<![CDATA[Two-wheeled balancing Mobile Robots (2WBMRs) are inherently unstable, posing significant challenges in control. This paper addresses the problem of optimizing control parameters for such systems to improve stability and overall performance. The proposed solution integrates Hierarchical Sliding Mode Control (HSMC) with the Firefly Algorithm, which is a stochastic algorithm inspired by the flashing behavior of fireflies, to optimize control performance. The research contribution is the development of an optimized control system where the Firefly Algorithm is used to fine-tune HSMC parameters, ensuring improved stability and responsiveness. Additionally, the integration of Sliding Mode Control (SMC) within the HSMC framework provides precise yaw angle stabilization, contributing to comprehensive robot control. In this approach, the Firefly Algorithm is applied to optimize the HSMC parameters due to its capability to optimize multidimensional variables and its robust optimization abilities, aiming to enhance the stability of the vehicle in the best possible way. Simulations were conducted to compare the proposed method before and after applying the optimization algorithm, evaluating key performance metrics such as response time and stability. The results indicate a (10%) improvement in stability, demonstrating that the Firefly Algorithm significantly enhances control performance. These findings suggest that the optimized control system not only improves the stability of 2WBMRs but also has potential applications in broader dynamic control systems. In conclusion, based on the research results, we can conclude that the use of the HSMC-SMC controller for nonlinear systems like 2WBMRs is feasible and can be applied to many other nonlinear systems. Furthermore, the Firefly Algorithm has proven to be a powerful tool for optimizing parameters in control systems and can be applied in robotics and automation systems.]]>
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