# Safe Autonomous Navigation for Systems with Learned SE(3) Hamiltonian Dynamics

arXiv: https://arxiv.org/abs/2112.04639 · HTML: https://mlsanity.com/paper/2112.04639/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2021.

## Built on by (most cited first, 1 of 1)

- [Learning Control-Oriented Dynamical Structure from Data](https://mlsanity.com/paper/2302.02529/) (2023)

## Abstract (arXiv)

Safe autonomous navigation in unknown environments is an important problem for mobile robots. This paper proposes techniques to learn the dynamics model of a mobile robot from trajectory data and synthesize a tracking controller with safety and stability guarantees. The state of a rigid-body robot usually contains its position, orientation, and generalized velocity and satisfies Hamilton's equations of motion. Instead of a hand-derived dynamics model, we use a dataset of state-control trajectories to train a translation-equivariant nonlinear Hamiltonian model represented as a neural ordinary differential equation (ODE) network. The learned Hamiltonian model is used to synthesize an energy-shaping passivity-based controller and derive conditions which guarantee safe regulation to a desired reference pose. We enable adaptive tracking of a desired path, subject to safety constraints obtained from obstacle distance measurements. The trade-off between the robot's energy and the distance to safety constraint violation is used to adaptively govern a reference pose along the desired path. Our safe adaptive controller is demonstrated on a simulated hexarotor robot navigating in an unknown environments.