State-transition-matrix optimization for reconfiguration manoeuvres of formation-flying satellites

Abstract

The on-orbit reconfiguration of a pair of formation-flying satellites in low Earth orbit is studied in the presence of J₂–J₆ gravitational perturbations. A methodology for determining a robust and accurate impulsive thrusting scheme is developed with the aim of minimizing reconfiguration overshoot errors and fuel expenditure (Δ V). The method uses a state transition matrix based on the Hill–Clohessy–Wiltshire linear equations of relative motion and the analytical solution to the state-space model to solve for a pair of impulsive thrusts. The manoeuvre is then propagated through a fully nonlinear orbital simulator with the thrusts implemented non-impulsively. A Sequential Quadratic Programming optimizer adjusts the inputs to the linear state transition matrix to produce impulses that, when applied in the high-fidelity orbital propagator, mitigates the Δ V of the manoeuvre while maintaining acceptable overshoot errors.

Keywords:

• formation-flying satellites
• overshoot error
• reconfiguration optimization
• state transition matrix

Acknowledgements

The authors would like to gratefully acknowledge the ongoing contributions of the CanX student team: Norman Deschamps, Jonathan Gryzmisch, Liam O'Brian, Nathan Orr, Adam Philip, Chris Short and Maria Short. In addition, the authors wish to thank the SFL staff for their support: Alex Beattie, Stuart Eagleson, Cordell Grant, Daniel Kekez, Stephen Mauthe, Freddy Pranajaya, Tarun Tuli, and Rob Zee.

Notes

A similar equation can be written for the velocity overshoot error, . However, the velocity errors associated with the reconfiguration manoeuvres in this study are comparatively low and as such E _v is not considered a primary performance metric. The velocity errors are still considered as optimization constraints in Section 3.