In this paper, a primal-dual neural network based on linear variational inequalities (LVI) is presented for the online repetitive motion planning of PA10 robot arm, a kinematically redundant manipulator. To do this, a drift-free criterion is exploited. In addition, the physical constraints such as joint limits and joint velocity limits are incorporated into the problem formulation of such a redundancy-resolution scheme. The scheme is finally reformulated as a quadratic-programming (QP) problem. As a QP real-time solver, the LVI-based primal-dual neural network is designed based on the QP-LVI conversion and Karush-Kuhn-Tucker (KKT) condition. With simple piecewise-linear dynamics and global exponential convergence to optimal solutions, it can handle general QP and linear programming (LP) problems in the same inverse-free manner. The repetitive motion planning scheme and the LVI-based primal-dual neural network are simulated successfully based on PA10 robot arm, with effectiveness demonstrated.

The Wang neural network, together with its improved circuit implementation, could solve online a set of simultaneous linear equations. Global exponential convergence is presented for the Wang neural network, compared to the previously-presented asymptotical convergence. In addition, global stability results are presented for the Wang neural network. Illustrative examples further demonstrate the characteristics of the Wang neural network.

One of state-of-the-art recurrent neural networks (RNN) is dual neural network (DNN). It can solve quadratic programs (QP) in real time. The dual neural network is of simple piecewise-linear dynamics and has global (exponential) convergence to optimal solutions. In this chapter, we firstly introduce the QP problem formulation and its online solution based on recurrent neural networks. Some related concepts and definitions are also given. Secondly, we present the dual neural network and its design method. In addition to the general design method, for non-diagonal, non-analytical and/or time-varying cases, a matrix-inverse neural network could be combined into such a design procedure of dual neural network for online computation of its matrixinverse related term. Thirdly, we show the analysis results of dual neural networks. In addition to the general analysis results, we investigate the proof complexity of the exponential convergence condition of dual neural networks. Fourthly, we present the numerical simulation and illustrative example of using the dual neural network to solve static QP problems. Finally, we exploit the dual neural network to online solve motion planning problems of redundant robot manipulators, which is illustrated as engineering-application examples.

A gradient neural network (CNN) for solving online a set of simultancous linsr equations is gencralized and investigated in this paper. Instead if the carlier-prcesented asymptotical convergence, global exponontial convergence could be proved for such a class of ncural networks, In addition, superior convergcnce could be achicved using power-sigmoid avtivation-funcitionsm, compared with tiing lincar activation-functions Computer-simulation results substantiate further the above analysis and efficacy of such neural network.

A quadratic performance index is investigated for the online neural remedy for drift phenomenon of redundant robot manipulators. Computer simulations performed based on a three-link planar robot arm show the efficacy of such a quadratic-index based neural-remedy scheme.