Construction of Motion Transformation Matrices Based on the D-H Parameter Method and Solving Multi-Objective Optimization Models Using Genetic Algorithms

This paper addresses the modeling and optimization of a six-degree-of-freedom robotic arm. We establish a comprehensive mathematical model to describe its kinematic and dynamic characteristics using the Denavit-Hartenberg (D-H) parameter method. By constructing the corresponding homogeneous transformation matrices, we develop the forward kinematics model, detailing the movement from the base to the end-effector. The resulting kinematic equations, which include transformation matrices for each joint, enable precise calculations of the end-effector’s position and orientation. A nonlinear optimization model is then formulated with the objective of minimizing end-effector error, solved using the genetic algorithm to determine optimal joint angles. Additionally, we consider the arm’s kinetic and potential energy to develop an energy consumption model. This leads to a multi-objective optimization model with two goals: minimizing end-effector error and minimizing energy consumption. The model is solved using a genetic algorithm.