Jerk-Level Zhang Neurodynamics Equivalency of Bound Constraints, Equation Constraints, and Objective Indices for Cyclic Motion of Robot-Arm Systems

Equivalency is a powerful approach that can transform an original problem into another problem that is relatively more ready to be resolved. In recent years, Zhang neurodynamics equivalency (ZNE), in the form of neurodynamics or recurrent neural networks (RNNs), has been investigated, abstracted, and proposed as a process that can equivalently solve equations at different levels. After long-term research, we have noticed that the ZNE can not only work with equations, but also inequations. Thus, the ZNE of inequation type is proposed, proved, and applied in this study. The ZNE of inequation type can transform different-level bound constraints into unified-level bound constraints. Applications of the jerk-level ZNE of bound constraints, equation constraints, and objective indices ultimately build up effective time-varying quadratic-programming schemes for cyclic motion planning and control (CMPC) of single and dual robot-arm systems. In addition, as an effective time-varying quadratic-programming solver, a projection neural network (PNN) is introduced. Experimental results with single and dual robot-arm systems substantiate the correctness and efficacy of ZNE and especially the ZNE of inequation type. Comparisons with conventional methods also exhibit the superiorities of ZNE.