Energy-Efficient Trajectory Optimization for a 4-DOF Serial Manipulator Using Adaptive Dolphin-Eagle Algorithm with Joint-Aware Energy Weighting

Energy efficiency in industrial robotic manipulators is vital for reducing operational costs and carbon footprints. This paper presents the Adaptive Dolphin-Eagle Algorithm (ADEA), a hybrid metaheuristic for energy-optimal trajectory planning of a 4-DOF serial manipulator. ADEA combines dolphin echolocation-based global exploration with eagle Lévy-flight exploitation. It is augmented by Joint-Aware Energy Weighting (JAEW), a physics-informed mechanism that amplifies search steps for high-activation joints, embedding dynamic load structures into the optimization without altering the fitness function. Based on a CAD-accurate robot model under full Newton-Euler inverse dynamics, trajectories are parameterized using quintic polynomial segments through two intermediate waypoints to minimize mechanical energy. Comparative evaluations against Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), and a JAEW-augmented Starfish Optimization (SFO) baseline across 30 independent runs demonstrate that ADEA achieves the lowest mean energy consumption. Significant performance gains are confirmed by Wilcoxon signed-rank tests (p < 0.05). Unlike baseline methods that plateau mid-run, ADEA exhibits sustained convergence, offering a robust framework for energy-aware motion planning in industrial tasks.