Polynomial optimization for the solution of fuel-optimal impulsive rendezvous using primer vector theory

In this paper, the optimal fuel impulsive time-fixed rendezvous problem is considered. Under some simplifying assumptions, this problem may be recast as a non convex polynomial optimization problem. A numerical solving algorithm using a convex relaxation based on sum-of-squares representation of positive polynomials is proposed. Numerical results are evaluated on the PRISMA technology in-orbit formation flying testbed mission.