Optimal Cooperative Power-Limited Rendezvous with Propellant Constraints

Minimum-fuel cooperative rendezvous of two power-limited spacecraft is investigated. Both vehicles are active and provide thrust to complete the rendezvous. Total propellant consumption is minimized subject to propellant constraints. Two gravitational models are investigated: the Hill-Clohessy-Wiltshire linearized field and the two-body, inverse-square field. Analytical solutions are obtained for the linearized gravitational field. A numerical method using direct collocation with nonlinear programming is used for the nonlinear gravitational field. Numerical results are presented and compared for various efficiencies, as measured by spacecraft power-to-mass ratios. For vehicles having different efficiencies, an interesting paradox can occur. Due to a propellant constraint on the more efficient vehicle, the optimal solution can require the initially less efficient vehicle to provide the majority of the thrusting, leaving the initially more efficient vehicle with a surplus of propellant. An explanation of this paradox is provided.