A Convex Formulation for Collision Avoidance Maneuver Strategies During Low-Thrust Phases

Conjunctions between spacecraft are increasingly common across orbital regimes, demanding reliable and efficient collision avoidance (CA) strategies. The typical solution to the CA problem is to compute a maneuver that reduces the collision risk while minimizing fuel expenditure. If the spacecraft is in a continuously propelled phase, this approach must be modified since the thrust profile is determined a priori, aiming to reach a final orbit. This work proposes using convex optimization to solve the fuel-optimal short-term encounter CA problem in such conditions. The optimization problem is two-fold: (i) the collision must be avoided, i.e., the collision risk must be reduced below a certain threshold; (ii) after the conjunction, the spacecraft must be rerouted into the correct trajectory to reach the final state that is the end-point of the original thrust trajectory. Through the casting of the problem as a sequential convex program, the original nonlinear optimal control problem is solved iteratively, recovering an optimal solution. Within the second-order cone program framework, three methods are proposed to address the problem: (i) determining the optimal switch-off time to evade collision while minimizing deviation from the nominal trajectory; (ii) computing a new thrust profile, deviating as little as possible from the original one; (iii) combining the previous methods, the thrust is switched off prior to conjunction and after the encounter a new thrust profile is computed. The three strategies are tested on practical operational scenarios, using the nominal thrust profile from a low-thrust Geostationary Transfer Orbit and conjunction details from a Conjunction Data Message.