Collision Avoidance Maneuvers Optimization in the Presence of Multiple Encounters

TL;DR

This paper presents a novel optimization framework for fuel-efficient collision avoidance maneuvers in multi-encounter scenarios, combining advanced mathematical techniques to accurately propagate uncertainties and generate effective maneuver plans.

Contribution

It introduces a combined approach using sequential convex programming, second-order cone programming, and differential algebra for multi-encounter CAM optimization with uncertainty propagation.

Findings

Effective fuel reduction in collision avoidance maneuvers.

Accurate uncertainty propagation using Gaussian mixture models.

Successful case studies demonstrating operational constraints adherence.

Abstract

The optimization of fuel-optimal low-thrust collision avoidance maneuvers (CAMs) in scenarios involving multiple encounters between spacecraft is addressed. The optimization's objective is the minimization of the total fuel consumption while respecting constraints on the total probability of collision. The solution methodology combines sequential convex programming, second-order cone programming, and differential algebra to approximate the non-convex optimal control problem progressively. A Gaussian mixture model method is used to propagate the initial covariance matrix of the secondary spacecraft, allowing us to split it into multiple mixands that can be treated as different objects. This leads to an accurate propagation of the uncertainties. No theoretical guarantee is given for the convergence of the method to the global optimum of the original optimal control problem. Nonetheless, good performance is demonstrated through case studies involving multiple short- and long-term encounters, showcasing the generation of fuel-efficient CAMs while respecting operational constraints.