  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.
