Comparative Analysis of Satellite Relative Dynamics and Fuel-Optimal Trajectory Planning of Satellites Using Minimum Distance Assignment

Abstract

In this paper, we present a fuel-optimal trajectory optimization (TO) problem for satellite formation flying (SFF) in near-circular low-earth orbits (LEO) under perturbations and modeling uncertainties. Non-spherical gravity (J2) of the earth and air drag are two dominant perturbing forces in LEO which cause significant orbital measurement errors and eventually sub-optimal actuation and trajectory prediction by the TO algorithm. By quantifying uncertainties and modeling errors associated with various relative dynamical models of satellites, we identify a model that is suitable for the TO problem. However, one of the key challenges to design of a computationally efficient TO algorithm for satellite swarms pertains to the assignment of each satellite to a location in a given final formation. To address this, we first decouple the final configuration assignment problem from the TO, derive minimum distance assignment between initial and final formation pairs, and then by using this minimum distance assignment in the TO algorithm, we efficiently compute near-optimal trajectories and actuation under given mission specifications. Our proposed formulation is scalable to large swarm sizes and it allows the computation load to be distributed over the satellite swarm at the expense of small loss in fuel-optimality.