Path planning for multiple tethered robots is a challenging problem due to the complex interactions among the cables and the possibility of severe entanglements. Previous works on this problem either consider idealistic cable models or provide no guarantee for entanglement-free paths. In this work, we present a new approach to address this problem using the theory of braids. By establishing a topological equivalence between the physical cables and the space-time trajectories of the robots, and identifying particular braid patterns that emerge from the entangled trajectories, we obtain the key finding that all complex entanglements stem from a finite number of interaction patterns between 2 or 3 robots. Hence, non-entanglement can be guaranteed by avoiding these interaction patterns in the trajectories of the robots. Based on this finding, we present a graph search algorithm using the permutation grid to efficiently search for a feasible topology of paths and reject braid patterns that result in an entanglement. We demonstrate that the proposed algorithm can achieve 100% goal-reaching capability without entanglement for up to 10 drones with a slack cable model in a high-fidelity simulation platform. The practicality of the proposed approach is verified using three small tethered UAVs in indoor flight experiments.

翻译：多系绳机器人的路径规划因缆线间的复杂相互作用及严重缠结的可能性而极具挑战性。以往研究或采用理想化缆线模型，或无法保证无缠结路径。本文提出一种基于辫带理论的新方法。通过建立物理缆线与机器人时空轨迹之间的拓扑等价性，并识别缠结轨迹中出现的特定辫带模式，我们获得关键发现：所有复杂缠结均源于两或三个机器人之间的有限种相互作用模式。因此，通过避免机器人轨迹中出现这些相互作用模式即可保证无缠结。基于此发现，我们提出一种利用置换网格的图搜索算法，高效搜索可行路径拓扑并排除导致缠结的辫带模式。实验表明，在基于松弛缆线模型的高保真仿真平台上，该算法可使多达10架无人机实现100%无缠结目标到达能力。我们通过三架小型缆系无人机室内飞行实验验证了所提方法的实用性。