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

TL;DR

This paper introduces a novel application of Model Predictive Static Programming (MPSP) for low-thrust space transfer guidance with bang-off-bang control, optimizing fuel use in interplanetary missions.

Contribution

It pioneers the use of MPSP for bang-off-bang control in low-thrust guidance, incorporating a two-loop algorithm and sensitivity analysis for improved trajectory optimization.

Findings

Effective guidance scheme demonstrated on interplanetary CubeSat mission

Enhanced control accuracy through analytical derivatives and compensation at switching points

Successful handling of large perturbations with continuation method

Abstract

Model Predictive Static Programming (MPSP) was always used under the assumption of continuous control, which impedes it for applications with bang-off-bang control directly. In this paper, MPSP is employed for the first time as a guidance scheme for low-thrust transfers with bang-off-bang control where the fuel-optimal trajectory is used as the nominal solution. In our method, dynamical equations in Cartesian coordinates are augmented by the mass costate equation, while the unconstrained velocity costate vector is used as control variable, and is expressed as a combination of Fourier basis functions with corresponding weights. A two-loop MPSP algorithm is designed where the weights and the initial mass costate are updated in the inner loop and continuation is conducted on the outer loop in case of large perturbations. The sensitivity matrix (SM) is recursively calculated using analytical derivatives and SM at switching points is compensated based on calculus of variations. An sample interplanetary CubeSat mission to an asteroid is used as study case to illustrate the effectiveness of the method developed.