Energy-Efficient Collaborative Transport of Tether-Suspended Payloads via Rotating Equilibrium

Abstract

Collaborative aerial transportation of tethered payloads is fundamentally limited by space, power, and weight constraints. Conventional approaches rely on static equilibrium conditions, where each vehicle tilts to generate the forces that ensure they maintain a formation geometry that avoids aerodynamic interactions and collision. This horizontal thrust component represents a significant energy penalty compared to the ideal case in which each vehicle produces purely vertical thrust to lift the payload. Operating in tighter tether configurations can minimize this effect, but at the cost of either having to fly the vehicles in closer proximity, which risks collision, or significantly increasing the length of the tether, which increases complexity and reduces potential use-cases. We propose operating the tether-suspended flying system at a rotating equilibrium. By maintaining steady circular motion, centrifugal forces provide the necessary horizontal tether tension, allowing each quadrotor to generate purely vertical thrust and thus reducing the total force (and power) required compared to an equilibrium where the thrusts are not vertical. It also allows for a wider range of tether configurations to be used without sacrificing efficiency. Results demonstrate that rotating equilibria can reduce power consumption relative to static lifting by up to 20%, making collaborative aerial solutions more practically relevant.

Figures (8)

• Figure 1: Overlayed pictures showing a rotating payload transport system. As it can be observed, even with large tether angles, the vehicles thrust axes are nearly vertical. In this particular experiment, the tether angle $\beta=45^\circ$ from vertical, and the vehicles are rotating with a tangential velocity of $\sim1.8\,\mathrm{m\cdot s^{-1}}$.
• Figure 2: Diagram of two quadcopters transporting a point mass payload through a tether. The $C$ reference frame has origin on the payload attachment point, and the two quadcopters lie on the plane defined by $\text{span}(\mathbf{1}_C, \mathbf{3}_C)$. The $C$ frame rotates with respect to the earth-fixed frame $E$ with angular velocity $\omega_C \mathbf{3}_C$, and its orientation with respect to $E$ is described by a rotation by $\theta$ about $\mathbf{3}_E$. When $\omega_C = 0$ the system is a classical, static dual-UAV transport system.
• Figure 3: Block diagram of the system architecture. The higher level LQR controller runs at $50\,\mathrm{Hz}$, while the quadcopters' onboard attitude controllers run at $500\,\mathrm{Hz}$, providing an effective separation of timescales.
• Figure 4: Free body diagram of a quadcopter in the rotating frame.
• Figure 5: Plot of power consumption (according to \ref{['eq:power-consmp']}) versus tether angle for both the static case and the optimal spinning case, where $\omega_C = \omega_C^*$. As it is possible to observe, in the static case the power consumption grows, approaching infinity as $\beta\rightarrow90^\circ$, while in the rotating case it remains constant.