Motion Optimization of a Six-Degree-of-Freedom Robotic Arm Based on Denavit-Hartenberg Parameter Method and NSGA-II

This paper presents an optimization approach for the motion of a six-degree-of-freedom robotic arm based on the Denavit-Hartenberg (D-H) parameter method and NSGA-II. The forward kinematic model of the robotic arm is established using the D-H parameter method, and the minimization of end-effector error is formulated as a nonlinear optimization problem. An adaptive gradient descent algorithm is employed, integrating momentum terms and adaptive learning rates to enhance convergence speed and stability. The algorithm incorporates multiple random initialization strategies to avoid local optima. The optimized joint configurations result in precise end-effector positioning, with a minimal end-effector error of 2.1819 × 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">–5</sup> mm. Furthermore, an energy minimization objective is introduced, leading to the development of a multi-objective optimization model. This model accounts for the kinetic and potential energy changes resulting from joint rotations, integrating energy consumption into the optimization framework. The NSGA-II algorithm is utilized for solving the multi-objective optimization problem, incorporating adaptive crossover and mutation operations to improve search efficiency. The results demonstrate a trade-off relationship between end-effector error and energy consumption.