Research on Adaptive Planning of Three-Dimensional Trajectory for Uncrewed Aerial Vehicle Inspection Based on Nonlinear Weibull Algorithm

Traditional methods for solving the path planning problem of inspection UAVs in complex environments often suffer from issues such as convergence to locally optimal paths and poor global search accuracy. To address these shortcomings, this study proposes a Non-linear Weibull Flight Reptile Search Algorithm (NWFRSA) for adaptive path planning of inspection UAVs. By introducing an improved Iterative Chaotic Map with Infinite Collapses (ICMIC) initialization strategy, the diversity and quality of initial path solutions are enhanced. An S-shaped characteristic function-based nonlinear evolution factor is employed to balance global exploration and local exploitation of the optimal path, while a Weibull flight operator mutation strategy is designed to enable the algorithm to escape from locally optimal paths, enrich the search space, and improve convergence accuracy. Meanwhile, this study constructs a path planning model for inspection UAVs and designs a weighted objective function considering total path length, flight altitude, flight turning angle, and threat model, thereby transforming path planning in three-dimensional space into a constrained multi-objective optimization problem. The results show that under flight environments with varying complexity of obstacle and threat region distribution, compared with the Particle Swarm Optimization algorithm (PSO), Butterfly Optimization Algorithm (BOA), and Reptile Search Algorithm (RSA), NWFRSA can effectively reduce the path cost (by 4.53%–34.47%), contributing to improved.