Comparison between analytical and optimal control techniques in the differential drag based rendez-vous

The focus of this study is on differential drag for propellantless satellite rendez-vous. This technique is particularly attractive for low-Earth-orbit small satellites for which stringent weight constraints apply. Most existing contributions are based on bang-bang strategies, which may be difficult to implement in practice. This is why the present paper proposes a novel strategy integrating pseudospectral optimal control for maneuver planning and model predictive control for dealing with uncertainties and unmodeled dynamics. One important advantage of this methodology is that it can naturally account for attitude dynamics and constraints, which, in turn, paves the way for the practical realization of differential drag-based rendez-vous. A realistic scenario involving two nanosatellites of the QB50 constellation is considered to illustrate and validate the proposed developments. In addition, a comparison of this numerical technique with an existing analytic solution is carried out, and their respective pros and cons are discussed.

[1]  Andrew W. Lewin.  Low-Cost Operation of the ORBCOMM Satellite Constellation , 1998 .

[2]  R. Bevilacqua,et al.  Multiple Spacecraft Assembly Maneuvers by Differential Drag and Low Thrust Engines , 2010 .

[3]  R. Sedwick,et al.  High-Fidelity Linearized J Model for Satellite Formation Flight , 2002 .

[4]  Gaëtan Kerschen,et al.  Orbital rendez-vous using differential drag in the QB50 constellation , 2012 .

[5]  Lappas,et al.  Spacecraft Formation Flying using Lorentz Forces , 2007 .

[6]  William W. Hager,et al.  A unified framework for the numerical solution of optimal control problems using pseudospectral methods , 2010, Autom..

[7]  Riccardo Bevilacqua,et al.  Rendezvous Maneuvers of Multiple Spacecraft Using Differential Drag Under J2 Perturbation , 2008 .

[8]  Balaji Shankar Kumar,et al.  A Bang -Bang Control Approach to Maneuver Spacecraft in a Formation with Differential Drag , 2008 .

[9]  Riccardo Bevilacqua,et al.  Differential drag spacecraft rendezvous using an adaptive Lyapunov control strategy , 2013 .

[10]  Carolina Lee Leonard,et al.  Formationkeeping of spacecraft via differential drag , 1991 .

[11]  K. Alfriend,et al.  State Transition Matrix of Relative Motion for the Perturbed Noncircular Reference Orbit , 2003 .

[12]  Trevor Williams,et al.  Uses of solar radiation pressure for satellite formation flight , 2002 .

[13]  Balaji Shankar Kumar,et al.  Time-Optimal Low-Thrust Formation Maneuvering Using a Hybrid Linear/Nonlinear Controller , 2009 .

[14]  Alfred Ng,et al.  Implementation and performance of formation flying using differential drag , 2012 .