In industrial and service robotics, autonomous mobile robots must achieve accurate trajectory tracking while maintaining low energy consumption to avoid frequent recharging and performance degradation. Energy efficiency is particularly critical because locomotion accounts for 45%–65% of total power consumption, directly limiting operational range and autonomy. This paper proposes an energy-aware trajectory tracking framework that optimizes a fractional-order proportional-integral-derivative (FOPID) controller using an Enhanced Whale Optimization Algorithm (E-WOA). The key contributions are threefold: (1) the E-WOA hybridizes Differential Evolution (DE)’s global exploration with WOA’s local exploitation to overcome premature convergence in high-dimensional FOPID parameter spaces; (2) a composite fitness function jointly minimizes tracking error and energy consumption; and (3) controller parameters optimized on a single circular trajectory generalize effectively to complex paths without retuning. The proposed framework is evaluated on multiple trajectory configurations, including circular, eight-shaped, square, and rhombus paths, under stochastic environmental disturbances. Statistical analysis based on ten independent runs and validated using Analysis of Variance (ANOVA) was conducted against six classical and recent optimization methods: DE, WOA, Particle Swarm Optimization (PSO), Bat Algorithm (BA), Artificial Hummingbird Algorithm (AHA), and Rime Optimization Algorithm (RIME). The results show that E-WOA-FOPID achieves an average improvement of 15.14% in mean fitness and a 30.69% reduction in performance variability compared to the best-performing benchmark. These findings confirm its robustness as an energy-efficient solution for high-precision mobile robot trajectory tracking.

This paper reviews recent advancements in system identification methods for perturbed motorized systems, focusing on brushed DC motors, brushless DC motors, and permanent magnet synchronous motors. It examines data acquisition setups and evaluates conventional and metaheuristic optimization algorithms, highlighting their advantages, limitations, and applications. The paper explores emerging trends in model structures and parameter optimization techniques that address specific perturbations such as varying loads, noise, and friction. A comparative performance analysis is also included to assess several widely used optimization methods, including least squares (LS), particle swarm optimization (PSO), grey wolf optimizer (GWO), bat algorithm (BA), genetic algorithm (GA) and neural network for system identification of a specific case of a perturbed DC motor in both open-loop (OL) and closed-loop (CL) settings. Results show that GWO achieves the lowest error overall, excelling in OL scenarios, while PSO performs best in CL due to its synergy with feedback control. LS proves efficient in CL settings, whereas GA and BA rely heavily on feedback for improved performance. The paper also outlines potential research directions aimed at advancing motor modeling techniques, including integration of advanced machine learning methods, hybrid learning-based methods, and adaptive modeling techniques. These insights offer a foundation for advancing motor modeling techniques in real-world applications.