  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 incorporating Lagrangian
or Hamiltonian dynamics into the design of the neural network architecture.
However, these existing approaches are based on differential equations, which
does not allow discontinuity in the states, and thereby limits the class of
systems one can learn. Real 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, both frictionless and frictional, as well
as both elastic and 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 properties and system properties. We
demonstrate this framework on a series of challenging 2D and 3D physical
systems with different coefficients of restitution and friction.
