Path Planning for Multiple Tethered Robots Using Topological Braids

Muqing Cao
Nanyang Technological University
Kun Cao
Nanyang Technological University
Shenghai Yuan
Nanyang Technological University
Kangcheng Liu
Nanyang Technological University
Yan Loi Wong
National University of Singapore
Lihua Xie
Nanyang Technological University
Paper Website

Paper ID 106

Session 14. Multi-Robot and Aerial Systems

Poster Session Friday, July 14

Poster 10

Abstract: 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.