# Context-Aware Deep Lagrangian Networks for Model Predictive Control

arXiv: https://arxiv.org/abs/2506.15249 · HTML: https://mlsanity.com/paper/2506.15249/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 18 Jun 2025.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Preparing for the Unknown: Learning a Universal Policy with Online System Identification](https://mlsanity.com/paper/1702.02453/) (2017)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems](https://mlsanity.com/paper/1907.04489/) (2019)
- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [HPIPM: a high-performance quadratic programming framework for model predictive control](https://mlsanity.com/paper/2003.02547/) (2020)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Bayesian Multi-Task Learning MPC for Robotic Mobile Manipulation](https://mlsanity.com/paper/2211.10270/) (2022)
- [Port-Hamiltonian Neural ODE Networks on Lie Groups For Robot Dynamics Learning and Control](https://mlsanity.com/paper/2401.09520/) (2024)
- [Metalearning generalizable dynamics from trajectories](https://mlsanity.com/paper/2301.00957/) (2023)
- [Meta Learning MPC using Finite-Dimensional Gaussian Process Approximations](https://mlsanity.com/paper/2008.05984/) (2020)
- [Adaptive Control of SE(3) Hamiltonian Dynamics with Learned Disturbance Features](https://mlsanity.com/paper/2109.09974/) (2021)
- [Machine Learning with Physics Knowledge for Prediction: A Survey](https://mlsanity.com/paper/2408.09840/) (2024)
- [Safe Machine-Learning-supported Model Predictive Force and Motion Control in Robotics](https://mlsanity.com/paper/2303.04569/) (2023)
- [Physically Consistent Online Inertial Adaptation for Humanoid Loco-manipulation](https://mlsanity.com/paper/2405.07901/) (2024)
- [Adaptive Control based Friction Estimation for Tracking Control of Robot Manipulators](https://mlsanity.com/paper/2409.05054/) (2024)
- [Meta-Learning Augmented MPC for Disturbance-Aware Motion Planning and Control of Quadrotors](https://mlsanity.com/paper/2410.06325/) (2024)

## Built on by (most cited first, 2 of 2)

- [STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matching](https://mlsanity.com/paper/2603.08478/) (2026)
- [Data-Driven Physics Embedded Dynamics with Predictive Control and Reinforcement Learning for Quadrupeds](https://mlsanity.com/paper/2603.14333/) (2026)

## Abstract (arXiv)

Controlling a robot based on physics-consistent dynamic models, such as Deep Lagrangian Networks (DeLaN), can improve the generalizability and interpretability of the resulting behavior. However, in complex environments, the number of objects to potentially interact with is vast, and their physical properties are often uncertain. This complexity makes it infeasible to employ a single global model. Therefore, we need to resort to online system identification of context-aware models that capture only the currently relevant aspects of the environment. While physical principles such as the conservation of energy may not hold across varying contexts, ensuring physical plausibility for any individual context-aware model can still be highly desirable, particularly when using it for receding horizon control methods such as model predictive control (MPC). Hence, in this work, we extend DeLaN to make it context-aware, combine it with a recurrent network for online system identification, and integrate it with an MPC for adaptive, physics-consistent control. We also combine DeLaN with a residual dynamics model to leverage the fact that a nominal model of the robot is typically available. We evaluate our method on a 7-DOF robot arm for trajectory tracking under varying loads. Our method reduces the end-effector tracking error by 39%, compared to a 21% improvement achieved by a baseline that uses an extended Kalman filter.