Automated Symbolic Processes for Dynamic Modeling of Redundant Manipulator Robots

Abstract

In this study, groundbreaking software has been developed to automate the generation of equations of motion for manipulator robots with varying configurations and degrees of freedom (DoF). The implementation of three algorithms rooted in the Lagrange–Euler (L-E) formulation is achieved through the utilization of .m files in MATLAB R2020a software.This results in the derivation of a symbolic dynamic model for industrial manipulator robots. To comprehend the unique features and advantages of the developed software, dynamic simulations are conducted for two 6- and 9-DoF redundant manipulator robots as well as for a 3-DoF non-redundant manipulator robot equipped with prismatic and rotational joints, which is used to simplify the dynamic equations of the redundant prototypes. Notably, for the 6-DoF manipulator robot, model predictive control (MPC) is employed using insights gained from the dynamic model. This enables optimal control by predicting the future evolution of state variables: specifically, the values of the robot’s joint variables. The software is executed to model the dynamics of different types of robots, and the CPU time for a MacBook Pro with a 3 GHz Dual-Core Intel Core i7 processor is less than a minute. Ultimately, the theoretical findings are validated through response graphs and performance indicators of the MPC, affirming the accurate functionality of the developed software. The significance of this work lies in the automation of motion equation generation for manipulator robots, paving the way for enhanced control strategies and facilitating advancements in the field of robotics.