  In this article, we investigate the optimal path planning for aerial load
transportation in complex, dynamic, and static environments using Particle
Swarm Optimization (PSO). A hierarchical optimal control system is designed for
a quadrotor equipped with a cable-suspended payload, employing Euler-Lagrange
equations of motion. To navigate through obstacles, an improved artificial
potential field combined with the PSO algorithm is used to determine the
shortest path for a virtual point, acting as a leader. This leader guides the
system toward the target point while avoiding collisions with both fixed and
moving obstacles. The gravitational and repulsion coefficient forces using
various PSO methods are fine-tuned to achieve the best trajectory and minimize
time duration. The identified point serves as the desired location for
quadrotor position control, based on a sliding mode strategy. Finally, we
present numerical results to demonstrate the successful transportation of the
payload by the system.
