Modeling and control of a Multirotor UAV with a cable-suspended rigid body payload: A double-pendulum approach

The use of Multirotor Unmanned Aerial Vehicles (MUAVs) for aerial payload delivery has recently been a prominent research topic in the robotics community with various applications in many sectors. This paper presents a comprehensive study on the modeling and control of a generic MUAV carrier with a cable-suspended rigid body payload. A new nonlinear fifteen-degree-of-freedom dynamics model is derived accounting for practical imperfections such as shifted centers of gravity and arbitrary attachment points of the suspension cable on the carrier and payload. Additionally, this model incorporates the elastic behavior of the cable, including slackening and tightening dynamics, and introduces a double-pendulum representation for the payload. An optimal Linear Quadratic Regulator (LQR) with output weighting is proposed to stabilize the system and enable smooth tracking of the desired MUAV trajectory, while effectively reducing payload oscillations and radial movements. The developed controller successfully maintained the oscillation peak of the suspended payload below $15°$ for both stability and missions’ tracking. Unlike previous controllers, the proposed strategy regulates an arbitrary point on the MUAV, specifically the origin of its body axes, rather than the MUAV’s center of gravity or the payload. Computational analysis is used to validate the effectiveness of the proposed control strategy. The findings of this study provide valuable insights for the development of advanced MUAV-based aerial load transportation systems.