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Differentiable simulation enables gradients to be back-propagated throughphysics simulations. In this way, one can learn the dynamics and properties ofa physics system by gradient-based optimization or embed the wholedifferentiable simulation as a layer in a deep learning model for downstreamtasks, such as planning and control. However, differentiable simulation at itscurrent stage is not perfect and might provide wrong gradients that deteriorateits performance in learning tasks. In this paper, we study differentiablerigid-body simulation with contacts. We find that existing differentiablesimulation methods provide inaccurate gradients when the contact normaldirection is not fixed - a general situation when the contacts are between twomoving objects. We propose to improve gradient computation by continuouscollision detection and leverage the time-of-impact (TOI) to calculate thepost-collision velocities. We demonstrate our proposed method, referred to asTOI-Velocity, on two optimal control problems. We show that with TOI-Velocity,we are able to learn an optimal control sequence that matches the analyticalsolution, while without TOI-Velocity, existing differentiable simulationmethods fail to do so.

Improving Gradient Computation for Differentiable Physics Simulation with Contacts