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.

本文提出一种可微分的接触模型，扩展了拉格朗日和哈密敦神经网络的范围，并演示了在各种不同的物理系统上，该学习动态可以用作下游基于梯度的优化任务（如计划和控制）的不同 iable 物理模拟器。