Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control

TL;DR

This paper introduces a Hamiltonian neural ODE framework on the SE(3) manifold that guarantees energy conservation for modeling rigid body dynamics, enabling stable control and trajectory tracking across diverse robotic platforms.

Contribution

It presents a novel Hamiltonian neural ODE model on SE(3) that inherently conserves energy and integrates control methods for stabilization and tracking in robotic systems.

Findings

Energy-conserving neural ODE accurately models rigid body dynamics.

Unified control approach effective across multiple robotic platforms.

Enhanced stability and trajectory tracking demonstrated in experiments.

Abstract

Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This motivates the use of machine learning techniques to approximate the robot dynamics over a training set of state-control trajectories. The dynamics of many robots, including ground, aerial, and underwater vehicles, are described in terms of their SE(3) pose and generalized velocity, and satisfy conservation of energy principles. This paper proposes a Hamiltonian formulation over the SE(3) manifold of the structure of a neural ordinary differential equation (ODE) network to approximate the dynamics of a rigid body. In contrast to a black-box ODE network, our formulation guarantees total energy conservation by construction. We develop energy shaping and damping injection control for the learned, potentially under-actuated SE(3) Hamiltonian dynamics to enable a unified approach for stabilization and trajectory tracking with various platforms, including pendulum, rigid-body, and quadrotor systems.