In recent years, several mission concepts involving multiple satellites operating in close formation have been investigated. A critical aspect of these studies is the optimal computation of collision avoidance manoeuvres for short-term encounters with external secondary. The specific requirements of formation flying impose additional constraints, particularly the need to maintain a safe minimum separation between satellites and to minimize the duration of mission interruption. 

This study presents two different approaches for implementing avoidance manoeuvres compatible with formation flying. For each, two representative configurations are considered: (i) a trailing formation, where satellites follow one another along the same orbital path with a short time offset, and (ii) a regular polygon formation, where satellites maintain a polygonal formation with fixed inter-satellite distance, as in TRISKEL mission project.  

The first method is a direct approach using Successive Convexification Optimization. The dynamics are linearized using the Differential Algebra of Orekit (an open-source flight dynamics software package). The algorithm relies on two nested loops: a major loop for dynamics linearization, using Orekit to propagate the orbit with Differential Algebra, and a minor loop for constraint convexification (including collision avoidance, thrust restrictions, and inter-satellite distance).  

The alternative approach solves the optimization problem with a standard direct NonLinear Programming approach.  

Then, both methods are comprehensively compared. Finally, the formulation and modelling of constraints are discussed. Constraint modelling relies on a semi-infinite programming formulation to guarantee a minimum separation distance between satellites in the constellation. An additional optimization loop performs a continuous-time check of these distances, using dichotomic searches to locate the points of closest approach. Whenever a new violation is detected, a discrete separation constraint is added at the corresponding time, ensuring that the final solution satisfies the continuous-time safety requirement.