Static and Dynamic Path Planning Using Enhanced Firefly Algorithm with B-spline for Mobile Robot Navigation

This study presents a path-planning framework that ensures smooth, safe, and efficient navigation in environments characterized by uncertainty, dynamic obstacles, and moving targets. An Enhanced Firefly Algorithm (EFA) is introduced, incorporating a gradient-based refinement term, adaptive attractiveness, and randomization decay to balance exploration and exploitation effectively. To achieve curvature-continuous trajectories, B-spline smoothing is applied to the optimized waypoints. The proposed EFA–B-spline approach is validated through extensive simulations under both static and dynamic conditions, including dynamic-goal scenarios, and benchmarked against Neural Network (NN), Artificial Potential Field (APF), Elman Neural Network (ENN), Functional Firefly Algorithm (FFA), and Ant Colony Optimization (ACO) variants. Quantitative results show that EFA reduces path length by 17.72% (NN), 36.92% (APF), 9.62% (ENN), and 8.77% (FFA). Compared to ACO variants, EFA achieves the shortest mean path of 28.64 m (σ = 0.359) with only 5.67 iterations, outperforming ACO (23.1), IACO (9.8), and IAACO (6.5) iterations. Moreover, relative to FFA, EFA further decreases path length by 6.33% and simulation time by 22.0%. In dynamic-goal experiments, the framework adapts effectively to lateral and converging targets while maintaining collision-free motion. Overall, the EFA–B-spline method provides real-time–ready, smooth trajectories suitable for autonomous vehicles, rescue robots, and mobile surveillance systems.