Particle Swarm Optimization-Based Costate Initialization for Minimum Time Transfers Between Cislunar Periodic Orbits

Due to the low controllability of low-thrust spacecrafts, their orbital transfers are difficult to compute. Indirect methods can be applied to solve these transfers due to the small number of unknown costates; the most promising is Particle Swarm Optimization (PSO). PSO has previously been used to study specific singular transfers, including spiral trajectories from geostationary transfer orbit (GTO); it has not been applied to solve transfers with cislunar periodic orbits. This work uses a PSO-based costate initialization method to solve minimum time low-thrust transfers between cislunar periodic orbits with the Circular Restricted Three Body Problem (CRTBP) model. Five distinct orbital transfers were investigated, including L2 halo orbits and distant retrograde orbits (DROs). Maximum allowable thrust was reduced from 1.0 N to 0.1 N, and the Jacobi Integral of the final state was tested as a constraint. The approximate probabilities of PSO converging to a solution per thrust and time-of-flight (TOF) were calculated to evaluate this stochastic method. As maximum allowable thrust decreased, the transfer TOF increased across all cases. The solutions found, with the smallest TOF for each thrust magnitude, between orbits in the same family followed similar trajectory paths. The method is found to work well for L2 halo orbits and DROs. PSO struggled to solve transfers to and from the near rectilinear halo orbit (NRHO); this is likely due to its stability and the low thrust considered in this work.