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.

我们提出了Jade，一个可微分的用于关节刚体的物理引擎，采用线性互补问题（LCP）模型来建模接触。与现有的可微分模拟相比，Jade提供了诸如无交叉碰撞模拟和多摩擦接触的稳定LCP解等特性。我们使用连续碰撞检测来检测碰撞时间并采用回溯策略来防止具有复杂几何形状的物体之间的交叉。我们推导出梯度计算以确保整个模拟过程在回溯机制下可微分。我们修改了流行的Dantzig算法，以获得多个摩擦接触下的有效解。我们进行了大量实验证明了我们可微分物理模拟在各种接触密集任务中的有效性。

Jade: 可微分的铰接刚体物理引擎，无交叉摩擦接触