Fuel-Optimal Convex Trajectory Optimization of Rendezvous on Elliptical Orbits

In this paper a new approach to constrained low-thrust trajectory optimization for rendezvous on elliptical orbits is presented. The approach is derived from a technique developed in the control engineering community, known as Sum Of Squares. Approximating the solution as a polynomial with respect to time, the constraints are reduced to bounds on polynomials. The polynomial bounding problem is then formulated as a convex optimization problem which does not require an initial guess for the solution. This approach is well suited for problems under linear dynamic equations, therefore perfectly fitting the case of spacecraft relative motion.