A Unified Arbitrarily Predefined -Time Convergent Recurrent Neural Network for Motion Control of Redundant Robot Manipulators: A Unified Paradigm
提出一种统一范式，基于分段演化公式和B类函数构建任意预定义时间收敛的递归神经网络，用于实时求解冗余机器人的运动控制问题，具有收敛时间可任意精确预定义和计算成本低的优势。
In general, the motion control problem of redundant robot manipulators (RRMs) can be transformed into a constrained time-varying quadratic programming (TVQP) problem. Recently, various recurrent neural networks (RNNs) with predefined time convergence (PTC) abilities have been proposed to solve this constrained TVQP problem in real-time. However, there is still a lack of a unified paradigm to guide researchers and engineers design such RNNs more effectively based on specific requirements. To bridge this gap, we propose a unified paradigm derived from a novel segmentation evolution formula incorporating a special <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathfrak{B}$</tex-math></inline-formula>–<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Class</i> function. This paradigm enables the construction of various RNNs, collectively referred to as unified arbitrarily predefined-time convergent RNNs (U-APTC-RNNs). Compared with most existing RNNs, the constructed U-APTC-RNN has two significant advantages: 1) it has the arbitrarily PTC (APTC) ability, meaning its actual convergence time can be arbitrarily and precisely predefined without setting other model parameters and 2) using a novel piecewise computation strategy, redundant nonlinear calculations are effectively minimized, leading to a notable reduction in computational costs. The stability and APTC ability of the constructed U-APTC-RNN are demonstrated through detailed theoretical analysis. Numerical simulation experiments confirm the APTC capabilities of various U-APTC-RNNs constructed using the proposed unified paradigm. Comparative experiments show that U-APTC-RNN has more competitive convergence performance and lower computational cost than other state-of-the-art RNNs with PTC abilities. Finally, simulation and physical motion control experiments on the Jaco and UR5 robotic arms demonstrate the superiority and practicality of the proposed U-APTC-RNN.