A Fifth-Order POE-Based Method for Kinematic Identification and Inverse Kinematics of Serial Robots

Current numerical methods for solving kinematic identification (KI) and inverse kinematics (IK) are limited in accuracy, convergence rates, and robustness, necessitating further enhancement. This paper presents a modified Halley method for solving the KI and IK problems of serial robots based on the product of exponentials formula, achieving quintic convergence. Specifically, a general error model is first established based on exponential coordinates, and KI and IK are reformulated as root-finding problems. Next, the modified Halley method, which we prove to be a fifth-order method and incorporates a damping strategy, is proposed to resolve the singularity issue and enhance robustness. Subsequently, the Jacobian and Hessian matrices required for the proposed method are analytically derived based on the time differential of exponentials. Furthermore, highly simplified explicit formulas for these matrices are presented for the IK problem. Simulations on serial robots with various configurations validate the proposed method's accuracy, convergence rates, and robustness in solving KI and IK problems, as well as its advantages over the state-of-the-art. Additionally, experimental validation of KI on two physical robots further demonstrates the effectiveness of the proposed method. Our custom-written MATLAB and C++ codebases are made publicly available for download.