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The incorporation of appropriate inductive bias plays a critical role inlearning dynamics from data. A growing body of work has been exploring ways toenforce energy conservation in the learned dynamics by encoding Lagrangian orHamiltonian dynamics into the neural network architecture. These existingapproaches are based on differential equations, which do not allowdiscontinuity in the states and thereby limit the class of systems one canlearn. However, in reality, most physical systems, such as legged robots androbotic manipulators, involve contacts and collisions, which introducediscontinuities in the states. In this paper, we introduce a differentiablecontact model, which can capture contact mechanics: frictionless/frictional, aswell as elastic/inelastic. This model can also accommodate inequalityconstraints, such as limits on the joint angles. The proposed contact modelextends the scope of Lagrangian and Hamiltonian neural networks by allowingsimultaneous learning of contact and system properties. We demonstrate thisframework on a series of challenging 2D and 3D physical systems with differentcoefficients of restitution and friction. The learned dynamics can be used as adifferentiable physics simulator for downstream gradient-based optimizationtasks, such as planning and control.

Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models