Dojo: A Differentiable Physics Engine for Robotics

We present Dojo, a differentiable physics engine for robotics that prioritizes stable simulation, accurate contact physics, and differentiability with respect to states, actions, and system parameters. Dojo achieves stable simulation at low sample rates and conserves energy and momentum by employing a variational integrator. A nonlinear complementarity problem, with second-order cones for friction, models hard contact and is reliably solved using a custom primal-dual interior-point method. Special properties of the interior-point method are exploited using the implicit-function theorem to efficiently compute smooth gradients that provide useful information through contact events. We demonstrate Dojo's unique ability to simulate hard contact while providing smooth, analytic gradients with a number of examples, including trajectory optimization, reinforcement learning, and system identification.