# Tube Stochastic Optimal Control for Nonlinear Constrained Trajectory Optimization Problems

arXiv: https://arxiv.org/abs/2202.12158 · HTML: https://mlsanity.com/paper/2202.12158/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2022.

## Built on by (most cited first, 1 of 1)

- [RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environments](https://mlsanity.com/paper/2609.39854/) (2026)

## Abstract (arXiv)

Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control problem. This problem is among the most complex in control theory, and no practically applicable method to low-thrust trajectory optimization problems has been proposed to date. This paper presents a new algorithm to solve stochastic optimal control problems with nonlinear systems and constraints. The proposed algorithm uses the unscented transform to convert a stochastic optimal control problem into a deterministic problem, which is then solved by trajectory optimization methods such as differential dynamic programming. Two numerical examples, one of which applies the proposed method to low-thrust trajectory design, illustrate that it automatically introduces margins that improve robustness. Finally, Monte Carlo simulations are used to evaluate the robustness and optimality of the solution.