Discrete-Time ZND Models Solving ALRMPC via Eight-Instant General and Other Formulas of ZeaD

Repetitive motion planning and control (RMPC) of redundant robot manipulators is a fundamental and important problem widely existing in industrial manufacturing. In this paper, the acceleration-level RMPC (ALRMPC) is studied and solved in a discrete-time manner. For solving this problem, a new ALRMPC scheme with feedback control term is derived and presented at first. Then, by adopting Lagrange's undetermined multipliers method and zeroing neural dynamics (ZND), a continuous-time ZND model, which is based on the new ALRMPC scheme, is developed and proposed. Besides, an eight-instant general formula with high precision is constructed, proposed and analyzed. By using this eight-instant general formula and other multiple-instant Zhang et al discretization (ZeaD) formulas to discretize the continuous-time ZND model, four discrete-time ZND (DTZND) models for solving ALRMPC are thus obtained. Finally, theoretical analyses and computer simulation experiment results further substantiate the effectiveness and accuracy of the proposed DTZND models.