# RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network

arXiv: https://arxiv.org/abs/2209.09025 · HTML: https://mlsanity.com/paper/2209.09025/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 19 Sep 2022.

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

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Risk Averse Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1904.00511/) (2019)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Data-Driven MPC for Quadrotors](https://mlsanity.com/paper/2102.05773/) (2021)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators](https://mlsanity.com/paper/2109.10793/) (2021)
- [Robust Model-free Reinforcement Learning with Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1910.13399/) (2019)
- [Adaptive MPC for Iterative Tasks](https://mlsanity.com/paper/1804.09831/) (2018)
- [Learning High-Level Policies for Model Predictive Control](https://mlsanity.com/paper/2007.10284/) (2020)
- [Bridging the Gap: Machine Learning to Resolve Improperly Modeled Dynamics](https://mlsanity.com/paper/2008.12642/) (2020)

## Built on by (most cited first, 12 of 12)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Metamizer: a versatile neural optimizer for fast and accurate physics simulations](https://mlsanity.com/paper/2410.19746/) (2024)
- [MetaSym: A Symplectic Meta-learning Framework for Physical Intelligence](https://mlsanity.com/paper/2502.16667/) (2025)
- [Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systems](https://mlsanity.com/paper/2408.14951/) (2024)
- [Deep Operator Neural Network Model Predictive Control](https://mlsanity.com/paper/2505.18008/) (2025)
- [ASMA: An Adaptive Safety Margin Algorithm for Vision-Language Drone Navigation via Scene-Aware Control Barrier Functions](https://mlsanity.com/paper/2409.10283/) (2024)
- [PI-WAN: A Physics-Informed Wind-Adaptive Network for Quadrotor Dynamics Prediction in Unknown Environments](https://mlsanity.com/paper/2507.00816/) (2025)
- [Data-efficient, Explainable and Safe Box Manipulation: Illustrating the Advantages of Physical Priors in Model-Predictive Control](https://mlsanity.com/paper/2303.01563/) (2023)
- [Structured Deep Neural Network-Based Backstepping Trajectory Tracking Control for Lagrangian Systems](https://mlsanity.com/paper/2403.00381/) (2024)
- [Neuro-LIFT: A Neuromorphic, LLM-based Interactive Framework for Autonomous Drone FlighT at the Edge](https://mlsanity.com/paper/2501.19259/) (2025)
- [Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Control](https://mlsanity.com/paper/2504.20019/) (2025)
- [Object Identification Under Known Dynamics: A PIRNN Approach for UAV Classification](https://mlsanity.com/paper/2509.21405/) (2025)

## Abstract (arXiv)

Model Predictive Control (MPC) is a state-of-the-art (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional constraints, increasing the hardness of the problem. The problem exacerbates in performance-critical applications, when more compute is required in lesser time. Data-driven regression methods such as Neural Networks have been proposed in the past to approximate system dynamics. However, such models rely on high volumes of labeled data, in the absence of symbolic analytical priors. This incurs non-trivial training overheads. Physics-informed Neural Networks (PINNs) have gained traction for approximating non-linear system of ordinary differential equations (ODEs), with reasonable accuracy. In this work, we propose a Robust Adaptive MPC framework via PINNs (RAMP-Net), which uses a neural network trained partly from simple ODEs and partly from data. A physics loss is used to learn simple ODEs representing ideal dynamics. Having access to analytical functions inside the loss function acts as a regularizer, enforcing robust behavior for parametric uncertainties. On the other hand, a regular data loss is used for adapting to residual disturbances (non-parametric uncertainties), unaccounted during mathematical modelling. Experiments are performed in a simulated environment for trajectory tracking of a quadrotor. We report 7.8% to 43.2% and 8.04% to 61.5% reduction in tracking errors for speeds ranging from 0.5 to 1.75 m/s compared to two SOTA regression based MPC methods.