Reliability-Based Soft Landing Trajectory Optimization near Asteroid with Uncertain Gravitational Field

Abstract

This paper investigates a reliability-based trajectory optimization method for the design of soft landing trajectory on an irregular shape asteroid with highly uncertain gravitational field. First, the gravitational field of the irregular asteroid is described by the finite particle model. Second, to avoid the singularity and reduce the sensitivity, the original finite particle model is modified to an “N-body/two-body” switching dynamic model. The trajectory optimization problem in the switching dynamic model is summarized as an optimal control problem and is then transformed into a two-point boundary value problem by Pontryagin’s maximum principle. By solving the two-point boundary value problem with a homotopic continuation procedure, the nominal optimal trajectory is obtained. Third, the uncertainty caused by the nonuniform mass distribution of the asteroid is considered. With high uncertainty, the deterministic optimal control problem becomes a parameter optimization problem with reliability constraints. This problem is then solved by a sequential optimization and reliability assessment, and the parallel computation technique is adopted. Finally, two soft landing trajectories are optimized using the proposed method to demonstrate the effectiveness of the technique.