Optimal closed-loop robust rendezvous guidance with the observability constraint of angles-only navigation

Abstract

This paper proposes an optimal closed-loop rendezvous guidance algorithm with the observability constraint of angles-only navigation using robust convex optimization. First, the relative dynamics equation is established based on the well-known Clohessy–Wiltshire (CW) equation, and the measurement equation which includes a set of azimuth and elevation is also established. Then, a geometrical observability analysis is introduced to analyze the observability of angles-only navigation. And then, taking the geometrical observability of angles-only navigation as the variable, taking the total fuel cost as the optimization objective, and considering other various constraints such as relative motion and thrust magnitude constraints. And then, the mathematical expression of the closed-loop rendezvous guidance with the observability constraint of angles-only navigation is established. A robust convex optimization method is introduced to solve the problem proposed in real time online. Finally, the performances of the proposed algorithm are analyzed by means of numerical simulation, which verifies the effectiveness of the algorithm proposed in this paper.