Meta-Heuristic UAV path planning in Spherical Coordinates

Safe three-dimensional UAV path planning over terrain with no-fly and threat regions requires balancing feasibility, smoothness, and safety under limited computational budgets. This paper evaluates a spherical, segment-based waypoint encoding in which each path segment is parameterized by its length, elevation angle, and azimuth angle, enabling compact representation and straightforward constraint handling in 3D environments. We study how well this encoding transfers across different metaheuristic optimizers under a matched functionevaluation (FE) budget to ensure fair comparison. SafetyEnhanced Particle Swarm Optimization (SPSO) is used as a reference method, and we benchmark spherical variants of Differential Evolution (S-DE), the Sine Cosine Algorithm (S-SCA), and CMA-ES (S-CMA). In addition, we introduce safety-guided extensions that incorporate SPSO-inspired memory and problemaware step scaling to improve feasibility preservation and search efficiency in constrained spaces. Experiments are conducted on nine digital elevation map (DEM)-based scenarios with increasing threat density and constraint severity. Results show that SPSO provides the most robust overall performance across scenarios, while S-DE and safety-guided S-SCA frequently achieve nearbaseline solution quality at substantially lower runtime. In the most constrained scenarios, performance becomes more scenariodependent, highlighting the importance of feasibility preservation and adequate exploration strength. Overall, the findings support spherical encoding as an effective, optimizer-agnostic modeling choice for safety-constrained UAV path planning, offering a strong quality-runtime trade-off under fixed evaluation budgets.