Penalty-enhanced error-redefinition RNN for time-varying QP problems with multiple constraints and robot arm applications Penalty-enhanced error-redefinition RNN

• Published in: Nonlinear dynamics Vol. 113; no. 17; pp. 23259 - 23283
• Main Authors: Zhang, Tongyang, Yang, Song
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2025
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Classical Mechanics; Control; Dynamical Systems; Physics; Physics and Astronomy; Statistical Physics and Dynamical Systems; Vibration; Time-varying quadratic programming; Equality- and inequality-constraints; Zeroing neural dynamics; Recurrent neural network; Motion planning of robot arms
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-025-11349-z

Time-varying quadratic programming (QP) problems with multiple constraints (i.e., equality and inequality constraints) arise in various applications, including the motion planning of robotic arms. To achieve an efficient and accurate solution for these optimization problems, this paper proposes a novel penalty-enhanced error-redefinition recurrent neural network (PERNN) model based on the zeroing neural dynamics formula. Unlike conventional ERNN-based methods, which are incapable of handling inequality constraints, the PERNN model employs a dynamically weighted penalty function to transform inequality constraints into penalty terms, thereby seamlessly integrating them into the optimization criterion. This approach guarantees the simultaneous satisfaction of both equality and inequality constraints while achieving a fast convergence rate. The global convergence and robustness of the PERNN model are rigorously proven and further validated via simulations. Subsequently, the PERNN model is applied to solve the motion planning problem for robot arms subject to multiple constraints. Furthermore, some application experiments involving three different robot arms are conducted to verify the effectiveness and anti-disturbance capacity of the proposed PERNN model, as well as the applicability to actual robotic systems. Comparative results demonstrate that the PERNN model outperforms other modern RNN-based solvers in terms of tracking accuracy, computational efficiency and time-varying disturbance suppression.