  We present Jade, a differentiable physics engine for articulated rigid
bodies. Jade models contacts as the Linear Complementarity Problem (LCP).
Compared to existing differentiable simulations, Jade offers features including
intersection-free collision simulation and stable LCP solutions for multiple
frictional contacts. We use continuous collision detection to detect the time
of impact and adopt the backtracking strategy to prevent intersection between
bodies with complex geometry shapes. We derive the gradient calculation to
ensure the whole simulation process is differentiable under the backtracking
mechanism. We modify the popular Dantzig algorithm to get valid solutions under
multiple frictional contacts. We conduct extensive experiments to demonstrate
the effectiveness of our differentiable physics simulation over a variety of
contact-rich tasks.
