Analytical framework for space debris collision avoidance maneuver design

TL;DR

This paper presents an analytical framework for designing space debris collision avoidance maneuvers, optimizing for maximum deviation and minimum collision probability using eigenproblem solutions and covariance propagation.

Contribution

It introduces an analytical formulation that simplifies the optimization of collision avoidance maneuvers and compares different strategies across various conjunction geometries.

Findings

Maximum deviation and collision probability are constrained by uncertainties over time.

Eigenproblem approach effectively finds optimal maneuvers.

Lead time impacts collision probability reduction due to growing uncertainties.

Abstract

An analytical formulation for collision avoidance maneuvers involving a spacecraft and a space debris is presented, including solutions for the maximum deviation and minimum collision probability cases. Gauss' planetary equations and relative motion equations are used to map maneuvers at a given time to displacements at the predicted close approach. The model is then extended to map changes in state between two times, allowing one to propagate covariance matrices. The analytical formulation reduces the optimization problem to an eigenproblem, both for maximum deviation and minimum collision probability. Two maximum deviation cases, total deviation and impact parameter, are compared for a large set of spacecraft-debris conjunction geometries derived from European Space Agency's Meteoroid and Space Debris Terrestrial Environment Reference (MASTER-2009) model. Moreover, the maximum impact parameter and minimum collision probability maneuvers are compared assuming covariances known at the maneuver time, to evaluate the net effect of lead time in collision probability. In all cases, solutions are analyzed in the b-plane to leverage its natural separation of phasing and geometry change effects. Both uncertainties and maximum deviation grow along the time axis for long lead times, limiting the reduction in collision probability.