# Fast Homotopy for Spacecraft Rendezvous Trajectory Optimization with Discrete Logic

arXiv: https://arxiv.org/abs/2107.07001 · HTML: https://mlsanity.com/paper/2107.07001/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2021.

## Built on by (most cited first, 4 of 4)

- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)
- [Agile Tradespace Exploration for Space Rendezvous Mission Design via Transformers](https://mlsanity.com/paper/2510.03544/) (2025)
- [Language-Conditioned Safe Trajectory Generation for Spacecraft Rendezvous](https://mlsanity.com/paper/2512.09111/) (2025)
- [Semantic Constraint Synthesis for Adaptive Trajectory Optimization via Large Language Models](https://mlsanity.com/paper/2606.04123/) (2026)

## Abstract (arXiv)

This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods for these constraints require binary variables and mixed-integer programming, which is prohibitively slow and computationally expensive. This paper targets a fast solution that is capable of real-time implementation onboard spacecraft. To do so, a novel algorithm is developed that blends sequential convex programming and numerical continuation into a single iterative solution process. Inside the algorithm, discrete logic constraints are approximated by smooth functions, and a homotopy parameter governs the accuracy of this approximation. As the algorithm converges, the homotopy parameter is updated such that the smooth approximations enforce the exact discrete logic. The effectiveness of this approach is numerically demonstrated for a realistic rendezvous scenario inspired by the Apollo Transposition and Docking maneuver. In under 15 seconds of cumulative solver time, the algorithm is able to reliably find difficult fuel-optimal trajectories that obey the following discrete logic constraints: thruster minimum impulse-bit, range-triggered approach cone, and range-triggered plume impingement. The optimized trajectory uses significantly less fuel than reported NASA design targets.