Multi-constrained autonomous soft landing via geometric mechanics based fast model predictive control

Abstract

This paper addresses the spacecraft powered descent guidance and control on a celestial surface, where the rotational and translational motion are developed directly on SE(3). Multiple novel state-coupled geometrical models are designed to matching the constraints, e.g., the upper bound of the velocity constraint is designed related to altitude, ensuring that the spacecraft can descend rapidly while maintaining a low touchdown velocity. A geometric mechanics based fast model predictive control is derived for the closed-loop autonomous landing algorithm, in which the state constraints are incorporated into the augmented cost function by Lagrange multipliers in the form of penalty functions. Discrete-time dynamics used to predict the spacecraft model are updated by Lie group variational integrator (LGVI). An indirect shooting method based numerical solver is utilized to solve the necessary conditions of the optimization problem. The effectiveness and robustness of the landing algorithm are then discussed by numerical simulations.