# Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking

arXiv: https://arxiv.org/abs/2206.03305 · HTML: https://mlsanity.com/paper/2206.03305/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 18 of 18)

- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Temporal Convolutional Networks: A Unified Approach to Action Segmentation](https://mlsanity.com/paper/1608.08242/) (2016)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Deep Drone Acrobatics](https://mlsanity.com/paper/2006.05768/) (2020)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [NeuroBEM: Hybrid Aerodynamic Quadrotor Model](https://mlsanity.com/paper/2106.08015/) (2021)
- [Data-Driven MPC for Quadrotors](https://mlsanity.com/paper/2102.05773/) (2021)
- [HPIPM: a high-performance quadratic programming framework for model predictive control](https://mlsanity.com/paper/2003.02547/) (2020)
- [Learning Quadrotor Dynamics Using Neural Network for Flight Control](https://mlsanity.com/paper/1610.05863/) (2016)
- [AutoTune: Controller Tuning for High-Speed Flight](https://mlsanity.com/paper/2103.10698/) (2021)
- [PCMPC: Perception-Constrained Model Predictive Control for Quadrotors with Suspended Loads using a Single Camera and IMU](https://mlsanity.com/paper/2107.10888/) (2021)
- [Temporal Convolutions for Multi-Step Quadrotor Motion Prediction](https://mlsanity.com/paper/2110.04182/) (2021)
- [Systematic Online Tuning of Multirotor UAVs for Accurate Trajectory Tracking Under Wind Disturbances and In-Flight Dynamics Changes](https://mlsanity.com/paper/2106.03459/) (2021)

## Built on by (most cited first, 18 of 18)

- [Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2210.12583/) (2022)
- [SkyJEPA: Learning Long-Horizon World Models for Zero-Shot Sim-to-Real Control of Quadrotors](https://mlsanity.com/paper/2606.23444/) (2026)
- [PIETRA: Physics-Informed Evidential Learning for Traversing Out-of-Distribution Terrain](https://mlsanity.com/paper/2409.03005/) (2024)
- [Neural Moving Horizon Estimation for Robust Flight Control](https://mlsanity.com/paper/2206.10397/) (2022)
- [Constrained Reinforcement Learning using Distributional Representation for Trustworthy Quadrotor UAV Tracking Control](https://mlsanity.com/paper/2302.11694/) (2023)
- [Neural Potential Field for Obstacle-Aware Local Motion Planning](https://mlsanity.com/paper/2310.16362/) (2023)
- [Adaptive Asynchronous Control Using Meta-learned Neural Ordinary Differential Equations](https://mlsanity.com/paper/2207.12062/) (2022)
- [Building Hybrid B-Spline And Neural Network Operators](https://mlsanity.com/paper/2406.06611/) (2024)
- [Safety Filter Design for Neural Network Systems via Convex Optimization](https://mlsanity.com/paper/2308.08086/) (2023)
- [Learning Long-Horizon Predictions for Quadrotor Dynamics](https://mlsanity.com/paper/2407.12964/) (2024)
- [NOVA: Navigation via Object-Centric Visual Autonomy for High-Speed Target Tracking in Unstructured GPS-Denied Environments](https://mlsanity.com/paper/2506.18689/) (2025)
- [PI-WAN: A Physics-Informed Wind-Adaptive Network for Quadrotor Dynamics Prediction in Unknown Environments](https://mlsanity.com/paper/2507.00816/) (2025)
- [Learning-enhanced Nonlinear Model Predictive Control using Knowledge-based Neural Ordinary Differential Equations and Deep Ensembles](https://mlsanity.com/paper/2211.13829/) (2022)
- [Proto-MPC: An Encoder-Prototype-Decoder Approach for Quadrotor Control in Challenging Winds](https://mlsanity.com/paper/2401.15508/) (2024)
- [Dual Agent Learning Based Aerial Trajectory Tracking](https://mlsanity.com/paper/2410.23571/) (2024)
- [Dynamics-Invariant Quadrotor Control using Scale-Aware Deep Reinforcement Learning](https://mlsanity.com/paper/2503.09622/) (2025)
- [HUNT: High-Speed UAV Navigation and Tracking in Unstructured Environments via Instantaneous Relative Frames](https://mlsanity.com/paper/2509.19452/) (2025)
- [Comparison of neural network training strategies for the simulation of dynamical systems](https://mlsanity.com/paper/2512.03851/) (2025)

## Abstract (arXiv)

Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. The model needs to capture the system behavior in multiple flight regimes and operating conditions, including those producing highly nonlinear effects such as aerodynamic forces and torques, rotor interactions, or possible system configuration modifications. Classical approaches rely on handcrafted models and struggle to generalize and scale to capture these effects. In this paper, we present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions. In addition, physics constraints are embedded in the training process to facilitate the network's generalization capabilities to data outside the training distribution. Finally, we design a model predictive control approach that incorporates the learned dynamics for accurate closed-loop trajectory tracking fully exploiting the learned model predictions in a receding horizon fashion. Experimental results demonstrate that our approach accurately extracts the structure of the quadrotor's dynamics from data, capturing effects that would remain hidden to classical approaches. To the best of our knowledge, this is the first time physics-inspired deep learning is successfully applied to temporal convolutional networks and to the system identification task, while concurrently enabling predictive control.