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In recent years, an increasing amount of work has focused on differentiablephysics simulation and has produced a set of open source projects such as TinyDifferentiable Simulator, Nimble Physics, diffTaichi, Brax, Warp, Dojo andDiffCoSim. By making physics simulations end-to-end differentiable, we canperform gradient-based optimization and learning tasks. A majority ofdifferentiable simulators consider collisions and contacts between objects, butthey use different contact models for differentiability. In this paper, weoverview four kinds of differentiable contact formulations - linearcomplementarity problems (LCP), convex optimization models, compliant modelsand position-based dynamics (PBD). We analyze and compare the gradientscalculated by these models and show that the gradients are not always correct.We also demonstrate their ability to learn an optimal control strategy bycomparing the learned strategies with the optimal strategy in an analyticalform. The codebase to reproduce the experiment results is available athttps://github.com/DesmondZhong/diff_sim_grads.

Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?