Closed-Loop Guidance for Asteroid Landing Using Stability-Related Control and Three-Dimensional Convex Curvature Constraints

Abstract

For asteroid landing missions in uncertain environments, the thrust commands determined by a feedback control and a fuel-optimal landing trajectory may exceed the allowable thrust magnitude, which affects the stability of the controller. In contrast to the traditional method that designs the nominal trajectory and feedback control law separately, a novel closed-loop guidance method that generates an optimal trajectory while designing a stable feedback control law within the thrust limit is proposed. The method incorporates the feedback control design into the nominal trajectory optimization by shaping controlled trajectory bundles into a contractive invariant set centered on the nominal trajectory. To shape the trajectory bundles, the contractive invariant criterion is derived and augmented into the optimization with the feedback gain as an optimization variable. Then, the corresponding feedback control, expressed by the feedback gain and contractive invariant set, is introduced to form a stability-related control constraint, which keeps closed-loop thrust within the limit and ensures control stability. In addition, to improve the collision avoidance capability in uncertain terrains, a three-dimensional convex curvature constraint is proposed by constraining the geometric relationship between position and velocity vectors, and used as a soft constraint in the optimization. Finally, the proposed method is simulated using a landing mission on asteroid 433 Eros, which validates the superiority in the tracking performance and the collision avoidance capability.