Trajectory control of a suspended load with non-stopping flying carriers

TL;DR

This work tackles the problem of dynamically transporting a cable-suspended load with non-stopping flying carriers. It introduces a closed-loop framework that combines a load-wrench controller with an inner-loop trajectory generator and an online internal-force optimization to guarantee persistent carrier motion while achieving accurate load tracking. The approach leverages a time-varying grasp matrix $G(R_L)$ and its nullspace to shape internal forces $\lambda(t)$, with a necessary-and-sufficient condition ensuring carriers never stop. Validation includes preliminary experiments with three Crazyflie UAVs and simulations with four carriers, demonstrating load stability, feasible cable forces, and smooth carrier trajectories suitable for real-world deployment.

Abstract

This paper presents the first closed-loop control framework for cooperative payload transportation with non-stopping flying carriers. Building upon grasp-matrix formulations and internal force redundancy, we propose a feedback wrench controller that actively regulates the payload's pose while an optimization layer dynamically shapes internal-force oscillations to guarantee persistent carrier motion. Preliminary experimental results on multirotor UAVs validate the model assumptions, and numerical simulations demonstrate that the method successfully prevents carrier stagnation, achieves accurate load tracking, and generates physically feasible trajectories with smooth velocity profiles. The proposed framework not only advances the state of the art but also offers a reliable, versatile solution for future real-world applications requiring load transportation by coordinated non-stopping flying carriers.

Figures (11)

• Figure 1: Trajectory tracking of a suspended load using non-stopping flying carriers.
• Figure 2: Overall control scheme including the outer-loop load-wrench controller (green block), the inner-loop carrier-trajectory generator (blue blocks) and the optimization layer (red block).
• Figure 3: Experimental validation of the proposed model using three Crazyflie 2.0 UAVs. The results confirm that load motion and carrier velocities match the modeled dynamics.
• Figure 4: Components of the desired load trajectory. The load is initially static, then moves linearly along the x-axis, and finally remains static in its final position.
• Figure 5: Carrier trajectories (colored) without velocity optimization. Sharp turns lead to instantaneous stops of the carriers. A schematic representation of the vehicle is added in the last instants of the trajectories; higher transparency indicates a more distant time. Cables in the last configuration are represented as black lines, the attachment points on the load as dashed lines, and the load CoM as a cross. Axes are in meters.