Simulation and mathematical modeling of a 4-degree-of-freedom robotic ARM

Abstract

The following article shows in detail the development of the modeling process of a manipulator of a robotic arm corresponding to four degrees of freedom (4GL) this study was based on direct kinematics for the calculation and accuracy of the position of the end effector based on their joint directions. It starts from a particular position and its location in the plane is observed. The use of the method was done because it is important to identify the movement of the robot. The simulation was performed using Matlab software, in this program it was possible to illustrate the movement of the robot and how it correctly reaches the movement in the direction of a previously defined trajectory. Additionally, a test was implemented that helped to verify that the robot was able to position itself at the desired end point and that the errors generated were minimal. The results showed that the control system reached a steady behavior, and that the tracking error was reduced to converge to zero, demonstrating an efficient and precise movement, which occurred in a time of approximately 8 seconds, which evidences an adequate stability and an effective design of the control system. The stability of the movement was also evaluated by applying the Lyapunov criterion, which provides a theoretical confirmation of the reliability of the control system used. In summary, the results show that the robotic arm is capable of performing complex trajectories while maintaining a stable motion.