In this article we consider the problem of tether entanglement for tethered robots. In many applications, such as maintenance of underwater structures, aerial inspection, and underground exploration, tethered robots are often used in place of standalone (i.e., untethered) ones. However, the presence of a tether also introduces the risk for it to get entangled with obstacles present in the environment or with itself. To avoid these situations, a non-entanglement constraint can be considered in the motion planning problem for tethered robots. This constraint can be expressed either as a set of specific tether configurations that must be avoided, or as a quantitative measure of a `level of entanglement' that can be minimized. However, the literature lacks a generally accepted definition of entanglement, with existing definitions being limited and partial. Namely, the existing entanglement definitions either require a taut tether to come into contact with an obstacle or with another tether, or they require for the tether to do a full loop around an obstacle. In practice, this means that the existing definitions do not effectively cover all instances of tether entanglement. Our goal in this article is to bridge this gap and provide new definitions of entanglement, which, together with the existing ones, can be effectively used to qualify the entanglement state of a tethered robot in diverse situations. The new definitions find application mainly in motion planning for tethered robot systems, where they can be used to obtain more safe and robust entanglement-free trajectories. The present article focuses exclusively on the presentation and analysis of the entanglement definitions. The application of the definitions to the motion planning problem is left for future work.

翻译：本文研究了系绳机器人中缆绳缠绕的问题。在水下结构维护、空中巡检、地下勘探等应用中，系绳机器人常取代独立（即无系绳）机器人使用。然而，缆绳的存在也带来了与环境中障碍物或自身发生缠绕的风险。为避免此类情况，可在系绳机器人运动规划中引入非缠绕约束，该约束既可表述为必须避免的一组特定缆绳构型，也可表述为可最小化的"缠绕程度"定量度量。但现有文献缺乏普遍接受的缠绕定义，已有定义存在局限性和片面性：现有缠绕定义要么要求绷紧的缆绳与障碍物或其他缆绳接触，要么要求缆绳绕障碍物完成完整环绕。实践中这意味着现有定义无法有效涵盖所有缆绳缠绕情形。本文旨在弥补这一空白，提出新的缠绕定义，使其与现有定义相结合，能有效表征系绳机器人在不同场景下的缠绕状态。新定义主要应用于系绳机器人系统的运动规划，可用于获得更安全鲁棒的无缠绕轨迹。本文专注于缠绕定义的阐述与分析，将其应用于运动规划问题留待未来工作。