  This work presents a sequential convex program method to compute fuel-optimal
collision avoidance maneuvers for long-term encounters. The low-thrust
acceleration model is used to account for the control, but the method can
compute high-thrust maneuvers by increasing the maximum available acceleration.
Dealing with the long-term conjunction poses additional challenges compared to
the short-term problem because the encounter is not instantaneous. Thus, under
the assumption of Gaussian statistics, the probability of collision is replaced
by a simpler metric, the instantaneous probability of collision (IPoC) and a
keep-out zone constraint is formulated as a continuous condition to be
respected throughout the time frame of interest. The robustness of the solution
is improved by introducing a constraint on the sensitivity of the IPoC.
Furthermore, the collision avoidance problem is coupled with the classical
station-keeping requirement for geostationary Earth orbit satellites and with a
return to the nominal orbit condition for low Earth orbit satellites. Even
though no guarantee is given for the recovery of the global optimum solution,
numerical simulations in different orbital regimes show that the proposed
approach can yield a local fuel-optimal solution with a run-time suitable for
autonomous applications.
