Tube Stochastic Optimal Control for Nonlinear Constrained Trajectory Optimization Problems

TL;DR

This paper introduces a novel algorithm for solving nonlinear constrained stochastic optimal control problems, specifically applied to low-thrust space trajectory design, enhancing robustness through automatic margin introduction.

Contribution

It develops a new method combining the unscented transform with trajectory optimization to handle stochastic control problems with nonlinear systems and constraints.

Findings

Automatically introduces robustness margins in trajectories

Demonstrates improved robustness in low-thrust space missions

Validates solutions through Monte Carlo simulations

Abstract

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.