Modeling, Robust Control Design, and Experimental Verification for Quadrotor Carrying Cable-Suspended Payload

This paper originates from two well-accepted challenges in the control of a quadrotor with a cable-suspended payload: 1) designing a refined controller based on high-precision payload swing modeling to achieve the quantized prescribed robustness; and 2) resolving the trajectory tracking performance degradation issue caused by input saturation. To combat these challenges, we start with establishing a precise payload swing model. The experimental investigation reveals the fact that neglect of realistic factors like cable-joint dry friction and cable elasticity has significant impacts on the precision of the existing models, especially under small swing angles. Therefore, we propose a new integrated drag model including a novel sign of the payload airspeed-dependent term, which lumps all payload swing damping factors together. This model is experimentally verified to be precise to provide the payload swing disturbance spectrum for quantitatively designing the bandwidth of the uncertainty and disturbance estimator (UDE). Furthermore, we resolve the input saturation issue by augmenting the classic UDE-based controller with a tracking differentiator (TD). Rigorous performance analysis derives a clear relationship between the control performance and the UDE parameter, which forms a simple yet effective parameter tuning guideline for practical applications to ensure the prescribed robustness and trajectory tracking accuracy. The effectiveness and advantage of the proposed controller are verified via comparative experiments in different flight scenarios. Note to Practitioners—The control input saturation issue and multi-parameter optimization are frequently encountered in engineering practices. When applying the TD to address the input saturation, the selection of parameter r in the TD depends on the reference continuity. Specifically, if the reference is continuous, then r can be large; otherwise r should be small to smooth the reference to avoid input saturation. For the multi-parameter optimization, the feedback gains <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{p}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{d}$ </tex-math></inline-formula> should be tuned first to guarantee the system stability, followed by decreasing the UDE parameter T to improve the system robustness. However, the feasible range of T may be restricted by the measurement noise and actuator bandwidth in practice. The proposed algorithm is applicable not only in aerial transportation systems but also in addressing other disturbance rejection problems.