# Transformers for Trajectory Optimization with Application to Spacecraft Rendezvous

arXiv: https://arxiv.org/abs/2310.13831 · HTML: https://mlsanity.com/paper/2310.13831/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2023.

## Built on by (most cited first, 16 of 16)

- [Towards Robust Spacecraft Trajectory Optimization via Transformers](https://mlsanity.com/paper/2410.05585/) (2024)
- [Generalizable Spacecraft Trajectory Generation via Multimodal Learning with Transformers](https://mlsanity.com/paper/2410.11723/) (2024)
- [Diffusion Models for Generating Ballistic Spacecraft Trajectories](https://mlsanity.com/paper/2405.11738/) (2024)
- [Deep Learning Warm Starts for Trajectory Optimization on the International Space Station](https://mlsanity.com/paper/2505.05588/) (2025)
- [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)
- [Compositional Diffusion Models for Powered Descent Trajectory Generation with Flexible Constraints](https://mlsanity.com/paper/2410.04261/) (2024)
- [Unified Generation-Refinement Planning: Bridging Guided Flow Matching and Sampling-Based MPC for Social Navigation](https://mlsanity.com/paper/2508.01192/) (2025)
- [Intent-aligned Autonomous Spacecraft Guidance via Reasoning Models](https://mlsanity.com/paper/2604.17176/) (2026)
- [Semantic Constraint Synthesis for Adaptive Trajectory Optimization via Large Language Models](https://mlsanity.com/paper/2606.04123/) (2026)
- [Transformer-Based Warm-Starting for Feasible and Optimal Terminal Approach to Tumbling Objects with Space Manipulators](https://mlsanity.com/paper/2606.17317/) (2026)
- [Tight Constraint Prediction of Six-Degree-of-Freedom Transformer-based Powered Descent Guidance](https://mlsanity.com/paper/2501.00930/) (2025)
- [A Prefixed Patch Time Series Transformer for Two-Point Boundary Value Problems in Three-Body Problems](https://mlsanity.com/paper/2504.01464/) (2025)
- [Safety-Guaranteed Imitation Learning from Nonlinear Model Predictive Control for Spacecraft Close Proximity Operations](https://mlsanity.com/paper/2603.18910/) (2026)
- [Transformer-Informed Trajectory Optimization for Relative Motion in Cislunar Orbits](https://mlsanity.com/paper/2609.25460/) (2026)
- [Spacecraft Rendezvous Trajectory Generation with Modular Constraints via Diffusion Model Composition](https://mlsanity.com/paper/2610.05642/) (2026)

## Abstract (arXiv)

Reliable and efficient trajectory optimization methods are a fundamental need for autonomous dynamical systems, effectively enabling applications including rocket landing, hypersonic reentry, spacecraft rendezvous, and docking. Within such safety-critical application areas, the complexity of the emerging trajectory optimization problems has motivated the application of AI-based techniques to enhance the performance of traditional approaches. However, current AI-based methods either attempt to fully replace traditional control algorithms, thus lacking constraint satisfaction guarantees and incurring in expensive simulation, or aim to solely imitate the behavior of traditional methods via supervised learning. To address these limitations, this paper proposes the Autonomous Rendezvous Transformer (ART) and assesses the capability of modern generative models to solve complex trajectory optimization problems, both from a forecasting and control standpoint. Specifically, this work assesses the capabilities of Transformers to (i) learn near-optimal policies from previously collected data, and (ii) warm-start a sequential optimizer for the solution of non-convex optimal control problems, thus guaranteeing hard constraint satisfaction. From a forecasting perspective, results highlight how ART outperforms other learning-based architectures at predicting known fuel-optimal trajectories. From a control perspective, empirical analyses show how policies learned through Transformers are able to generate near-optimal warm-starts, achieving trajectories that are (i) more fuel-efficient, (ii) obtained in fewer sequential optimizer iterations, and (iii) computed with an overall runtime comparable to benchmarks based on convex optimization.