From Zeroing Dynamics to Zeroing-Gradient Dynamics for Solving Tracking Control Problem of Robot Manipulator Dynamic System with Linear Output or Nonlinear Output

With the vigorous development of mechanical intelligence in industrial manufacturing, tracking control dynamic systems have been widely applied in many aspects of industry. In this paper, we present one theorem to discuss the validity condition of a ZD model with order-n for solving the tracking control problem of a nonlinear problem by utilizing a Lie derivative. Moreover, we also give the unified formula of the ZD model with order-n and rigorously prove it mathematically. In addition, we present three other theorems to give the global exponential convergence property of the ZD controller u(t), and the steady-state tracking error bound of the ZGD controller u(t), and the radius bound where the steady-state tracking error converges exponentially. Finally, simulations are conducted to demonstrate the validity and parameter influences of the ZD model and ZGD model for solving the tracking control problem with a single linear or nonlinear output of the single-link manipulator with flexible joints.