Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models

TL;DR

This paper introduces a differentiable contact model that extends Lagrangian and Hamiltonian neural networks to handle discontinuities like contact and collision, enabling more accurate learning of physical systems with contacts.

Contribution

It presents a novel differentiable contact model that incorporates contact mechanics into energy-conserving neural networks, allowing learning of systems with discontinuities.

Findings

Successfully models contact-rich physical systems

Enables differentiable simulation for optimization tasks

Handles friction, elasticity, and inequality constraints

Abstract

The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or Hamiltonian dynamics into the neural network architecture. These existing approaches are based on differential equations, which do not allow discontinuity in the states and thereby limit the class of systems one can learn. However, in reality, most physical systems, such as legged robots and robotic manipulators, involve contacts and collisions, which introduce discontinuities in the states. In this paper, we introduce a differentiable contact model, which can capture contact mechanics: frictionless/frictional, as well as elastic/inelastic. This model can also accommodate inequality constraints, such as limits on the joint angles. The proposed contact model extends the scope of Lagrangian and Hamiltonian neural networks by allowing simultaneous learning of contact and system properties. We demonstrate this framework on a series of challenging 2D and 3D physical systems with different coefficients of restitution and friction. The learned dynamics can be used as a differentiable physics simulator for downstream gradient-based optimization tasks, such as planning and control.