Spherically Constrained Relative Motion Trajectories in Low Earth Orbit

Abstract

This paper considers a satellite inspection mission where the deputy satellite is required to remain a fixed distance away from the chief satellite. This constraint on the deputy’s state is modeled as the surface of a sphere. Finding minimum energy solutions to travel from one point to another point on the sphere requires solving a nonconvex optimal control problem. Various novel suboptimal algorithms are proposed that can guarantee a feasible solution. These algorithms are benchmarked by optimal values obtained via a global continuation method, and their computational performance is analyzed in a statistical setting.

Lyapunov Functions and Regions of Attraction for Spherically Constrained Relative Orbital Motion

“…The spherically constrained relative motion problem has been studied recently in the context of exact, convex control relaxations [10], computation of trajectories using splines [11], and nonlinear systems analysis identifying equilibria, periodicity, and chaotic behavior [12]. In the broader context of general spherically constrained motion, there is related work on balltype absorbers [13,14].…”