Mesh-Based Two-Step Convex Optimization for Spacecraft Landing Trajectory Planning on Irregular Asteroid

Abstract

The problem investigated in this paper is how to rapidly optimize a landing trajectory on an arbitrarily shaped asteroid, subject to practical constraints and a gravitational model suitable for irregular asteroids. The fundamental idea is to convert the nonlinearity involved in the gravitational field into an equivalent convex version and further generate the optimal trajectory using the two-step convex optimization technique to achieve efficient and robust computation. For a given mission area, the positional space is discretized as an exactly sufficient number of small tetrahedron meshes, within which the real gravitations are interpolated as the linear gravitational representation with nonconvex mesh tracking constraints. A solution space relaxation–penalization technique is proposed to convexify the mesh tracking constraints and keep the feasibility of the resulting convex optimization problem. A series of optimal active meshes are generated by solving this problem and transcribed as corresponding convex active meshing constraints, and further imposing them on the landing trajectory to construct the final convex optimization problem equaling to the original problem. The strength and correctness of this method are demonstrated from both perspectives of theoretical analyses and numerical simulations for landing on 4769 Castalia asteroid, with the comparisons of the state-of-the-art convex-optimization-based methods.