Model-Free and Pseudoinverse-Free Zhang Neurodynamics Scheme for Robotic Arms' Path Tracking Control

Path tracking control of robotic arms is regarded as a fundamental problem in the field of robotics. However, obtaining an accurate model of the robotic arm in practical engineering poses significant challenges. As a result, model-free schemes have become a focus of investigation. In contrast to traditional model-free schemes used for estimating the Jacobian matrix of the robotic arm, in this work, a novel estimator directly for the pseudoinverse (PI) of the Jacobian matrix based on Zhang neurodynamics (ZN) is proposed for the first time. In addition, a novel model-free and PI-free ZN (MFPIFZN) scheme for path tracking control of robotic arms is proposed. The MFPIFZN scheme not only significantly reduces the operation complexity by eliminating the requirement to compute the PI of the Jacobian matrix but also enhances the accuracy by eliminating the potential errors that may arise from the computation of the PI. Theoretical analyses provide guarantees for the convergence and stability of the MFPIFZN scheme. Finally, experimental results conducted on planar four-link and Kinova Jaco2 robotic arms vividly illustrate the excellent performance of the MFPIFZN scheme. Comparison experiments with four other model-free schemes further confirm the superiority of the MFPIFZN scheme.