Advanced Optimization Methods for Nonlinear Backstepping Controllers for Quadrotor-Slung Load Systems

Developments of computational platforms and metaheuristic algorithms increase the efficiency of various critical devices, including uncrewed aerial vehicles (UAVs), employed for monitoring, delivery, inspection, agriculture, military, and logistics applications. Consequently, many carriers prefer air transport for quicker delivery than land transport. This article introduces a nonlinear backstepping control (NBC) strategy for an underactuated quadrotor slung load system, tackling the challenge of trajectory tracking for a cable-suspended load. It models the quadrotor and slung load as rigid bodies and point mass, respectively. Using Lyapunov theory and the backstepping technique, it designs the controller optimally with precise thrust and angular velocity control laws to ensure the closed-loop system remains asymptotically stable. To achieve the stability mentioned, this article frames the task of finding the optimal parameters for the backstepping controller gains through an optimization problem where the minimization of the integral time squared error (ITSE) of the load position is considered as the objective function for the optimal design of the NBC parameters of the test system. Then the formulated optimization problem is then solved by employing two efficient metaheuristic algorithms, the improved grey wolf optimizer (IGWO) and the whale optimization algorithm (WOA). The effectiveness of the optimized controller is validated through simulation on the MATLAB/Simulink platform, and the results were compared with conventional NBC and literature-reported strategies. It is observed that the proposed NBC-IGWO and NBC-WOA achieve improved performance compared to the conventional and literature-reported strategy in the convergence of the load position trajectory to the desired path. The presented results confirm the efficacy of the proposed metaheuristic strategies.