High precision and low complexity control algorithm plays an important role in the developing of the end-effector instrumentation of different robot manipulators. In order to reduce the kinetic energy and the high-speed drift phenomenon of the repetitive motion tracking task, the robot manipulator needs to calibrate its configuration. In this paper, we formulate the configuration calibration of the robot manipulator for the repetitive motion task as a future quadratic programming optimization problem constrained with equality constraints, which is also regarded as a fundamental problem in artificial intelligence and modern control engineering. Zhang neural network, which is a canonical method, can be adopted to deal with the continuous form of the future optimization problem, named as temporally dependent quadratic programming problem with equality constraints. In order to overcome the issue of temporally dependent inverse computing, a novel Zhang neural network model and its uncertain disturbance tolerant model, which are termed as filtered reciprocal-kind Zhang neural network model and uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network model, respectively, are proposed by integrating the energy-type cost function and Zhang neural network design formula for solving the temporally dependent quadratic programming problem with equality constraints in this paper. Based on the Euler discrete formula and the models, the discrete filtered reciprocal-kind Zhang neural network and the discrete uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network algorithms are proposed for solving the future quadratic programming problem with equality constraints and the robot manipulator configuration calibration problem of repetitive motion. The convergence properties of the reciprocal-kind Zhang neural network model and its corresponding uncertain disturbance tolerant model are obtained by Lyapunov stability theory of nonlinear system and its corresponding perturbed system, while the convergence property of the filtered reciprocal-kind Zhang neural network model is analyzed by the limit thinking. For the repetitive motion task, three experiments for solving the configuration calibration problem of PUMA560, Kinova Jaco2, and Franka Emika Panda robot manipulators are performed to illustrate the effectiveness, robustness and superiority of our proposed discrete filtered reciprocal-kind Zhang neural network algorithms.

中文翻译：

---

基于Zhang神经网络重复运动的机器人机械臂构形标定优化


高精度、低复杂度的控制算法在不同机器人机械臂末端执行器仪表的开发中发挥着重要作用。为了减少重复运动跟踪任务的动能和高速漂移现象，机器人机械臂需要对其配置进行标定。在本文中，我们将重复运动任务的机器人机械手的配置标定制定为受等式约束的未来二次规划优化问题，这也被视为人工智能和现代控制工程的基本问题。张神经网络是一种典型的方法，可以用来处理连续形式的未来优化问题，称为具有等式约束的时间相关二次规划问题。为了克服时间相关逆计算问题，提出了一种新颖的Zhang神经网络模型及其不确定扰动容忍模型，分别称为滤波倒数Zhang神经网络模型和不确定扰动容忍滤波倒数Zhang神经网络模型，分别提出了本文通过结合能量型成本函数和张神经网络设计公式来解决具有等式约束的时间相关二次规划问题。基于欧拉离散公式和模型，提出了离散滤波倒数Zhang神经网络和离散不确定扰动滤波倒数Zhang神经网络算法，用于求解未来等式约束的二次规划问题和机器人机械臂配置问题。重复运动的标定问题。 利用非线性系统及其对应的扰动系统的Lyapunov稳定性理论得到了倒数Zhang神经网络模型及其对应的不确定扰动模型的收敛特性，并分析了滤波后的倒数Zhang神经网络模型的收敛特性通过极限思维。对于重复运动任务，进行了三个实验来解决 PUMA560、Kinova Jaco2 和 Franka Emika Panda 机器人机械臂的配置校准问题，以说明我们提出的离散滤波倒数型张神经网络算法的有效性、鲁棒性和优越性。