A Cartesian relative motion approach to optimal formation flight using Lorentz forces and impulsive thrusting

Hybrid combination of Lorentz forces and impulsive thrusts, provided by modulating spacecraft's electrostatic charge and propellant usage, respectively, is proposed for formation flight applications. A hybrid linear quadratic regulator, previously proposed in another work using a differential orbital elements-based model, is reconsidered for a Cartesian coordinates-based description of the spacecraft's relative states. In addition, the effects of adopting circular versus elliptic reference solutions on the performance of the controller are studied. Numerical simulation results are provided to demonstrate the functionality of the proposed controller in the presence of J2 perturbations, and to illustrate the improvements gained by assuming an elliptic reference and incorporating auxiliary impulsive thrusts.