# Deep L1 Stochastic Optimal Control Policies for Planetary Soft-landing

arXiv: https://arxiv.org/abs/2109.00183 · HTML: https://mlsanity.com/paper/2109.00183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 1 Sep 2021.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Real-time optimal control via Deep Neural Networks: study on landing problems](https://mlsanity.com/paper/1610.08668/) (2016)
- [Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs](https://mlsanity.com/paper/2009.01196/) (2020)
- [Learning Deep Stochastic Optimal Control Policies using Forward-Backward SDEs](https://mlsanity.com/paper/1902.03986/) (2019)
- [Learning Optimal Control via Forward and Backward Stochastic Differential Equations](https://mlsanity.com/paper/1509.02195/) (2015)
- [Deep Forward-Backward SDEs for Min-max Control](https://mlsanity.com/paper/1906.04771/) (2019)
- [Gradient-Based Adaptive Stochastic Search for Non-Differentiable Optimization](https://mlsanity.com/paper/1301.1333/) (2013)
- [NOVAS: Non-convex Optimization via Adaptive Stochastic Search for End-to-End Learning and Control](https://mlsanity.com/paper/2006.11992/) (2020)

## Abstract (arXiv)

In this paper, we introduce a novel deep learning based solution to the Powered-Descent Guidance (PDG) problem, grounded in principles of nonlinear Stochastic Optimal Control (SOC) and Feynman-Kac theory. Our algorithm solves the PDG problem by framing it as an L1 SOC problem for minimum fuel consumption. Additionally, it can handle practically useful control constraints, 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 (FBSDEs) and differentiable non-convex optimization neural-network layers 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 position of the spacecraft. After training offline, our controller can be activated once the spacecraft is within a pre-specified radius of the landing zone and at a pre-specified altitude i.e., 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 at the base of this cone while minimizing fuel consumption.