Using polynomial optimization to solve the fuel-optimal linear impulsive rendezvous problem

A numerical algorithm based on polynomial optimization and tools from algebraic geometry addressing the issue of time-fixed optimal rendezvous in a linear setting is proposed. The algorithm relying on polynomial optimization provides a guarantee of global optimality for its solution for a fixed number of impulses. The difficulty related to transcendental equations may be overcome through the use of a gridding technique providing a numerical approximation of the optimal impulse times. A numerically reliable procedure to determine the global solution of the impulsive linear rendezvous problem is available for the designer. The numerical results given by the procedure employed are consistent and may be obtained for different types of rendezvous, ranging from circular to highly elliptical orbits and from the classical two-impulse solutions to numerically involved four-impulse solutions.