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

TL;DR

This paper introduces a differential geometric approach to coordinating multiple aerial carriers holding a cable-suspended load, providing new solutions that ensure continuous motion and flexibility in configuration.

Contribution

It recasts the problem as an immersion of the circle into a configuration manifold and presents a family of simple linear solutions surpassing previous methods.

Findings

The configuration manifold is path connected under mild conditions.

A family of linear solutions effectively maintains continuous motion.

Simulations confirm the practical flexibility of the proposed solutions.

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.