Three-dimensional trajectory planning of unmanned aerial vehicles using improved particle swarm optimization algorithm integrating Levy flight

To address the UAV trajectory planning problem in three-dimensional environments, a novel dynamic adjustment strategy based on Levy flight is proposed to improve the Spherical Vector-Based Particle Swarm Optimization Algorithm (SPSO), resulting in the Spherical Vector Particle Swarm Optimization Algorithm for Dynamic Adjustment Strategy Based on Levy Flight (LDS-SPSO), which mitigates slow convergence and susceptibility to local optima. First, the trajectory planning problem is transformed into a multi-constraint objective optimization problem, with a fitness objective function constructed based on trajectory length, obstacle threat, smoothness, and altitude variation. Second, incorporating the kinematic equations of UAVs, a dynamic adjustment strategy for learning factors is introduced to enhance convergence speed. Third, when particles fall into local optima, a Levy flight perturbation factor is introduced to rapidly escape these local optima. Finally, an optimized UAV trajectory planning algorithm for three-dimensional environments is presented. Simulations of three-dimensional trajectory planning were conducted in four digital elevation models with varying complexities. The results validate the superior performance of the improved algorithm, demonstrating effective obstacle avoidance, lower trajectory costs, higher quality, and improved optimization accuracy along with faster convergence. In scenarios with dense obstacles, the LDS-SPSO algorithm achieved reductions of 22.92%, 0.51%, and 0.34% in best fitness values compared to traditional PSO, inertia-weight linearly decreasing SPSO (IPSO), and SPSO, respectively, with average fitness reductions of 31.18%, 6.33%, and 4.54%, and worst fitness reductions of 36.45%, 16.73%, and 14.77%. The findings indicate that the LDS-SPSO algorithm exhibits faster convergence, better stability, and reliability in three-dimensional trajectory planning.