Controllability Analysis of Propellant-Free Satellite Formation Flight

Abstract

This paper presents a comprehensive analysis of the controllability for the relative dynamics of satellites using space environment forces. First, the constraints of the space environment forces are illustrated for circular orbits, and the integration of space environment forces for achieving full controllability is considered. Two approaches are used to estimate the controllability of various configurations of space environment forces. The first approach relies on controllability theory for linear continuous and discrete systems, including a derivation of a new linear formulation for solar radiation pressure with lower constraints. The second approach exploits extensive numerical simulations for controllability analyses of nonlinear dynamics models. The linear quadratic regulator is designed for different dynamics models of the space environment forces and implemented numerically for nonlinear dynamics using an anti-windup scheme with bounded control inputs. The numerical simulations demonstrate that the Lorentz forces and the differential atmospheric drag are more effective control forces in the low Earth orbits than the solar radiation pressure.