# Neural representation of a time optimal, constant acceleration rendezvous

arXiv: https://arxiv.org/abs/2203.15490 · HTML: https://mlsanity.com/paper/2203.15490/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 29 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Real-time optimal control via Deep Neural Networks: study on landing problems](https://mlsanity.com/paper/1610.08668/) (2016)
- [On the stability analysis of deep neural network representations of an optimal state-feedback](https://mlsanity.com/paper/1812.02532/) (2018)
- [Revisiting high-order Taylor methods for astrodynamics and celestial mechanics](https://mlsanity.com/paper/2105.00800/) (2021)
- [Learning the optimal state-feedback via supervised imitation learning](https://mlsanity.com/paper/1901.02369/) (2019)
- [Deep Networks as Approximators of Optimal Transfers Solutions in Multitarget Missions](https://mlsanity.com/paper/1902.00250/) (2019)
- [Autonomous Time-Optimal Many-Revolution Orbit Raising for Electric Propulsion GEO Satellites via Neural Networks](https://mlsanity.com/paper/1909.08768/) (2019)

## Built on by (most cited first, 10 of 10)

- [Guidance and Control Networks with Periodic Activation Functions](https://mlsanity.com/paper/2405.18084/) (2024)
- [Selected Trends in Artificial Intelligence for Space Applications](https://mlsanity.com/paper/2212.06662/) (2022)
- [Optimality Principles in Spacecraft Neural Guidance and Control](https://mlsanity.com/paper/2305.13078/) (2023)
- [Certifying Guidance & Control Networks: Uncertainty Propagation to an Event Manifold](https://mlsanity.com/paper/2410.03729/) (2024)
- [High-order expansion of Neural Ordinary Differential Equations flows](https://mlsanity.com/paper/2504.08769/) (2025)
- [Comparing Behavioural Cloning and Reinforcement Learning for Spacecraft Guidance and Control Networks](https://mlsanity.com/paper/2507.19535/) (2025)
- [Neural Approximators for Low-Thrust Trajectory Transfer Cost and Reachability](https://mlsanity.com/paper/2508.02911/) (2025)
- [Learning Robust Satellite Attitude Dynamics with Physics-Informed Normalising Flow](https://mlsanity.com/paper/2508.07841/) (2025)
- [Reconfiguration of pivoting cube ensembles under local sensing constraints using geometric deep learning](https://mlsanity.com/paper/2509.03140/) (2025)
- [Pretrained Approximators for Low-Thrust Trajectory Cost and Reachability](https://mlsanity.com/paper/2605.26790/) (2026)

## Abstract (arXiv)

We train neural models to represent both the optimal policy (i.e. the optimal thrust direction) and the value function (i.e. the time of flight) for a time optimal, constant acceleration low-thrust rendezvous. In both cases we develop and make use of the data augmentation technique we call backward generation of optimal examples. We are thus able to produce and work with large dataset and to fully exploit the benefit of employing a deep learning framework. We achieve, in all cases, accuracies resulting in successful rendezvous (simulated following the learned policy) and time of flight predictions (using the learned value function). We find that residuals as small as a few m/s, thus well within the possibility of a spacecraft navigation Delta V budget, are achievable for the velocity at rendezvous. We also find that, on average, the absolute error to predict the optimal time of flight to rendezvous from any orbit in the asteroid belt to an Earth-like orbit is small (less than 4%) and thus also of interest for practical uses, for example, during preliminary mission design phases.