Mathematical Modeling and Multi Loop Control for 6-DOF 25kg Digital Servo Educational Desktop Robotic Arm V2

Abstract

This study presents the mathematical modeling and control of a 6-DOF 25 kg Digital Servo Educational Desktop Robotic Arm using a multi-loop control framework based on conventional PID and Particle Swarm Optimization (PSO)-tuned PID controllers. The robotic system was modeled as a nonlinear, coupled dynamic system incorporating inertia, Coriolis, and gravitational effects, alongside realistic actuator constraints derived from servo motor specifications. A simulation environment was developed to evaluate the tracking performance of both control strategies under a smooth reference trajectory applied to all joints. The PSO algorithm was employed to optimally tune the PID gains by minimizing tracking error, thereby enhancing controller adaptability to system nonlinearities. Performance evaluation was conducted using both qualitative and quantitative metrics, including trajectory tracking plots, error convergence, phase portraits, Integral of Absolute Error (IAE), and maximum absolute error. Results demonstrate that the PSO-based PID controller significantly improves tracking accuracy and reduces cumulative error across all joints compared to the conventional PID controller. Although peak errors in some joints remain unchanged due to system constraints and coupling effects, the overall dynamic response, stability, and convergence speed are greatly enhanced. The findings highlight the effectiveness of intelligent optimization techniques in improving classical control strategies for complex robotic systems.