Optimal Thrust Profile for Planetary Soft Landing Under Stochastic Disturbances

A study presents an application of the framework of stochastic control using forward and backward sampling developed by researchers. The problem considered within this paper is a combination of a stochastic L1-optimal control problem with a first-exit type of formulation. The motivation for this problem formulation stems from the fact that the proposed algorithm is intended to be deployed during the very last stage of the descent when the altitude is relatively low. In this setting, it is assumed that any constraints with respect to navigating toward the landing site have been already satisfied, and the final objective is to ensure that the spacecraft touches the ground smoothly, despite environmental disturbances. This study also illustrates the advantages of a control law stemming from our framework, as opposed to a closed-loop deterministic control law that does not directly take stochasticity into consideration. Specifically, it is shown that simply employing a deterministic closed-loop controller in a model-predictive control fashion does not mitigate the risk of a crash during landing.