High-order robust guidance of interplanetary trajectories based on differential algebra

Space trajectory design always requires the solution of an optimal control problem in order to maximize the payload launch-mass ratio while achieving the primary mission goals. A certain level of approximation always characterizes the dynamical models adopted to perform the design process. Furthermore the state identification is usually affected by navigation errors. Thus, after the nominal optimal solution is computed, a control strategy that assures the execution of mission goals in the real scenario must be implemented. In this frame differential algebraic techniques are here proposed as an effective alternative tool to design the guidance law. By using differential algebra the final state dependency on initial conditions, environmental and control parameters is represented by high order Taylor series expansions. The mission constraints can then be solved to high order using a so-called high order partial inversion of the polynomial relationship for every admissible uncertainty. The control strategy is eventually reduced to a simple function evaluation. The performances of the proposed methods are assessed by two examples of space mission trajectory design: a continuous propelled Earth-Mars transfer and an aerocapture maneuver at Mars