Abstract
<title>Abstract</title> <p>As we Know Robotics is at the intersection of mechanical engineering, electrical systems, and intelligent con- trol, driving innovation in industrial automation, autonomous vehicles, and healthcare systems. This research focuses on the mechanical engineering aspects of robotics, emphasizing the modeling, dynamics, and control of robotic manipulators and mobile platforms. Classical control approaches such as Propor- tional–Integral–Derivative (PID) control and Linear Quadratic Regulator (LQR) control, along with modern approaches like Model Predictive Control (MPC) and adaptive control, are reviewed to evaluate their performance in trajectory tracking and disturbance rejection. Mathematical formulations based on rigid-body dynamics, state-space representation, and kinematic analysis establish the theoretical foundation. The Simulations in MATLAB/Simulink compare controller performance across different robotic systems. Results reveal the trade-offs between simplicity, robustness, and adaptability: while PID is effective for basic tasks, MPC offers superior robustness and predictive capabilities for complex applications. The study on the Topic concludes by highlighting industrial, autonomous, and medical applications, and suggests future research directions including reinforcement learning-based adaptive control and digital twin integration with precision.</p>