Application of the Sequential Gradient Restoration Algorithm to the Solution of the Low Thrust Transfer Problem

Abstract

The Sequential Gradient Restoration Algorithm (SGRA) is an indirect optimisation method based on the iterative alternation of two phases: in the first one (gradient), the objective is the minimisation of the cost function; in the second phase (restoration) the objective is the fulfilment of the differential equations, equality and inequality path constraints and boundary conditions. This paper illustrates the application of the SGRA to the generation of very long transfer trajectories (up to some few thousand orbits during several months) in a typical GTO to GEO transfer scenario performed with electric propulsion. The reason for using electric propulsion in that case is the significant propellant mass savings if compared to the classical chemical propulsion strategies, at the expenses of an elongated transfer phase (from few days to some months). The electric propulsion system considered in this paper is characterised by thrust levels between 100 mN and 1 N (for some 3 to 5 tons launch mass) and high specific impulse, between 1000 s and 5000 s.