We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the task for which the system has been designed. From a purely topological point of view, this is a homotopy invariant of a map which generalizes the classical topological complexity of a space.

中文翻译：

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工作图的拓扑复杂度

我们介绍了与机器人系统相关的工作图的拓扑复杂性。从广义上讲，这衡量了任何算法控制的复杂性，不仅仅是给定系统的配置空间的运动，还有系统设计的任务。从纯粹拓扑的角度来看，这是一个映射的同伦不变量，它概括了空间的经典拓扑复杂性。