In order to make redundant robot manipulators (RRMs) track the complex time-varying trajectory, the motion-planning problem of RRMs can be converted into a constrained time-varying quadratic programming (TVQP) problem. By using a new punishment mechanism-combined recurrent neural network (PMRNN) proposed in this article with reference to the varying-gain neural-dynamic design (VG-NDD) formula, the TVQP problem-based motion-planning scheme can be solved and the optimal angles and velocities of joints of RRMs can also be obtained in the working space. Then, the convergence performance of the PMRNN model in solving the TVQP problem is analyzed theoretically in detail. This novel method has been substantiated to have a faster calculation speed and better accuracy than the traditional method. In addition, the PMRNN model has also been successfully applied to an actual RRM to complete an end-effector trajectory tracking task.

中文翻译：

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一种惩罚机制-结合递归神经网络解决冗余机器人机械臂运动规划问题

为了使冗余机器人机械手（RRMs）跟踪复杂的时变轨迹，RRMs 的运动规划问题可以转化为受约束的时变二次规划（TVQP）问题。利用本文提出的一种新的惩罚机制——组合循环神经网络（PMRNN），参考变增益神经动力学设计（VG-NDD）公式，可以解决基于TVQP问题的运动规划方案，并RRM 关节的最佳角度和速度也可以在工作空间中获得。然后从理论上详细分析了PMRNN模型在求解TVQP问题中的收敛性能。这种新方法已被证实比传统方法具有更快的计算速度和更好的准确性。此外，