# Equivariant Reinforcement Learning for Quadrotor UAV

arXiv: https://arxiv.org/abs/2206.01233 · HTML: https://mlsanity.com/paper/2206.01233/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 2 Jun 2022.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Control of a Quadrotor with Reinforcement Learning](https://mlsanity.com/paper/1707.05110/) (2017)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [Autonomous Drone Racing with Deep Reinforcement Learning](https://mlsanity.com/paper/2103.08624/) (2021)
- [Sim-to-(Multi)-Real: Transfer of Low-Level Robust Control Policies to Multiple Quadrotors](https://mlsanity.com/paper/1903.04628/) (2019)
- [Model-Based Meta-Reinforcement Learning for Flight with Suspended Payloads](https://mlsanity.com/paper/2004.11345/) (2020)
- [Multi-Agent MDP Homomorphic Networks](https://mlsanity.com/paper/2110.04495/) (2021)
- [Hierarchical Question Answering for Long Documents](https://mlsanity.com/paper/1611.01839/) (2016)

## Built on by (most cited first, 6 of 6)

- [SO(2)-Equivariant Downwash Models for Close Proximity Flight](https://mlsanity.com/paper/2305.18983/) (2023)
- [Leveraging Symmetry to Accelerate Learning of Trajectory Tracking Controllers for Free-Flying Robotic Systems](https://mlsanity.com/paper/2409.11238/) (2024)
- [Equivariant Reinforcement Learning Frameworks for Quadrotor Low-Level Control](https://mlsanity.com/paper/2502.20500/) (2025)
- [Symmetries-enhanced Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2501.01136/) (2025)
- [Multi-Task Reinforcement Learning of Drone Aerobatics by Exploiting Geometric Symmetries](https://mlsanity.com/paper/2602.10997/) (2026)
- [Physics-Aware End-to-End Deep Reinforcement Learning for Quadcopter Control with Actuator Dynamics](https://mlsanity.com/paper/2607.25985/) (2026)

## Abstract (arXiv)

This paper presents an equivariant reinforcement learning framework for quadrotor unmanned aerial vehicles. Successful training of reinforcement learning often requires numerous interactions with the environments, which hinders its applicability especially when the available computational resources are limited, or when there is no reliable simulation model. We identified an equivariance property of the quadrotor dynamics such that the dimension of the state required in the training is reduced by one, thereby improving the sampling efficiency of reinforcement learning substantially. This is illustrated by numerical examples with popular reinforcement learning techniques of TD3 and SAC.