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.

翻译：本文研究了在复杂、动态和静态环境中，使用粒子群优化（Particle Swarm Optimization，PSO）进行空中载荷运输的最优路径规划。针对搭载缆绳悬挂载荷的四旋翼飞行器，基于欧拉-拉格朗日运动方程设计了分层最优控制系统。为规避障碍物，采用改进人工势场法结合PSO算法确定虚拟引导点的最短路径，该引导点作为领导者引导系统向目标点移动，同时避免与固定和移动障碍物发生碰撞。通过多种PSO方法对引力和斥力系数进行调整，以获取最优轨迹并最小化时间消耗。确定的目标点作为基于滑模策略的四旋翼位置控制的期望位置。最后，我们给出数值仿真结果，验证了系统成功完成载荷运输任务。