Optimal trajectories of electric sail with uncertainties

An Electric Solar Wind Sail (E-sail) is an innovative propellantless propulsion system that generates a propulsive acceleration by exchanging momentum with the solar wind charged particles. Optimal E-sail trajectories are usually investigated by assuming an average value of the solar wind characteristics, thus obtaining a deterministic reference trajectory. However, recent analyses have shown that the solar wind dynamic pressure should be modelled as a random variable and an E-sail-based spacecraft may hardly be steered toward a target celestial body in an uncertain environment with just an open-loop control law. Therefore, this paper proposes to solve such a problem with a combined control strategy that suitably adjusts the grid electric voltage in response to the measured value of the dynamic pressure, and counteracts the effects of the solar wind uncertainties by rectifying the nominal trajectory at suitably chosen points. The effectiveness of such an approach is verified by simulation using two-dimensional transfer scenarios.