Constrained periodic spacecraft relative motion using non-negative polynomials

Abstract

International audienceA 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 tolerance box centered in a specified position. Unlike the classical time-sampling approaches, our method guarantees continuous satisfaction of the constraints on infinite horizon. This is done by reformulating the tolerance box constraints on the relative trajectory as conditions of non-negativity of some polynomials. The resulting problem is solved using semi-definite programming