Analysis and Performance Evaluation of the ZEM/ZEV Guidance and its Sliding Robustification for Autonomous Rendezvous in Relative Motion

Abstract

Devising closed-loop guidance algorithms for autonomous relative motion is an important problem within the field of orbital dynamics. In this paper, we study the guided relative motion of two spacecraft for which one of them is executing an autonomous rendezvous via the ZEM/ZEV feedback guidance and its robustified Optimal Sliding Guidance (OSG) counterpart. Starting from the classical Clohessy-Wiltshire (CW) model, we systematically analyze the ability of the ZEM/ZEV feedback guidance to generate closed loop trajectories that drive the deputy spacecraft to the chief satellite and evaluate its performance in terms of target accuracy and propellant consumption. It is shown that the guidance gains and the time of flight predicted by the theoretical solution generates a class of feedback trajectories that are accurate but suboptimal with respect to the open-loop fuel-optimal solution. Indeed, a parametric study shows that a different set of gains may generate relative guided trajectories that yields fuel consumption closer to the ideal optimal. The guidance algorithms are also demonstrated to be accurate in guiding the relative motion of the deputy toward a chief spacecraft in highly elliptical orbit where the Linearized Equations of Relative Motions (LERM) are employed to compute the Zero-Effort-Miss (ZEM) and Zero-Effort-Velocity (ZEV) necessary to compute the acceleration command as prescribed by the theory.