Robust Bang-Off-Bang Low-Thrust Guidance Using Model Predictive Static Programming

Abstract

Model Predictive Static Programming (MPSP) has been always used under the assumption of continuous or impulsive control, but never in low-thrust transfers featuring bang-off-bang control. Following the observation that the sensitivity matrix (SM) is discontinuous across the switching time, this work introduces a two-loop MPSP guidance scheme using fuel-optimal trajectories as nominal solutions. In our method, the equations of motion are augmented by the mass costate equation, while the velocity costate is the MPSP control, expressed by a weighted sum of Fourier basis functions. The SM is computed at the switching time by using calculus of variations. Both the MPSP control and the initial mass costate are updated in an inner loop using Newton’s method, and continuation is employed in an outer loop to face large perturbations. A sample interplanetary CubeSat mission to an asteroid is used as study case to illustrate the effectiveness and robustness of the method developed.