Optimal Guidance for Planetary Landing in Hazardous Terrains

In this paper, a minimum-fuel powered-descent optimal guidance algorithm that incorporates obstacle avoidance is presented. The approach is based on convex optimization which includes the obstacles using nonconvex functions. To convert these nonconvex obstacle constraints to convex ones, a simple linearization procedure is employed. It is proved that the optimal solution of the convex relaxation problem is also optimal for the original nonconvex one. The sensitivity of the multi-obstacle avoidance method to the relaxation factor and its effectiveness under different conditions are also investigated through simulations.