Unification and comparison of zeroing neural networks based on nonlinear complementary problem functions applied to serial and parallel robots

Abstract

Quadratic programming (QP) problems are frequently encountered in science, engineering, and robotic applications. Zeroing neural network (ZNN), as a special type of recurrent neural network (RNN), is an effective solver for solving QP. However, conventional ZNNs cannot solve QP with inequality and/or bound constraints. To obtain the optimal solution of QP with such constraints, the design of ZNN models roughly resorts to three techniques: slack variable, penalty function, and nonlinear complementary problem (NCP) function. Comparative results demonstrated that the NCP function-based ZNN (NCP-ZNN) has superior performance compared to ZNN models based on the other two techniques. Note that there exist various NCP functions that can be used to design different ZNN models by following similar procedures. One research gap is that these ZNN models have not been designed, presented and compared. To fill such a gap, this paper aims to design and investigate various NCP-ZNN models employing different NCP functions. Specifically, six NCP functions are used in this paper: the perturbed Fisher-Burmeister (pFB) function, Mangasarian and Solodov (MS) function, Evtushenko and Purtov I (EPI) function, EPII function, “discrete generalization” to the FB (D-FB) function, and Ranjbar, Effati, and Miri (REM) function. The performance of six NCP-ZNN models is validated by employing them to solve two QP problems in numerical comparisons. All NCP-ZNN models are successfully applied to parallel and serial robots with joint constraints to accomplish path-tracking tasks. Both simulative and experimental results demonstrate that six NCP-ZNN models can handle the joint constraints, with the best performance achieved by the MS-ZNN model.