Three-Dimensional Unmanned Aerial Vehicle Trajectory Planning Based on the Improved Whale Optimization Algorithm

The effective planning of UAV trajectories in a 3D environment presents a complex global optimization challenge that must account for numerous constraints, including urban settings, mountainous terrain, obstacles, no-fly zones, flight boundaries, travel distances, and trajectory change rates. This paper addresses the limitations of the whale optimization algorithm in 3D trajectory planning—specifically its slow convergence, low accuracy, and susceptibility to local optimum—by proposing an improved whale optimization algorithm. This enhancement incorporates an inverse learning mechanism to increase the diversity of the initial population and integrates a nonlinear convergence factor with a random number generation mechanism to optimize the balance between global and local search capabilities. Our findings indicate that for both the standard and improved whale optimization algorithms, each individual in the population represents a feasible solution, corresponding one-to-one with distributed trajectories in the search space. Given that route planning typically occurs in three dimensions, there is spatial symmetry among the multiple potential trajectories from the starting point to the endpoint. The optimization algorithm identifies the optimal solution by exploring these symmetric trajectory paths, ultimately selecting the most favorable one based on additional constraints (e.g., no-fly zones and fuel consumption). Moreover, the convergence of the whale optimization algorithm depends on the diversity of individuals in the population and the thorough exploration of the search space. This symmetry facilitates a more uniform exploration of various trajectories by the population. In some instances, the optimization algorithm has achieved a 7.00% improvement in fitness value, a 10.05% reduction in optimal distance, and a 28.73% decrease in standard deviation. The increase in optimal values and the decrease in worst-case values underscore the effectiveness of the optimization algorithm, while the reduction in standard deviation reflects the stability of the algorithm’s output data. These results further confirm the advantages of the optimized algorithm.