# Adaptive Control of SE(3) Hamiltonian Dynamics with Learned Disturbance Features

arXiv: https://arxiv.org/abs/2109.09974 · HTML: https://mlsanity.com/paper/2109.09974/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 21 Sep 2021.

## Builds on (most cited first, 13 of 13)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Learning to Fly -- a Gym Environment with PyBullet Physics for Reinforcement Learning of Multi-agent Quadcopter Control](https://mlsanity.com/paper/2103.02142/) (2021)
- [Meta-Learning Priors for Efficient Online Bayesian Regression](https://mlsanity.com/paper/1807.08912/) (2018)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [Meta-Adaptive Nonlinear Control: Theory and Algorithms](https://mlsanity.com/paper/2106.06098/) (2021)
- [Performance, Precision, and Payloads: Adaptive Nonlinear MPC for Quadrotors](https://mlsanity.com/paper/2109.04210/) (2021)
- [Asynchronous Deep Model Reference Adaptive Control](https://mlsanity.com/paper/2011.02920/) (2020)
- [L1-GP: L1 Adaptive Control with Bayesian Learning](https://mlsanity.com/paper/2004.14594/) (2020)
- [Geometric Adaptive Control with Neural Networks for a Quadrotor UAV in Wind fields](https://mlsanity.com/paper/1903.02091/) (2019)
- [Geometric Adaptive Tracking Control of a Quadrotor UAV on SE(3) for Agile Maneuvers](https://mlsanity.com/paper/1411.2986/) (2014)

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

- [When are dynamical systems learned from time series data statistically accurate?](https://mlsanity.com/paper/2411.06311/) (2024)
- [Pseudo-Hamiltonian neural networks for learning partial differential equations](https://mlsanity.com/paper/2304.14374/) (2023)
- [Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems](https://mlsanity.com/paper/2211.16006/) (2022)
- [Context-Aware Deep Lagrangian Networks for Model Predictive Control](https://mlsanity.com/paper/2506.15249/) (2025)
- [Pseudo-Hamiltonian system identification](https://mlsanity.com/paper/2305.06920/) (2023)
- [Optimal Potential Shaping on SE(3) via Neural ODEs on Lie Groups](https://mlsanity.com/paper/2401.15107/) (2024)

## Abstract (arXiv)

Adaptive control is a critical component of reliable robot autonomy in rapidly changing operational conditions. Adaptive control designs benefit from a disturbance model, which is often unavailable in practice. This motivates the use of machine learning techniques to learn disturbance features from training data offline, which can subsequently be employed to compensate the disturbances online. This paper develops geometric adaptive control with a learned disturbance model for rigid-body systems, such as ground, aerial, and underwater vehicles, that satisfy Hamilton's equations of motion over the SE(3) manifold. Our design consists of an offline disturbance model identification stage, using a Hamiltonian-based neural ordinary differential equation (ODE) network trained from state-control trajectory data, and an online adaptive control stage, estimating and compensating the disturbances based on geometric tracking errors. We demonstrate our adaptive geometric controller in trajectory tracking simulations of fully-actuated pendulum and under-actuated quadrotor systems.