Dual Quaternion Control of UAVs with Cable-suspended Load

TL;DR

The paper addresses the control problem of UAVs carrying a cable-suspended load, a challenging underactuated system due to load swing. It introduces a unified dual-quaternion framework that represents the UAV and sling-load kinematics and dynamics on $SE(3)$, enabling integrated lifting and trajectory-tracking control. The authors derive a dual-quaternion dynamic model, formulate error dynamics, and design separate control laws for slack and taut cable states along a three-mode lifting sequence (Setup, Pull, Raise). Two simulation studies demonstrate accurate load lifting and robust trajectory tracking with improved stability compared with a geometric controller. This work advances cargo-UAV control by leveraging dual quaternions for compact, singularity-free, and efficient pose representation.

Abstract

Modeling the kinematics and dynamics of robotics systems with suspended loads using dual quaternions has not been explored so far. This paper introduces a new innovative control strategy using dual quaternions for UAVs with cable-suspended loads, focusing on the sling load lifting and tracking problems. By utilizing the mathematical efficiency and compactness of dual quaternions, a unified representation of the UAV and its suspended load's dynamics and kinematics is achieved, facilitating the realization of load lifting and trajectory tracking. The simulation results have tested the proposed strategy's accuracy, efficiency, and robustness. This study makes a substantial contribution to present this novel control strategy that harnesses the benefits of dual quaternions for cargo UAVs. Our work also holds promise for inspiring future innovations in under-actuated systems control using dual quaternions.

Figures (7)

• Figure 1: Dual quaternion transformations among three frames. $R_I$ is the inertial frame, $\hat{\mathit{q}}_v$ denotes the transformation from $R_I$ to $R_v$ frame, and $\hat{\mathit{q}}_l$ is the transformation from $R_I$ to $R_l$. $\hat{\mathit{q}}_v^l$ indicates the transformation from $R_l$ to $R_v$.
• Figure 2: The lifting maneuver of the cargo UAV is separated into three modes: Setup, Pull, and Raise.
• Figure 3: States of the UAV during the lifting and trajectory tracking process. In these figures, the vertical black dashed lines indicate the time at which the UAV switches the mode to the next one, colored lines show the real values and shade areas are the errors with the desired values. The first figure depicts the position of the UAV and the second one presents the translational velocity. The two figures in the bottom row show the attitude and angular velocity of the UAV.
• Figure 4: States of the load during the lifting and tracking process. The vertical black dashed lines indicate the time at which the UAV switches the mode to the next one. The two figures in the first row show the position and translational velocity of the load. The figures in the bottom row depict the unit direction vector $\mathbf{q}_c$ and its derivative.
• Figure 5: State errors of the load during the lifting and tracking process. The vertical black dashed lines indicate the time at which the mode jumps from one to the next. The two figures in the first row show the position and translational velocity errors of the load. The figures in the bottom row depict the errors for the unit direction vector $q_c$ and its derivative.