Deep L1 Stochastic Optimal Control Policies for Planetary Soft Landing

Abstract

In this paper, a novel deep-learning-based solution is introduced to the Powered Descent Guidance problem, grounded in principles of nonlinear Stochastic Optimal Control (SOC) and Feynman–Kac theory. Our algorithm solves the problem by framing it as an L1-SOC problem for minimum fuel consumption. Additionally, it can handle practically useful control constraints and nonlinear dynamics and enforces state constraints as soft constraints. This is achieved by building off of recent work on deep forward-backward stochastic differential equations and differentiable neural-network layers for nonconvex optimization based on stochastic search. In contrast to previous approaches, our algorithm does not require convexification of the constraints or linearization of the dynamics and is empirically shown to be robust to stochastic disturbances and the initial conditions of the spacecraft. After training offline, our control policy can be activated once the spacecraft is within a prespecified radius of the landing zone and at a prespecified altitude, in other words, the base of an inverted cone with the tip at the landing zone. We demonstrate empirically that our controller can successfully and safely land all trajectories initialized in the vicinity of the base of this cone as well as with randomization in the starting velocities and spacecraft mass while minimizing fuel consumption.