IEEE Trans Neural Netw Learn Syst. 2023 Jun;34(6):3005-3018. doi: 10.1109/TNNLS.2021.3110777. Epub 2023 Jun 1.
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.
等效性是一种强大的方法，可以将原始问题转化为相对更容易解决的另一个问题。近年来，张神经动力学等效性（ZNE）以神经动力学或递归神经网络（RNN）的形式被研究、抽象和提出，作为可以在不同层次上等效求解方程的过程。经过长期研究，我们注意到 ZNE 不仅可以与方程一起工作，还可以与不等式一起工作。因此，提出了不等式型 ZNE，并在本研究中进行了证明和应用。不等式型 ZNE 可以将不同层次的边界约束转换为统一层次的边界约束。 jerk 级别的边界约束、方程约束和目标指标的 ZNE 的应用最终为单机器人臂和双机器人臂系统的循环运动规划和控制（CMPC）构建了有效的时变二次规划方案。此外，作为一种有效的时变二次规划求解器，引入了投影神经网络（PNN）。单机器人臂和双机器人臂系统的实验结果证实了 ZNE 及其不等式型 ZNE 的正确性和有效性。与传统方法的比较也显示了 ZNE 的优越性。
