Electric Sail displaced orbit control with solar wind uncertainties

The working principle of the Electric Solar Wind Sail, an innovative propellantless propulsion system proposed in 2004, is based on the electrostatic interaction between a spinning grid of tethers, kept at a high positive potential, and the incoming ions from the solar wind. Similar to the well-known solar sail concept, the E-sail could simplify the feasibility of advanced (deep space) missions which would otherwise require a significative amount of propellant, if enabled by conventional thrusters. However, the intrinsic variability of the solar wind properties makes accurate trajectory tracking a difficult task, since the perturbations of the solar wind dynamic pressure have the same order of magnitude as their mean value. To circumvent such a problem, in a recent study the plasma dynamic pressure was modelled as a random variable with a gamma probability density function and the sail grid voltage was suggested to be varied as a function of the instantaneous value of the solar wind properties. The aim of this paper is to improve those results, by discussing a more accurate statistical model of the solar wind dynamic pressure, which is used in the numerical simulations to estimate the actual impact of the solar wind uncertainties on the spacecraft heliocentric trajectory. In particular, the paper proposes a control law that is able to accurately track a nominal, non-Keplerian orbit.