Indirect Optimization of Finite-Thrust Cooperative Rendezvous

A time-constrained finite-thrust rendezvous between two cooperating spacecraft is investigated in detail in this paper. To ensure high numerical accuracy, the optimization is carried out by means of an indirect method that exploits an "a priori subdivision of the trajectory into burn and coast arcs, whose time lengths become additional unknown parameters. Issues related to simultaneous presence of two switching control structures, one for each maneuvering spacecraft, are analyzed. A peculiar approach, which relies on the adoption of a different timescale for each spacecraft, is proposed; the introduction of multiple decision vectors allows for an easy management of the switching control structures for missions involving two or more maneuvering spacecraft. As an example, a coplanar rendezvous is thoroughly analyzed; necessary conditions for optimality are comprehensively derived for both target/chaser and cooperative maneuvers. Numerical results are provided and solutions are discussed.