Despite recent progress on trajectory planning of multiple robots and path planning of a single tethered robot, planning of multiple tethered robots to reach their individual targets without entanglements remains a challenging problem. In this paper, we present a complete approach to address this problem. Firstly, we propose a multi-robot tether-aware representation of homotopy, using which we can efficiently evaluate the feasibility and safety of a potential path in terms of (1) the cable length required to reach a target following the path, and (2) the risk of entanglements with the cables of other robots. Then, the proposed representation is applied in a decentralized and online planning framework that includes a graph-based kinodynamic trajectory finder and an optimization-based trajectory refinement, to generate entanglement-free, collision-free and dynamically feasible trajectories. The efficiency of the proposed homotopy representation is compared against existing single and multiple tethered robot planning approaches. Simulations with up to 8 UAVs show the effectiveness of the approach in entanglement prevention and its real-time capabilities. Flight experiments using 3 tethered UAVs verify the practicality of the presented approach.

翻译：尽管近年来多机器人轨迹规划和单台系留机器人路径规划取得了进展，但规划多台系留机器人在不产生缠绕的情况下抵达各自目标仍是一个具有挑战性的问题。本文提出了一种完整的方法来解决该问题。首先，我们提出了一种多机器人的缆绳感知同伦表示方法，利用该方法可有效评估潜在路径的可行性和安全性，具体包括：(1)沿路径到达目标所需的缆绳长度，以及(2)与其他机器人缆绳发生缠绕的风险。随后，将该表示方法应用于一种分散式在线规划框架中，该框架包含基于图的运动动力学轨迹搜索器和基于优化的轨迹细化模块，以生成无缠绕、无碰撞且动态可行的轨迹。所提出的同伦表示的效率与现有的单台和多台系留机器人规划方法进行了比较。涉及多达8架无人机的仿真实验验证了该方法在防止缠绕方面的有效性及其实时能力。使用3架系留无人机的飞行实验进一步验证了所提方法的实用性。