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Path planning for multiple tethered robots is a challenging problem due tothe complex interactions among the cables and the possibility of severeentanglements. Previous works on this problem either consider idealistic cablemodels or provide no guarantee for entanglement-free paths. In this work, wepresent a new approach to address this problem using the theory of braids. Byestablishing a topological equivalence between the physical cables and thespace-time trajectories of the robots, and identifying particular braidpatterns that emerge from the entangled trajectories, we obtain the key findingthat all complex entanglements stem from a finite number of interactionpatterns between 2 or 3 robots. Hence, non-entanglement can be guaranteed byavoiding these interaction patterns in the trajectories of the robots. Based onthis finding, we present a graph search algorithm using the permutation grid toefficiently search for a feasible topology of paths and reject braid patternsthat result in an entanglement. We demonstrate that the proposed algorithm canachieve 100% goal-reaching capability without entanglement for up to 10 droneswith a slack cable model in a high-fidelity simulation platform. Thepracticality of the proposed approach is verified using three small tetheredUAVs in indoor flight experiments.

Path Planning for Multiple Tethered Robots Using Topological Braids