Extending Lagrangian and Hamiltonian Neural Networks with Differentiable\n Contact Models

Abstract

The incorporation of appropriate inductive bias plays a critical role in\nlearning dynamics from data. A growing body of work has been exploring ways to\nenforce energy conservation in the learned dynamics by encoding Lagrangian or\nHamiltonian dynamics into the neural network architecture. These existing\napproaches are based on differential equations, which do not allow\ndiscontinuity in the states and thereby limit the class of systems one can\nlearn. However, in reality, most physical systems, such as legged robots and\nrobotic manipulators, involve contacts and collisions, which introduce\ndiscontinuities in the states. In this paper, we introduce a differentiable\ncontact model, which can capture contact mechanics: frictionless/frictional, as\nwell as elastic/inelastic. This model can also accommodate inequality\nconstraints, such as limits on the joint angles. The proposed contact model\nextends the scope of Lagrangian and Hamiltonian neural networks by allowing\nsimultaneous learning of contact and system properties. We demonstrate this\nframework on a series of challenging 2D and 3D physical systems with different\ncoefficients of restitution and friction. The learned dynamics can be used as a\ndifferentiable physics simulator for downstream gradient-based optimization\ntasks, such as planning and control.\n