Comparisons of Slack Variable, NCP Function, and Penalty Function Based ZNNs for Solving Equality-and Inequality-Constrained QP Problems With Robotic Applications

Abstract

In science and engineering, especially robotic applications, optimization problems including quadratic programming (QP) with time-variant coefficients are commonly encountered. Zeroing neural network (ZNN) is a systematic and effective solution to time-variant problems solving. However, due to the inability to handle inequality constraints, conventional ZNNs can only solve equality-constrained QP problems. Aiming at overcoming such a drawback, recently, three techniques using slack variable, nonlinear complementarity problem (NCP) function, and penalty function have been successively introduced to handle inequality constraints, leading to three ZNNs (termed SV-ZNN, NCP-ZNN, and PF-ZNN hereafter) for solving QP problems with equality and inequality constraints. In the literature, there exists no comparative study investigating the differences between these three ZNNs. This paper focuses on this gap and performs comparisons of the three ZNNs for solving equality-and inequality-constrained QP problems with applications to kinematic control of joint-constrained redundant robots. Through comparative investigations, it is revealed that 1) for time-invariant QP problems solving, SV-ZNN and NCP-ZNN are superior to PF-ZNN; 2) for time-variant QP problems solving, SV-ZNN suffers from failure, and NCP-ZNN outperforms PF-ZNN; 3) for kinematic control of a joint-constrained redundant robot, both NCP-ZNN and PF-ZNN can complete the specified task with NCP-ZNN enforcing joint-limit avoidance more stringently (i.e., the resolved joint variable reaches its limit tightly without violation) as compared with PF-ZNN, whereas SV-ZNN suffers from task failure.