Optimal inspector satellite guidance to quasi-hover via relative teardrop trajectories

摘要

Metaheuristic methods and direct methods are used to find minimum time and minimum fuel solutions to inject an inspector satellite into and maintain a relative teardrop trajectory with respect to a resident space object in geosynchronous orbit. The optimal control problem is transcribed to a parameter optimization problem and solved with a particle swarm optimization algorithm, which is then fed as an initial guess for two different nonlinear programming problem solvers, one of which is the Radau pseudospectral method. Two angles are used to represent the direction of the finite thrust for the two burns in three dimensions for both the minimum time and minimum fuel formulations, and an analytic expression for the final six Hill-Clohessy-Wiltshire states after the two finite burns is employed to find the optimal burn directions and burn times. Thus, multiple optimization methods are used to find both minimum time and minimum fuel solutions, providing mission planners with multiple tools to enable optimal quasi-hovering in a prescribed three-dimensional teardrop in order to inspect and characterize a resident space object.