Catenary Tether Shape Analysis for a UAV - USV Team

Abstract

The quasi-static catenary curve of a semi-slack tether between an essentially stationary unmanned air vehicle (UAV) and a small unmanned surface vehicle (USV) is investigated and characterized. An empirical analysis, performed over a discretized space of vertical and horizontal separations of the two vehicles, determines an optimum cable length & tension for maximizing system robustness during the vertical heave of the USV due to high seas. Operating at this optimum condition allows for equal displacements of the USV in the up and down directions, minimizing the possibility of both fouling (with the tether touching the water) and excessive downforce on the UAV (with the tether pulled taut) during dynamic heave events. Scaling the horizontal offset, tether length, and tension by the flying height collapses all empirical results into convenient curves depending only on a nondimensional relative position parameter $(\Delta x/\Delta y)$, accurately fit by low order polynomials. This eliminates the need for a lookup table, and decreases computation time during implementation. The heave robustness analysis results in a recommended operating relative position of $\Delta x/\Delta y\approx.46$. Experimental results are presented and confirm the catenary analysis for the proposed tether.