Constrained optimization of n-impulse periodic close encounter orbits for inspection missions

A periodic close encounter orbit is an orbit that periodically surveys a target spacecraft. The design of such orbits is important for both military and civil missions. As an example, it can be used for a preliminary mission design to better plan the repair of damaged, expensive, strategic, or extremely critical space assets. Indeed, this paper proposes an optimization approach and algorithm to reach periodic close encounter orbits through n-impulse maneuvers within the framework of Keplerian motion. The optimization is constrained to several bound requirements, such as a) distance bounds at encounter, b) total Δvtot cost, c) single impulse cost Δvk, d) encounter illumination angle, e) daily observation time, f) minimum perigee radius, g) maximum repetition time, h) maximum eccentricity, and i) maximum encounter time. The optimization, performed using Genetic Algorithm, has been validated by several numerical examples using the TLEs of existing satellites. The simulations showed good results and the reliability of the proposed approach via the Genetic Algorithm has been validated by a comparison with the Particle Swarm Optimization algorithm.