This paper formally defines a robot system, including its sensing and actuation components, as a general, topological dynamical system. The focus is on determining general conditions under which various environments in which the robot can be placed are indistinguishable. A key result is that, under very general conditions, covering maps witness such indistinguishability. This formalizes the intuition behind the well studied loop closure problem in robotics. An important special case is where the sensor mapping reports an invariant of the local topological (metric) structure of an environment because such structure is preserved by (metric) covering maps. Whereas coverings provide a sufficient condition for the equivalence of environments, we also give a necessary condition using bisimulation. The overall framework is applied to unify previously identified phenomena in robotics and related fields, in which moving agents with sensors must make inferences about their environments based on limited data. Many open problems are identified.

翻译：本文正式将机器人系统（包括其感知与驱动组件）定义为一般拓扑动力系统，重点研究机器人可被放置于其中的各种环境在何种一般条件下不可区分。关键结论表明，在极为宽泛的条件下，覆盖映射可验证此类不可区分性——这形式化了机器人学中广泛研究的闭环问题背后的直观认知。一个重要的特例是传感映射报告环境局部拓扑（度量）结构的不变量，因为此类结构被（度量）覆盖映射所保持。尽管覆盖性提供了环境等价的充分条件，本文还利用互模拟给出了必要条件。该总体框架被应用于统一机器人学及相关领域中先前识别的现象——在这些领域内，携带传感器的移动主体必须基于有限数据对其所处环境进行推断。本文还指出了多个待解决的关键问题。