We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.

中文翻译：

---

ADD：具有摩擦接触的多体系统的解析可微动力学

我们提出了一个可微的动力学求解器，它能够在一个统一的框架内处理刚性和可变形物体的摩擦接触。通过法向和切向接触力的原则性缓和，我们的方法规避了摩擦接触的非光滑性质所固有的主要困难。我们将这种新的接触模型与完全隐式时间积分相结合，以获得可分析微分的强大且高效的动力学求解器。结合伴随敏感性分析，我们的公式可以实现基于梯度的优化，并在模拟精度和目标函数景观的平滑度之间进行自适应权衡。我们在一组涉及刚体、粘弹性材料和耦合多体系统的模拟示例上彻底分析了我们的方法。