Fuel-optimal, power-limited rendezvous with variable thruster efficiency

The problem of minimum-fuel, time-fixed, three-dimensional rendezvous for a solar electric propulsion spacecraft is discussed. The problem is solved via an indirect approach. The formulation takes into account both a variable bounded specific impulse and a variable thruster efficiency and permits us to manage solutions with coast arcs. The thruster efficiency is assumed to vary with the specific impulse through a polynomial approximation. The optimal specific impulse control law is found to depend on the instantaneous values of the primer vector modulus, the spacecraft mass, the mass costate, and the thruster model. Optimal interplanetary trajectories toward Mars are discussed. It is shown that the inclusion of a variable efficiency thruster model has important effects on fuel consumption. In particular, the classic constant efficiency thruster model overestimates the final spacecraft mass.