Robot arm control based on online resolution of nonlinear equation systems using novel matrix-pseudoinverse-free neurodynamics

Robot arm control plays a pivotal role in modern industrial automation. Designing a controller without matrix-pseudoinverse computation for robot arms from the acceleration-layer control perspective is a challenging topic. In this article, based on the temporal-variant nonlinear equation system (TVNES) problem, we propose a novel acceleration-layer TVNES (AL-TVNES) problem. By constructing an output function and an energy function, and applying twice Zhang neurodynamics (ZN) design formula, a new matrix-pseudoinverse-free acceleration-layer ZN (MPF-ALZN) controller is proposed. The controller effectively avoids the complicated computation of the temporal-variant matrix pseudoinverse, thereby reducing computational complexity. In addition, theoretical analyses and numerical experiments show the convergence and robustness of the MPF-ALZN controller. Finally, the proposed MPF-ALZN controller is successfully applied to the control of the Kinova Jaco2, Franka Emika Panda, and Kinova Gen3 robot arms, with the tracking errors between the desired paths and the actual trajectories being below 0.01 mm, which validates the efficiency of the proposed controller. Through various experiments in MATLAB, CoppeliaSim, and physical platforms, the high tracking accuracy and robustness of the MPF-ALZN controller are confirmed, indicating its practicality.