Predictor-Controller Approach for Q-Law 6th Element Targeting in Low-Thrust Trajectory Design

Abstract

Electric propulsion enables ambitious and affordable space missions by substantially reducing the fuel mass in comparison to lower specific impulse propulsion. However, the optimisation of the according transfer trajectories is particularly challenging due to their typically low thrust characteristics, resulting in many-revolution transfers with many local minima and highly non-linear dynamics. The Q-Law guidance algorithm can provide near-optimal low-thrust trajectories with minimal computational effort, which can be used either as an initial guess for the optimisation to ensure a faster convergence or directly for mission analysis. In the classical formulation presented by the Q-law does not allow to target a specific position in the final orbit, rendering a poor initial guess in cases where it is a constraint. Such a constraint could be the geographical longitude when acquiring a geostationary orbit, but also the position within a constellation of Low Earth Orbit and Medium Earth Orbitsatellites, or within a rendezvous scenario. This study proposes a predictor-controller approach to enable Q-Law targeting capabilities for this fast-moving orbital element in the final orbit, as a generalisation to a method proposed by [2] to target a geographical longitude in geostationary orbit. This work uses the semi-major axis augmented Modified Equinoctial Elements formulation of the Q-law and has been tested for a range of orbital transfers with varying inclinations and eccentricities. A sensitivity analysis on the key parameters of the algorithm, with respect to its convergence, is presented. This approach permits to quickly compute near-optimal transfers to a specified slot in the final orbit.