.  Earth-Moon libration point orbit stationkeeping: Theory, modeling, and operations $ , 2014 .

[9]  Ilya Kolmanovsky,et al.  FBstab: A proximally stabilized semismooth algorithm for convex quadratic programming , 2019, Autom..

[10]  Gerard Gómez,et al.  Station-keeping of real Earth-Moon libration point orbits using discrete-time sliding mode control , 2014, Commun. Nonlinear Sci. Numer. Simul..

[11]  D. Folta,et al.  ARTEMIS: The First Mission to the Lunar Libration Orbits , 2009 .

[12]  Diane C. Davis,et al.  STATIONKEEPING ANALYSIS FOR SPACECRAFT IN LUNAR NEAR RECTILINEAR HALO ORBITS , 2017 .

[13]  Diane C. Davis,et al.  Orbit Maintenance and Navigation of Human Spacecraft at Cislunar Near Rectilinear Halo Orbits , 2017 .

[14]  Diane C. Davis,et al.  IAA-AAS-DyCoSS 3125 NEAR RECTILINEAR HALO ORBITS AND THEIR APPLICATION IN CIS-LUNAR SPACE , 2017 .

[15]  Avishai Weiss,et al.  Control Strategy for Long-Term Station-Keeping on Near-Rectilinear Halo Orbits , 2020 .

[16]  Brian Dunbar.  What is Artemis , 2019 .

[17]  James E. Polk,et al.  Overview of the Development and Mission Application of the Advanced Electric Propulsion System (AEPS) , 2017 .

[18]  John V. Breakwell,et al.  Almost rectilinear halo orbits , 1982 .

[19]  Helen Durand,et al.  A tutorial review of economic model predictive control methods , 2014 .

[20]  Roland Martinez,et al.  Options for staging orbits in cislunar space , 2016, 2016 IEEE Aerospace Conference.