Constrained periodic spacecraft relative motion using non-negative polynomials

A new method for obtaining constrained periodic relative motion between spacecraft on Keplerian orbits is presented. The periodic relative trajectory is required to evolve autonomously inside a predefined tolerance region. Unlike the classical time-sampling approaches, our method guarantees continuous satisfaction of the constraints over an infinite horizon. This is done by reformulating the tolerance region constraints on the relative trajectory as conditions of non-negativity of some polynomials. The resulting problem is solved using semi-definite programming.