Collision-Free Trajectory Design for Long-Distance Hopping Transfer on Asteroid Surface Using Convex Optimization

Abstract

The irregular shapes and gravitational fields of asteroids challenge the design of collision-free asteroid surface hopping trajectories. A novel collision-free long-distance transfer trajectory design algorithm based on the convex optimization is presented in this article. A combinatorial keepout zone consisting of three spheres is defined to avoid the spacecraft colliding with the asteroid surface during the transfer. The boundary of the keepout zone is close to the surface of the target asteroid. With the Taylor expansion approximation, the nonconvex keepout zone constraint becomes convex. Two convex glide-slope constraints are employed for avoiding colliding during the ascent and descent. Thereafter, a convex optimization problem for solving a collision-free long-distance transfer trajectory between arbitrary two surface points is formulated. Moreover, an ant colony optimization algorithm combined with the proposed method is used to solve the optimal hopping sequence problem for exploring multiple points on the asteroid surface. Finally, several numerical simulation examples for the asteroid 433 Eros validate the feasibility and effectiveness of the algorithm.