# Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems

## TL;DR

This paper introduces DeLaN 4EC, an extension of Deep Lagrangian Networks that learns energy-based control laws for under-actuated systems, demonstrating real-time control and swing-up capabilities on a physical pendulum.

## Contribution

It presents the first model learning approach capable of energy control using deep networks, integrating energy conservation and passivity into control of complex systems.

## Key findings

- DeLaN 4EC successfully controls a physical Furuta Pendulum in real-time.
- It learns to swing-up the pendulum, outperforming traditional system identification methods.
- The approach bridges model-based control insights with deep learning flexibility.

## Abstract

Applying Deep Learning to control has a lot of potential for enabling the intelligent design of robot control laws. Unfortunately common deep learning approaches to control, such as deep reinforcement learning, require an unrealistic amount of interaction with the real system, do not yield any performance guarantees, and do not make good use of extensive insights from model-based control. In particular, common black-box approaches -- that abandon all insight from control -- are not suitable for complex robot systems. We propose a deep control approach as a bridge between the solid theoretical foundations of energy-based control and the flexibility of deep learning. To accomplish this goal, we extend Deep Lagrangian Networks (DeLaN) to not only adhere to Lagrangian Mechanics but also ensure conservation of energy and passivity of the learned representation. This novel extension is embedded within generic model-based control laws to enable energy control of under-actuated systems. The resulting DeLaN for energy control (DeLaN 4EC) is the first model learning approach using generic function approximation that is capable of learning energy control. DeLaN 4EC exhibits excellent real-time control on the physical Furuta Pendulum and learns to swing-up the pendulum while the control law using system identification does not.