A Spatio-Temporal Collaborative Improved Multi-Strategy Dung Beetle Optimization Algorithm for 3D Path Planning of Multiple Unmanned Aerial Vehicles in Cities

Three-dimensional collaborative path planning for multiple unmanned aerial vehicles (UAVs) in low-altitude urban environments with dense buildings constitutes a typical high-dimensional NP-hard problem. Conventional swarm intelligence algorithms suffer from critical limitations such as poor initial population quality, imbalance between global exploration and local exploitation, inadequate collaborative performance, susceptibility to local optima, and weak adaptability to dynamic environments. To overcome these challenges, this paper proposes a Spatio-Temporal Cooperative Improved Multi-Strategy Dung Beetle Optimization (STC-IMSDBO) algorithm tailored for 3D collaborative path planning of multi-UAV in urban area. The algorithm integrates five core enhancement strategies: first, an airspace-constrained sampling strategy enhances the uniformity and validity of initial population distribution; second, a spatio-temporal coupled iteration strategy achieves adaptive balancing between individual obstacle avoidance and multi-UAV coordination; third, a cooperative adaptive weight strategy optimizes iterative stability; fourth, a game mechanism theoretically guarantees collision-free Nash equilibrium for multi-UAV paths; and finally, a receding horizon strategy enables real-time path replanning in dynamic environments. Additionally, a multi-objective optimization function encompassing both individual flight costs and multi-UAV collaborative costs is formulated, comprehensively addressing core requirements including energy consumption, trajectory smoothness, obstacle avoidance, airspace compliance, and collision prevention. STC-IMSDBO is benchmarked against six mainstream path planning algorithms using test functions and four urban scenarios of varying complexity. Experimental results demonstrate that STC-IMSDBO exhibits superior stability, higher solution accuracy, and faster convergence in most benchmark functions. In path planning experiments, the algorithm achieves 6.12%–36.24% shorter mean path lengths, 14.1%–39.47% faster convergence, zero collision rate, 100% dynamic obstacle avoidance success, along with improved path smoothness and reduced energy consumption. Ablation studies, theoretical convergence proofs, nonparametric statistical tests, and real-world urban scenario simulations further validate the effectiveness of individual strategies and the algorithm’s global optimality. The proposed method demonstrates broad applicability in urban multi-UAV operations such as logistics delivery, emergency inspection, and traffic management.