# Aggressive Online Control of a Quadrotor via Deep Network Representations of Optimality Principles

arXiv: https://arxiv.org/abs/1912.07067 · HTML: https://mlsanity.com/paper/1912.07067/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2019.

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

- [The Artificial Intelligence behind the winning entry to the 2019 AI Robotic Racing Competition](https://mlsanity.com/paper/2109.14985/) (2021)
- [Actor-Critic Physics-informed Neural Lyapunov Control](https://mlsanity.com/paper/2403.08448/) (2024)
- [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)
- [Constrained Imitation Learning for a Flapping Wing Unmanned Aerial Vehicle](https://mlsanity.com/paper/2206.03987/) (2022)
- [TACO: General Acrobatic Flight Control via Target-and-Command-Oriented Reinforcement Learning](https://mlsanity.com/paper/2503.01125/) (2025)
- [Neural Network Optimal Feedback Control with Guaranteed Local Stability](https://mlsanity.com/paper/2205.00394/) (2022)
- [Neural network optimal feedback control with enhanced closed loop stability](https://mlsanity.com/paper/2109.07466/) (2021)
- [High-order expansion of Neural Ordinary Differential Equations flows](https://mlsanity.com/paper/2504.08769/) (2025)

## Abstract (arXiv)

Optimal control holds great potential to improve a variety of robotic applications. The application of optimal control on-board limited platforms has been severely hindered by the large computational requirements of current state of the art implementations. In this work, we make use of a deep neural network to directly map the robot states to control actions. The network is trained offline to imitate the optimal control computed by a time consuming direct nonlinear method. A mixture of time optimality and power optimality is considered with a continuation parameter used to select the predominance of each objective. We apply our networks (termed G&CNets) to aggressive quadrotor control, first in simulation and then in the real world. We give insight into the factors that influence the `reality gap' between the quadrotor model used by the offline optimal control method and the real quadrotor. Furthermore, we explain how we set up the model and the control structure on-board of the real quadrotor to successfully close this gap and perform time-optimal maneuvers in the real world. Finally, G&CNet's performance is compared to state-of-the-art differential-flatness-based optimal control methods. We show, in the experiments, that G&CNets lead to significantly faster trajectory execution due to, in part, the less restrictive nature of the allowed state-to-input mappings.