Entanglement Definitions for Tethered Robots: Exploration and Analysis

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.