Linear Covariance Techniques for Orbital Rendezvous Analysis and Autonomous Onboard Mission Planning

TLDR

The tools, techniques, and mathematical formulations presented for orbital rendezvous are applicable to a wide range of space missions and GN&C problems, including atmospheric entry, low‑thrust electric propulsion, translunar injection, lunar orbit insertion, lunar ascent/descent, and formation‑flying missions. The study develops a novel trajectory control and navigation analysis software approach. The software rapidly computes trajectory dispersions, navigation errors, and required Δv at key points by linearizing nonlinear dynamics and applying linear covariance analysis to a closed‑loop GN&C system, enabling mission design, planning, and autonomous flight optimization. The approach is demonstrated with two simple examples.

Abstract

A novel trajectory control and navigation analysis software approach is developed. The program quickly determines trajectory dispersions, navigation errors, and required maneuver Δv at selected key points along a nominal trajectory. It can be used for mission design and planning activities or in autonomous flight systems to help determine the best trajectories, the best maneuver locations, and the best navigation update times to ensure mission success. These features are illustrated with two simple examples. The software works by applying linear covariance analysis techniques to a closed-loop guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight software models of a closed-loop six-degree-of-freedom Monte Carlo simulation are linearized. Then, linear covariance techniques are used to produce a program that will accurately predict 3-σ trajectory dispersions, navigation errors, and Av variations. Although the application presented is orbital rendezvous, the tools, techniques, and mathematical formulations are applicable to a variety of other space missions and GN&C problems including atmospheric entry, low-thrust electric propulsion missions, translunar injection and lunar orbit insertion, lunar ascent/descent, and formation-flying missions.