# Constrained Imitation Learning for a Flapping Wing Unmanned Aerial Vehicle

arXiv: https://arxiv.org/abs/2206.03987 · HTML: https://mlsanity.com/paper/2206.03987/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 8 Jun 2022.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 15 of 15)

- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [DART: Noise Injection for Robust Imitation Learning](https://mlsanity.com/paper/1703.09327/) (2017)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Learning High-Speed Flight in the Wild](https://mlsanity.com/paper/2110.05113/) (2021)
- [Query-Efficient Imitation Learning for End-to-End Autonomous Driving](https://mlsanity.com/paper/1605.06450/) (2016)
- [Deep Drone Acrobatics](https://mlsanity.com/paper/2006.05768/) (2020)
- [Learning Deep Control Policies for Autonomous Aerial Vehicles with MPC-Guided Policy Search](https://mlsanity.com/paper/1509.06791/) (2015)
- [PLATO: Policy Learning using Adaptive Trajectory Optimization](https://mlsanity.com/paper/1603.00622/) (2016)
- [Teaching the Old Dog New Tricks: Supervised Learning with Constraints](https://mlsanity.com/paper/2002.10766/) (2020)
- [Improving Deep Learning Models via Constraint-Based Domain Knowledge: a Brief Survey](https://mlsanity.com/paper/2005.10691/) (2020)
- [Aggressive Online Control of a Quadrotor via Deep Network Representations of Optimality Principles](https://mlsanity.com/paper/1912.07067/) (2019)
- [Iterative Supervised Learning for Regression with Constraints](https://mlsanity.com/paper/2201.06529/) (2022)
- [Dynamics and Control of a Flapping Wing UAV with Abdomen Undulation Inspired by Monarch Butterfly](https://mlsanity.com/paper/2102.07851/) (2021)
- [Geometric Optimal Controls for Flapping Wing UAV on a Lie Group](https://mlsanity.com/paper/2107.08008/) (2021)

## Built on by (most cited first, 3 of 3)

- [UAVs Meet LLMs: Overviews and Perspectives Toward Agentic Low-Altitude Mobility](https://mlsanity.com/paper/2501.02341/) (2025)
- [CrowdTransfer: Enabling Crowd Knowledge Transfer in AIoT Community](https://mlsanity.com/paper/2407.06485/) (2024)
- [Neural-Primitive: An Efficient End-to-end Local Planner with Primitive-based Imitation Learning for Autonomous Flight](https://mlsanity.com/paper/2608.20948/) (2026)

## Abstract (arXiv)

This paper presents a data-driven optimal control policy for a micro flapping wing unmanned aerial vehicle. First, a set of optimal trajectories are computed off-line based on a geometric formulation of dynamics that captures the nonlinear coupling between the large angle flapping motion and the quasi-steady aerodynamics. Then, it is transformed into a feedback control system according to the framework of imitation learning. In particular, an additional constraint is incorporated through the learning process to enhance the stability properties of the resulting controlled dynamics. Compared with conventional methods, the proposed constrained imitation learning eliminates the need to generate additional optimal trajectories on-line, without sacrificing stability. As such, the computational efficiency is substantially improved. Furthermore, this establishes the first nonlinear control system that stabilizes the coupled longitudinal and lateral dynamics of flapping wing aerial vehicle without relying on averaging or linearization. These are illustrated by numerical examples for a simulated model inspired by Monarch butterflies.