In many systems motion occurs on deformed and deformable surfaces, setting up the possibility for dynamical interactions solely mediated by the coupling of the entities with their environment. Here we study the "two-body" dynamics of robot locomotion on a highly deformable spandex membrane in two scenarios: one in which a robot orbits a large central depression and the other where the two robots affect each other's motion solely through mutual environmental deformations. Inspired by the resemblance of the orbits of the single robot with those of general relativistic orbits around black holes, we recast the vehicle plus membrane dynamics in physical space into the geodesic motion of a "test particle" in a fiducial curved space-time and demonstrate how this framework facilitates understanding the observed dynamics. The two-robot problem also exhibits a resemblance with Einstein's general relativistic view of gravity, which in the words of Wheeler: "spacetime tells matter how to move; matter tells spacetime how to curve." We generalize this case the mapping to include a reciprocal coupling that translates into robotic curvature-based control schemes which modify interaction (promoting avoidance or aggregation) without long-range sensing. Our work provides a starting point for developing a mechanical analog gravity system as well as develops a framework that can provide insights into active matter in deformable environments and robot exploration in complex landscapes.

中文翻译：

---

氨纶上的自推进：广义相对论启发了变形环境中的机器人交互动力学

在许多系统中，运动发生在变形和可变形的表面上，建立了仅由实体与其环境耦合介导的动态相互作用的可能性。在这里，我们研究了机器人在两种情况下在高度可变形的氨纶膜上运动的“双体”动力学：一种是机器人绕着一个大的中央凹陷运行，另一种是两个机器人仅通过相互环境变形来影响彼此的运动。受单个机器人轨道与黑洞周围一般相对论轨道相似性的启发，我们将物理空间中的运载器和膜动力学重铸为基准弯曲时空中“测试粒子”的测地线运动，并证明该框架如何促进理解观察到的动态。两个机器人的问题也表现出与爱因斯坦关于引力的一般相对论观点的相似之处，用惠勒的话来说：“时空告诉物质如何运动；物质告诉时空如何弯曲。” 我们将这种情况下的映射概括为包括互逆耦合，该耦合转换为基于机器人曲率的控制方案，该方案修改交互（促进避免或聚集）而无需远程感知。我们的工作为开发机械模拟重力系统提供了一个起点，并开发了一个框架，可以深入了解可变形环境中的活性物质和复杂景观中的机器人探索。