论文标题
与触点的可区分物理模拟：它们具有正确的梯度W.R.T.位置，速度和控制？
Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?
论文作者
论文摘要
近年来，越来越多的工作集中在可区分的物理模拟上，并产生了一系列开源项目，例如微小的可区分模拟器，敏捷物理，difftaichi，brax，brax，warp，dojo和diffcosim。通过使物理模拟端到端可区分，我们可以执行基于梯度的优化和学习任务。大多数可区分的模拟器都考虑对象之间的碰撞和接触，但它们使用不同的触点模型来实现可怜性。在本文中，我们概述了四种可区分的接触公式：线性互补问题（LCP），凸优化模型，合规模型和基于位置的动力学（PBD）。我们分析和比较这些模型计算的梯度，并表明梯度并不总是正确的。我们还通过将学习策略与分析形式的最佳策略进行比较，证明了他们学习最佳控制策略的能力。复制实验结果的代码库可在https://github.com/desmondzhong/diff_sim_grads上获得。
In recent years, an increasing amount of work has focused on differentiable physics simulation and has produced a set of open source projects such as Tiny Differentiable Simulator, Nimble Physics, diffTaichi, Brax, Warp, Dojo and DiffCoSim. By making physics simulations end-to-end differentiable, we can perform gradient-based optimization and learning tasks. A majority of differentiable simulators consider collisions and contacts between objects, but they use different contact models for differentiability. In this paper, we overview four kinds of differentiable contact formulations - linear complementarity problems (LCP), convex optimization models, compliant models and position-based dynamics (PBD). We analyze and compare the gradients calculated by these models and show that the gradients are not always correct. We also demonstrate their ability to learn an optimal control strategy by comparing the learned strategies with the optimal strategy in an analytical form. The codebase to reproduce the experiment results is available at https://github.com/DesmondZhong/diff_sim_grads.
