# Multi-objective minimum time optimal control for low-thrust trajectory design

arXiv: https://arxiv.org/abs/2103.08813 · HTML: https://mlsanity.com/paper/2103.08813/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2021.

## Built on by (most cited first, 2 of 2)

- [Certified Approximate Reachability (CARe): Formal Error Bounds on Deep Learning of Reachable Sets](https://mlsanity.com/paper/2503.23912/) (2025)
- [Verification of safety critical control policies using kernel methods](https://mlsanity.com/paper/2203.12407/) (2022)

## Abstract (arXiv)

We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed trajectory will be guaranteed to be weakly Pareto optimal. The proposed method can be used as a benchmark for future research of applying reachability analysis to low-thrust spacecraft trajectory design.