Dynamics Modeling and Nonlinear Optimal Control of an Underactuated Dual-Unmanned Aerial Helicopters Slung Load System

This paper focuses on the dynamics modeling and control methods for an underactuated Dual-Unmanned Aerial Helicopter Slung Load System (DUH-SLS), which consists of two Unmanned Aerial Helicopters (UAHs) connected to the suspended load via two sling cables. The DUH-SLS is a multi-body coupled system with internal ideal constraint forces and has seven motion degrees of freedom (DOFs) in the longitudinal plane. In this paper, a set of independent and complete generalized coordinates is selected to describe the system’s motion. The dynamics model of DUH-SLS is established using Lagrange analytical mechanics. This approach, which avoids system internal forces, greatly improves modeling efficiency. Finally, the correctness of this dynamics model is validated using a virtual prototype of the DUH-SLS developed in the multi-body dynamics simulation software ADAMS. The DUH-SLS is a complex nonlinear controlled object, and the iterative Linear Quadratic Regulator (iLQR) method is introduced to design an integrated optimal controller to achieve trajectory tracking and swing suppression for the DUH-SLS. This method transforms the quadratic optimal control problem of nonlinear systems into a series of linear quadratic optimal control (LQR) problems through iterative optimization in function space, thus obtaining an optimal solution. The iLQR optimal controller requires offline iterative computation, but the optimal control obtained has a state feedback closed-loop form, which ensures robustness during online control. Numerical simulation results demonstrate that the proposed iLQR optimal controller exhibits excellent control performance in complex multi-task scenarios. Particularly in trajectory tracking tasks, the maximum average position tracking error of the iLQR controller is only 0.14 m, compared to 3.57 m and 3.11 m for the LQR and LMC (Lyapunov Method Controller) controllers, respectively. Furthermore, the controller demonstrates strong robustness against internal parameter perturbations and external complex wind disturbances, fully validating the effectiveness and superiority of the proposed approach.