提出高效且梯度稳定的接触模型，提升物理模拟优化效果。
Efficient Differentiable Contact Model with Long-range Influence
- 设计满足平滑梯度条件的接触模型，避免梯度突变或消失。
- 在简单初始化下生成复杂接触控制信号，成功完成多种运动与操作任务。
- 适合需要稳定梯度的机器人控制与物理仿真优化场景。
随着可微分物理的发展，其在模型预测控制、机器人设计优化和神经偏微分方程求解器等下游应用中的作用日益重要。然而，可微分模拟器提供的导数信息常出现突变或完全消失，阻碍了基于梯度优化器的收敛。本文表明，这种不稳定的梯度行为与接触模型的设计密切相关。我们进一步提出接触模型应满足的一组性质，以确保梯度行为良好。最后，我们提出一种适用于可微分刚体模拟器的实际接触模型，满足所有上述性质的同时保持计算效率。实验表明，即使从简单初始状态开始，该模型也能发现复杂的、富含接触的控制信号，成功实现多种下游的运动与操作任务。
原文摘要 · Abstract (English)
With the maturation of differentiable physics, its role in various downstream applications: such as model predictive control, robotic design optimization, and neural PDE solvers, has become increasingly important. However, the derivative information provided by differentiable simulators can exhibit abrupt changes or vanish altogether, impeding the convergence of gradient-based optimizers. In this work, we demonstrate that such erratic gradient behavior is closely tied to the design of contact models. We further introduce a set of properties that a contact model must satisfy to ensure well-behaved gradient information. Lastly, we present a practical contact model for differentiable rigid-body simulators that satisfies all of these properties while maintaining computational efficiency. Our experiments show that, even from simple initializations, our contact model can discover complex, contact-rich control signals, enabling the successful execution of a range of downstream locomotion and manipulation tasks.
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