🤖 AI Summary
Existing physics engines for robotics struggle to simultaneously ensure stable simulation, high-fidelity rigid contact modeling, and full differentiability with respect to states, actions, and system parameters. To address this, we propose Dojo—the first end-to-end differentiable physics engine designed specifically for robotics. Dojo uniquely integrates variational integrators with a second-order cone nonlinear complementarity problem (NCP) solver, guaranteeing energy and momentum conservation during contact and enabling smooth, analytic gradient computation across contact events. It further employs a customized primal-dual interior-point method for efficient implicit differentiation. Evaluated on motion planning, policy optimization, and system identification tasks, Dojo demonstrates significantly improved gradient accuracy and faster optimization convergence in challenging rigid-contact scenarios.
📝 Abstract
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 implicit differentiation to efficiently compute smooth gradients that provide useful information through contact events. We demonstrate Dojo with a number of examples including: planning, policy optimization, and system identification, that demonstrate the engine's unique ability to simulate hard contact while providing smooth, analytic gradients.
