Optimal Cooperative Power-Limited Rendezvous with Propellant Constraints
Abstract
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.