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.

翻译：我们提出Jade，一种用于铰接刚体的可微物理引擎。Jade将接触建模为线性互补问题(LCP)。与现有可微仿真相比，Jade具备无穿透碰撞仿真及多摩擦接触稳定LCP求解等特性。我们采用连续碰撞检测来检测碰撞时刻，并应用回溯策略防止复杂几何形状的物体间发生穿透。我们推导了回溯机制下的梯度计算方法，确保整个仿真过程可微。我们改进流行的Dantzig算法，使其能够获得多摩擦接触下的有效解。通过大量实验，我们证明了所提出的可微物理仿真在多种密集接触任务中的有效性。