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.

本文提出了一种可处理摩擦接触的可微动力学求解器，它统一了刚体和可变形物体。通过正交和切向接触力的原则性平滑化，我们的方法规避了摩擦接触非光滑特性的主要难题。我们将这种新接触模型与全隐式时间积分相结合，得到了一个具有解析微分性和健壮高效的动力学求解器。与伴随灵敏度分析相结合，我们的公式为目标函数景观的优化提供了自适应权衡模拟准确性和平滑性的梯度。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，我们对我们的方法进行了全面分析。我们还展示了我们的可微模拟器在可变形物体的参数估计、机器人操纵的运动规划、合规步行机器人的轨迹优化以及高效的自我监督学习控制策略方面的应用。