A Differentiable Contact Model to Extend Lagrangian and Hamiltonian Neural Networks for Modeling Hybrid Dynamics

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.