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：尽管近年来在多机器人轨迹规划与单系留机器人路径规划方面取得了进展，但规划多个系留机器人在不产生缠绕的情况下到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解决方案。首先，我们提出了一种多机器人缆索感知的同伦表示方法，通过该方法可高效评估潜在路径的可行性与安全性，具体包括：（1）沿路径到达目标所需缆索长度；（2）与其他机器人缆索发生缠绕的风险。随后，我们将该表示方法应用于一种分布式在线规划框架中，该框架包含基于图的运动动力学轨迹搜索器与基于优化的轨迹优化器，可生成无缠绕、无碰撞且动力学可行的轨迹。所提同伦表示方法的效率与现有单/多系留机器人规划方法进行了比较。包含多达8架无人机的仿真实验验证了该方法在防止缠绕及实时性方面的有效性。搭载3架系留无人机的飞行实验进一步验证了该方法的实用性。