Performance Evaluation of Metaheuristics for LQR Controller Optimization: A Two-Wheel Balancing Robot Case Study

Two-wheeled balancing robots are commonly modeled as inverted pendulum systems, which are inherently unstable and present significant challenges for control due to their nonlinear and underactuated dynamics. One of the main problems in their control is achieving stability and precise position tracking under real-world disturbances and dynamic uncertainties. This research addresses these challenges by proposing a methodology to optimize a linear quadratic regulator (LQR) controller using metaheuristic algorithms. Specifically, the parameters $ Q $ and $ R $ of the LQR are tuned using three optimization strategies: artificial bee colony (ABC), differential evolution (DE), and global-best harmony search (GHS). The performance of each algorithm is evaluated through a comparative analysis, focusing on control stability and dynamic responsiveness. Experimental results demonstrate that the controller optimized by differential evolution achieves the lowest root mean square error (0.4910 degrees), outperforming ABC (0.5187 degrees) and GHS (0.5195 degrees). These findings underscore the effectiveness of metaheuristic algorithms in enhancing control performance for dynamically unstable systems, facilitating their implementation in real-world autonomous control applications.