Discrete acceleration-level pseudoinverse-free zeroing neurodynamics for robotic manipulator path tracking control

Predicting the unknown next-instant state of the future nonlinear equation system (FNES) is critical for high-performance robotic manipulator path tracking control. While various algorithms have been developed to solve the FNES problem, many existing methods often focus on velocity-level solutions and rely on computationally expensive Jacobian matrix pseudoinverse operation, which impair both efficiency and accuracy. To bridge the gap, this paper proposes an innovative discrete acceleration-level pseudoinverse-free zeroing neurodynamics (DALPFZN) algorithm. By reformulating the FNES problem as a future nonlinear output-zeroing problem and operating at the acceleration level, the proposed algorithm effectively avoids the need for complicated pseudoinverse computation. Theoretical analyses show the convergence and stability of the DALPFZN algorithm. Numerical comparisons illustrate its superior efficiency and accuracy against existing methods. Furthermore, experimental results on MATLAB and CoppeliaSim platforms substantiate the effectiveness and outstanding performance of the DALPFZN algorithm. When the proposed DALPFZN algorithm is applied to the robotic manipulator path tracking control, the mean of the maximum steady-state output errors (MSSOEs) is 0.05 mm, and the mean of the average computing time per updating (ACTPUs) is 0.1 ms. Compared with the velocity-level pseudoinverse algorithm, the performance improvement rate of the ACTPU is 8.96%. Compared with the velocity-level pseudoinverse-free algorithm, the performance improvement rate of the MSSOE is 87.65%.