Minimum Bounds on Multispacecraft Optimal Cooperative Rendezvous

Abstract

Time- and orientation-free optimal transfers are used to investigate optimal rendezvous orbits for cooperative systems of two and more spacecraft. The problem of finding total optimal cooperative rendezvous orbits is formulated and solved as a nonlinear programming problem using analytic expressions for optimal orbit transfer costs. Each spacecraft has propulsive abilities, and optimal rendezvous orbits are found for planar (match semimajor axis and eccentricity) and three-dimensional (match semimajor axis, eccentricity, and inclination) scenarios. The costs found for this type of rendezvous are lower-bound costs for finite-time full rendezvous where all spacecraft would have matching sets of all six orbit elements. This lower-bound cost, which is realizable for full rendezvous given infinite time and secular perturbations, is shown to be also realizable for finite-time full rendezvous if certain initial conditions can be met. Finally, application of the cooperative rendezvous problem to constellation deployment is briefly discussed.