  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.
