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This work presents a method to compute fuel-optimal collision avoidancemaneuvers for long-term encounters. The fuel-optimal problem is formulated as asequential convex program employing successive convexification of the dynamicsand a projection and linearization algorithm to convexify the keep-out zoneconstraint. Dealing with the long-term conjunction poses additional challengesw.r.t. the short-term problem because the encounter is not instantaneous. Thus,the collision avoidance (CA) constraint is formulated as a continuous conditionto be respected throughout the time frame of interest. The robustness of thesolution is improved by the introduction of a condition on the sensitivity ofthe collision metric. Furthermore, the CA problem is coupled with the classicalstation-keeping requirement for GEO satellites and with a return to the nominalorbit condition for LEO satellites. A new trust region definition is employedto mitigate the effect of the linearization of the dynamics. The proposedapproach calculates optimal solutions for many initial conditions and differentorbital scenarios. The optimizer only takes a few seconds to find a solution,making the method suitable for autonomous calculations.

Fuel-Optimal Collision Avoidance Maneuvers in Long-Term Encounters with Station-Keeping Constraints