让机器人仿真在形态大变时仍能求导，支持形状与控制联合优化。
SDRS: Shape-Differentiable Robot Simulator
- 用凸多面体表示机器人形状，实现几何拓扑变化下的全局可微。
- 引入分离超平面作为无质量辅助实体，保证接触力学可微。
- 适合需要联合优化机器人结构与运动的智能设计场景。
机器人仿真在多个领域不可或缺，近期研究通过引入梯度信息提升了其功能。然而，现有可微机器人仿真器在机器人经历显著形状变化时会遭遇不可微奇点。为此，我们提出形状可微机器人仿真器（SDRS），可在机器人形状发生显著变化时保持可微性。SDRS的核心创新在于使用一组凸多面体表示机器人形状，从而将任意一对凸多面体间的接触力学推广为平滑的罚函数形式。基于分离超平面定理，SDRS为每对接触的凸多面体引入一个分离平面，该平面作为零质量辅助实体，其状态由最小作用量原理决定。这一设计确保了即使在几何和拓扑发生显著变化时仍保持全局可微性。为展示SDRS的实际价值，我们提供了机器人协同设计实例，其中机器人形状与控制动作同时优化。
原文摘要 · Abstract (English)
Robot simulators are indispensable tools across many fields, and recent research has significantly improved their functionality by incorporating additional gradient information. However, existing differentiable robot simulators suffer from non-differentiable singularities, when robots undergo substantial shape changes. To address this, we present the Shape-Differentiable Robot Simulator (SDRS), designed to be differentiable under significant robot shape changes. The core innovation of SDRS lies in its representation of robot shapes using a set of convex polyhedrons. This approach allows us to generalize smooth, penalty-based contact mechanics for interactions between any pair of convex polyhedrons. Using the separating hyperplane theorem, SDRS introduces a separating plane for each pair of contacting convex polyhedrons. This separating plane functions as a zero-mass auxiliary entity, with its state determined by the principle of least action. This setup ensures global differentiability, even as robot shapes undergo significant geometric and topological changes. To demonstrate the practical value of SDRS, we provide examples of robot co-design scenarios, where both robot shapes and control movements are optimized simultaneously.
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