On the Structure of the Optimal Guidance Policy of the Soft Landing Problem

We revise the Soft Landing Problem deriving the Optimal Guidance Policy and the Value Function of the minimum time problem in its Controllable Set. Using this Guidance Policy the lander can be guided not only along the nominal trajectory or in its neighborhood but in all conditions that can have a possible successful landing, thus providing a safer approach to changes in planning, failures or other unknown conditions. In addition to the classic solutions of this problem we have fully described a new class of broken extremals which occur when the lander is falling with an high vertical speed and can be used in case of failures or unplanned conditions.