构建连续拓扑模型，高效解决系绳机器人的路径规划问题。
Efficient Computation of a Continuous Topological Model of the Configuration Space of Tethered Mobile Robots
- 基于工作区多边形建模，建立配置空间与覆盖空间的联系。
- 计算时间仅为传统同伦图的几分之一，且支持连续路径规划。
- 适用于多种路径规划算法，提升效率与灵活性。
尽管系绳机器人路径规划问题在过去几十年受到广泛关注，现有方法通常依赖配置空间的离散表示，未能同时捕捉系绳的拓扑特性与机器人的连续位置。本文从工作区的多边形表示出发，显式构建系绳机器人的配置空间拓扑模型。首先建立系绳机器人配置空间与工作区通用覆盖空间之间的联系，进而提出一种算法，计算配置空间的单纯复形模型。实验证明，该方法显著优于其他配置空间表示方法。所提模型计算耗时仅为传统同伦增强图的一小部分，且保持连续性，可兼容多种路径规划算法，有效提升求解效率。
原文摘要 · Abstract (English)
Despite the attention that the problem of path planning for tethered robots has garnered in the past few decades, the approaches proposed to solve it typically rely on a discrete representation of the configuration space and do not exploit a model that can simultaneously capture the topological information of the tether and the continuous location of the robot. In this work, we explicitly build a topological model of the configuration space of a tethered robot starting from a polygonal representation of the workspace where the robot moves. To do so, we first establish a link between the configuration space of the tethered robot and the universal covering space of the workspace, and then we exploit this link to develop an algorithm to compute a simplicial complex model of the configuration space. We show how this approach improves the performances of existing algorithms that build other types of representations of the configuration space. The proposed model can be computed in a fraction of the time required to build traditional homotopy-augmented graphs, and is continuous, allowing to solve the path planning task for tethered robots using a broad set of path planning algorithms.
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