Mathematics of attitude-constrained optimal low-thrust orbit transfer

Abstract

The mathematics of the problem of optimal low-thrust transfer with constant exhaust velocity, in which the instantaneous thrust direction is constrained in roll is presented. Thus only pitch and yaw are free while roll is held constant at zero. This attitude-constrained transfer mode allows the practitioners to carry out trade-off analyses between RCS (Reaction Control System) propellant and main propulsion system propellant expenditure. Snap-roll maneuvers needed to orient the solar panels normal to the sun can be eliminated, saving RCS propellant at the expense of additional transfer Δ V and time, due to the inability to orient the panels normal to the sun, which results in reduced power output, and therefore, thrust.

This constrained case extends previous analyses of the optimal solution for the minimum-time low-thrust transfer, namely the unconstrained thrust direction case, and the zero pitch case. The thrust vector specification requires the specification of two polar angles in three-dimensional space, and the optimal panel orientation angle is now a function of these two control angles which are derived themselves from the optimality conditions.

The optimal panel orientation angle in terms of the thrust vector orientation, for maximum power output, is derived for both the pitch-yaw and yaw-pitch sequences.