# KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots

arXiv: https://arxiv.org/abs/2109.04821 · HTML: https://mlsanity.com/paper/2109.04821/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 10 Sep 2021.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Low Level Control of a Quadrotor with Deep Model-Based Reinforcement Learning](https://mlsanity.com/paper/1901.03737/) (2019)
- [ContactNets: Learning Discontinuous Contact Dynamics with Smooth, Implicit Representations](https://mlsanity.com/paper/2009.11193/) (2020)
- [NeuroBEM: Hybrid Aerodynamic Quadrotor Model](https://mlsanity.com/paper/2106.08015/) (2021)
- [Augmenting Physical Simulators with Stochastic Neural Networks: Case Study of Planar Pushing and Bouncing](https://mlsanity.com/paper/1808.03246/) (2018)
- [Data-Driven MPC for Quadrotors](https://mlsanity.com/paper/2102.05773/) (2021)
- [Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systems](https://mlsanity.com/paper/2002.05514/) (2020)
- [How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification](https://mlsanity.com/paper/1905.08061/) (2019)
- [Knowledge-Based Learning of Nonlinear Dynamics and Chaos](https://mlsanity.com/paper/2010.03415/) (2020)
- [Bridging the Gap: Machine Learning to Resolve Improperly Modeled Dynamics](https://mlsanity.com/paper/2008.12642/) (2020)

## Built on by (most cited first, 26 of 26)

- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Online Dynamics Learning for Predictive Control with an Application to Aerial Robots](https://mlsanity.com/paper/2207.09344/) (2022)
- [RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network](https://mlsanity.com/paper/2209.09025/) (2022)
- [SO(2)-Equivariant Downwash Models for Close Proximity Flight](https://mlsanity.com/paper/2305.18983/) (2023)
- [Traffic expertise meets residual RL: Knowledge-informed model-based residual reinforcement learning for CAV trajectory control](https://mlsanity.com/paper/2408.17380/) (2024)
- [Learning Globally Smooth Functions on Manifolds](https://mlsanity.com/paper/2210.00301/) (2022)
- [Neural Potential Field for Obstacle-Aware Local Motion Planning](https://mlsanity.com/paper/2310.16362/) (2023)
- [Action Flow Matching for Continual Robot Learning](https://mlsanity.com/paper/2504.18471/) (2025)
- [Neural Predictive Control to Coordinate Discrete- and Continuous-Time Models for Time-Series Analysis with Control-Theoretical Improvements](https://mlsanity.com/paper/2508.01833/) (2025)
- [Adaptive Asynchronous Control Using Meta-learned Neural Ordinary Differential Equations](https://mlsanity.com/paper/2207.12062/) (2022)
- [Learning the References of Online Model Predictive Control for Urban Self-Driving](https://mlsanity.com/paper/2308.15808/) (2023)
- [ASV Station Keeping under Wind Disturbances using Neural Network Simulation Error Minimization Model Predictive Control](https://mlsanity.com/paper/2310.07892/) (2023)
- [Flying Quadrotors in Tight Formations using Learning-based Model Predictive Control](https://mlsanity.com/paper/2410.09727/) (2024)
- [Context-Aware Deep Lagrangian Networks for Model Predictive Control](https://mlsanity.com/paper/2506.15249/) (2025)
- [Safety Filter Design for Neural Network Systems via Convex Optimization](https://mlsanity.com/paper/2308.08086/) (2023)
- [Knowledge-based Neural Ordinary Differential Equations for Cosserat Rod-based Soft Robots](https://mlsanity.com/paper/2408.07776/) (2024)
- [LEARNEST: LEARNing Enhanced Model-based State ESTimation for Robots using Knowledge-based Neural Ordinary Differential Equations](https://mlsanity.com/paper/2209.08185/) (2022)
- [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)
- [Structured Deep Neural Network-Based Backstepping Trajectory Tracking Control for Lagrangian Systems](https://mlsanity.com/paper/2403.00381/) (2024)
- [External-Wrench Estimation for Aerial Robots Exploiting a Learned Model](https://mlsanity.com/paper/2504.08156/) (2025)
- [Control of dynamical systems with neural networks](https://mlsanity.com/paper/2510.12810/) (2025)
- [Gradient-Enhanced Partitioned Gaussian Processes for Real-Time Quadrotor Dynamics Modeling](https://mlsanity.com/paper/2602.12487/) (2026)
- [T2S-MPC: Time-Embedded Online Adaptive Model Predictive Control for Time-Varying Dynamics](https://mlsanity.com/paper/2605.24852/) (2026)
- [Learning Manifold and Ito Dynamics with Branched Neural Rough Differential Equations](https://mlsanity.com/paper/2606.05272/) (2026)
- [Language-Guided Terrain-Adaptive Neural MPC for Autonomous Traversal of Articulated Tracked Robots](https://mlsanity.com/paper/2609.13083/) (2026)

## Abstract (arXiv)

In this work, we consider the problem of deriving and incorporating accurate dynamic models for model predictive control (MPC) with an application to quadrotor control. MPC relies on precise dynamic models to achieve the desired closed-loop performance. However, the presence of uncertainties in complex systems and the environments they operate in poses a challenge in obtaining sufficiently accurate representations of the system dynamics. In this work, we make use of a deep learning tool, knowledge-based neural ordinary differential equations (KNODE), to augment a model obtained from first principles. The resulting hybrid model encompasses both a nominal first-principle model and a neural network learnt from simulated or real-world experimental data. Using a quadrotor, we benchmark our hybrid model against a state-of-the-art Gaussian Process (GP) model and show that the hybrid model provides more accurate predictions of the quadrotor dynamics and is able to generalize beyond the training data. To improve closed-loop performance, the hybrid model is integrated into a novel MPC framework, known as KNODE-MPC. Results show that the integrated framework achieves 60.2% improvement in simulations and more than 21% in physical experiments, in terms of trajectory tracking performance.