Optimal spacecraft swarm reconfiguration through chief orbit refinement

Abstract This work presents a novel approach to minimizing delta-v for spacecraft swarm reconfiguration through refinement of the real or virtual chief spacecraft orbit, which is a closed orbit of arbitrary eccentricity. Given a desired relative motion configuration, the optimal target end-state of the swarm is solved for to provide minimum delta-v expenditure. The relative orbital elements (ROE) representation of relative motion is leveraged to produce two quadratically constrained linear programs (QCLPs). One program minimizes the sum of delta-v usage across the swarm, and the second minimizes the maximum delta-v usage among the swarm or co-orbiting spacecraft. The two objectives are designed to balance delta-v usage across the swarm to maximize mission lifetime. Furthermore, both optimization programs can be solved efficiently with interior point methods. While the minimization is applicable to any ROE set, the quasi-nonsingular ROE are exploited in this work to produce analytical solutions for arbitrary swarm geometry reconfigurations in non-equatorial orbits. If analytical solutions are not available, guidance is provided to minimize the effort required by convex optimization solvers in finding solutions. The delta-v savings enabled by the refinement of the swarm’s reference orbit are demonstrated using a state-of-the-art solver that produces the minimum reachable delta-v for a given reconfiguration. Therefore, leveraging a small refinement in the reference orbit for swarm reconfiguration through a QCLP can provide significant delta-v savings, extending mission lifetime.