RECORD
Tube Stochastic Optimal Control for Nonlinear Constrained Trajectory Optimization Problems
Optimization and Control · Submitted 24 Feb 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Two numerical examples, one of which applies the proposed method to low-thrust trajectory design, illustrate that it automatically introduces margins that improve robustness.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. | background 1.00 | 0.04 | 0.03 | asserted 0.99 |
| s1 | In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control problem. | background 1.00 | 0.12 | 0.03 | asserted 1.00 |
| s2 | 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. | gap 1.00 | 0.07 | 0.04 | asserted 1.00 |
| s3 | This paper presents a new algorithm to solve stochastic optimal control problems with nonlinear systems and constraints. | contribution 1.00 | 0.93 | 0.38 | asserted 1.00 |
| s4 | 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. | method 0.99 | 0.87 | 0.11 | asserted 1.00 |
| s5 | Two numerical examples, one of which applies the proposed method to low-thrust trajectory design, illustrate that it automatically introduces margins that improve robustness. | result 0.95 | 0.93 | 0.44 | asserted 1.00 |
| s6 | Finally, Monte Carlo simulations are used to evaluate the robustness and optimality of the solution. | method 0.98 | 0.93 | 0.09 | asserted 0.93 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original 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.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.