The Geometry of Coordinated Trajectories for Non-stop Flying Carriers Holding a Cable-Suspended Load

Abstract

This work considers the problem of using multiple aerial carriers to hold a cable-suspended load while remaining in periodic motion at all times. Using a novel differential geometric perspective, it is shown that the problem may be recast as that of finding an immersion of the unit circle into the smooth manifold of admissible configurations. Additionally, this manifold is shown to be path connected under a mild assumption on the attachment points of the carriers to the load. Based on these ideas, a family of simple linear solutions to the original problems is presented that overcomes the constraints of alternative solutions previously proposed in the literature. Simulation results demonstrate the flexibility of the theory in identifying suitable solutions.