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To effectively solve the multi-objective motion planning problem for redundant robot manipulators, a penalty neural multi-criteria optimization (PNMCO) scheme is proposed and investigated. The scheme includes two parts: a constrained multi-criteria optimization (CMCO) subsystem, and a varying-parameter recurrent neural network combined with penalty function (VP-RNN-PF) subsystem. Specifically, the CMCO subsystem is made up of velocity two norm, repetitive motion, and infinity norm. With these criteria, it can achieve energy minimization, repetitive motion, and avoidance of speed peaks. In addition, the CMCO subsystem is then transformed into a standard quadratic programming (QP) problem, and the VP-RNN-PF subsystem is applied to solve the QP problem. Results of computer simulations based on the JACO<sup>2</sup> robot manipulator demonstrate that the proposed PNMCO scheme is effective and feasible to plan the multi-objective motion tasks. Comparison experiments of two complex paths tracking between VP-RNN-PF and the traditional neural networks (e.g., simplified linear-variational-inequality-based primal-dual neural network, S-LVI-PDNN) shows that the proposed scheme as well as the neural network is more accurate and more efficient for solving multi-objective motion planning problem.

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A Varying-Parameter Recurrent Neural Network Combined With Penalty Function for Solving Constrained Multi-Criteria Optimization Scheme for Redundant Robot Manipulators