A Convex Optimization Method for Multiple Encounters Collision Avoidance Maneuvers

This work presents a novel approach for the optimization of fuel-optimal collision avoidance maneuvers (CAMs) in scenarios involving multiple encounters. The considered risk mitigation strategy spans beyond immediate conjunctions, encompassing subsequent encounters over an extended window of interest. Two operational cases are considered: multiple encounters between a maneuverable primary spacecraft and a set of secondaries and repeating encounters between a spacecraft and a single secondary. The optimization’s objective is the minimization of the total fuel consumption while respecting conditions on the minimization of the total probability of collision (TPoC). Only short-term encounters are addressed in this work, but the proposed approach is also valid for long-term encounters. In the former case, the TPoC is a nonlinear combination of the probability of collision for the single conjunctions. Moreover, a Gaussian mixture model method is used to propagate the uncertainty of the secondary spacecraft. This allows for the splitting of the secondary into multiple mixands, which are treated as if they were different objects. The problem is solved using convex optimization due to its demonstrated effectiveness in addressing complex aerospace engineering problems. It combines sequential convex programming, second-order cone programming, and differential algebra to approximate the non-convex optimal control problem progressively. Additionally, a trust region technique is introduced to enhance convergence. The efficiency of the approach is demonstrated through case studies involving multiple encounters, showcasing the generation of fuel-efficient CAMs.