关于定向（参数化）运动规划算法的序列拓扑复杂性
On the Sequential topological complexity of directed (parametrized) motion planning algorithms
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中文总结 AI 辅助
该研究引入定向（参数化）拓扑复杂性的序列类似物，构建其基础理论并确立基本性质，计算发现同一基础空间上不同定向结构的该不变量取值不同。
中文摘要 AI 辅助
我们在运动规划问题的背景下，引入定向（参数化）拓扑复杂性的序列类似物，此类问题要求系统在遵循定向动力学和变化的外部参数的同时，遍历规定的中间状态序列。我们构建其基础理论，确立基本性质，并对若干类实例进行计算。我们的计算尤其表明，同一基础空间上不同的定向结构可具有该不变量的不同值。
英文摘要
We introduce sequential analogues of directed (parametrized) topological complexity, in the context of motion planning problems requiring a system to traverse a prescribed sequence of intermediate states while respecting directed dynamics and varying external parameters. We develop their basic theory, establish fundamental properties, and compute them for several classes of examples. Our computations show, in particular, that distinct directed structures on the same underlying space can have different values of this invariant.
