提出可微软体机器人仿真方法，支持摩擦接触下的精确梯度计算。
Differentiable Simulation of Soft Robots with Frictional Contacts
- 基于有限元框架，统一求解含接触的力学方程导数。
- 能处理碰撞与摩擦阶段的非光滑动态，保持计算效率。
- 适合强化学习控制、系统校准等需要梯度的任务。
近年来，软体机器人仿真器已具备模拟多种材料（如弹性、超弹性）和驱动方式（如气动、缆线驱动、伺服电机）的功能，并支持校准、设计和控制等任务。然而，在存在物理接触交互的情况下，高效且准确地计算导数仍是难题。引入这些导数可显著提升强化学习和轨迹优化等控制方法的收敛速度，支持基于梯度的设计优化，或实现模型降维的端到端机器学习方法。本文提出一种在有限元框架内统一计算力学方程导数的方法，包含以非线性互补问题建模的接触交互。该方法同时处理碰撞与摩擦阶段，考虑其非光滑动力学特性，并利用网格模型带来的稀疏性。通过多个软体系统控制与校准实例验证了其有效性。
原文摘要 · Abstract (English)
In recent years, soft robotics simulators have evolved to offer various functionalities, including the simulation of different material types (e.g., elastic, hyper-elastic) and actuation methods (e.g., pneumatic, cable-driven, servomotor). These simulators also provide tools for various tasks, such as calibration, design, and control. However, efficiently and accurately computing derivatives within these simulators remains a challenge, particularly in the presence of physical contact interactions. Incorporating these derivatives can, for instance, significantly improve the convergence speed of control methods like reinforcement learning and trajectory optimization, enable gradient-based techniques for design, or facilitate end-to-end machine-learning approaches for model reduction. This paper addresses these challenges by introducing a unified method for computing the derivatives of mechanical equations within the finite element method framework, including contact interactions modeled as a nonlinear complementarity problem. The proposed approach handles both collision and friction phases, accounts for their nonsmooth dynamics, and leverages the sparsity introduced by mesh-based models. Its effectiveness is demonstrated through several examples of controlling and calibrating soft systems.
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