The fuel-optimal trajectory for finite-thrust LUNAR ASCENT

This paper investigates the fuel-optimal scheme of a finite-thrust lunar ascent mission. First, we apply an indirect method with the homotopy method to solve the bang-bang control associated with the finite-thrust fuel-optimal problem. Then, a simplified dynamic equation is used to obtain the analytical criterion of the on and off thrust conditions in the form of co-states. For the first burn arc, the optimal co-states are estimated from the analytical results of the minimum-time problem. The co-states from the previous coast arc are used to calculate the booting condition for the second burn arc, which is the necessary condition for the on and off thrust conditions; the numerical method is used to determine the sufficient conditions. Combining the analytical criterion and numerical results, a criterion for the thrust on and off switching times of the fuel-optimal lunar ascent problem is derived, and the total flight time can be estimated. The criterion is validated by several numerical simulations.