We present a method for efficient differentiable simulation of articulated
bodies. This enables integration of articulated body dynamics into deep
learning frameworks, and gradient-based optimization of neural networks that
operate on articulated bodies. We derive the gradients of the forward dynamics
using spatial algebra and the adjoint method. Our approach is an order of
magnitude faster than autodiff tools. By only saving the initial states
throughout the simulation process, our method reduces memory requirements by
two orders of magnitude. We demonstrate the utility of efficient differentiable
dynamics for articulated bodies in a variety of applications. We show that
reinforcement learning with articulated systems can be accelerated using
gradients provided by our method. In applications to control and inverse
problems, gradient-based optimization enabled by our work accelerates
convergence by more than an order of magnitude.

本文提供了一种高效的可微分仿真方法，实现了关节体动力学与深度学习框架的集成，以及运用于操作关节体的神经网络的基于梯度的优化。通过空间代数和伴随方法，我们导出了前向动力学的梯度，并发现此方法比自动微分工具快一个数量级，且在仿真过程中只需保存初始状态即可，从而将内存需求减少了两个数量级。我们在多个应用中演示了关节体高效可微分动力学的实用性，特别是在强化学习、控制和逆问题方面，通过我们的方法实现的基于梯度的优化加速了收敛一个数量级以上。