Finite-time tracking control for uncertain robotic manipulators using backstepping method and novel extended state observer

Abstract

This article considers finite-time trajectory tracking control problem for robotic manipulators with parameter uncertainties and external disturbances. A finite-time controller that achieves high precision and strong robustness is proposed without the requirement of the exact dynamic model. First, a novel finite-time model-assisted extended state observer is designed to compensate the system uncertainties with complex and uncertain dynamics. Then, a composite finite-time controller is developed for trajectory tracking control with the help of finite-time model-assisted extended state observer. Compared to the classic extended state observer, it is proved that the estimation error of finite-time modelassisted extended state observer can be stabilized in finite time. Meanwhile, the finite-time convergence of the closed-loop system with the proposed controller can also be proved through Lyapunov's stability theory. A variable structure term is employed to compensate the estimation errors of finite-time model-assisted extended state observer. The validity of the control scheme is demonstrated by simulations and experiments.

Robust composite nonlinear feedback control for uncertain robot manipulators

“…where l min ðQÞ is the minimum eigenvalue of Q and d is the upper bound in closed region k vk 2 < e. It can be seen from equation (24) that when k vk 2 < e, to make _ V < 0, we choose That is, for any reference input q d and initial state, eð0Þ _ eð0Þ ½ T 2 L v ðcÞ the trajectory starting from qð0Þ _ qð0Þ ½ T will converge to q d ðtÞ _ q d ðtÞ ½…”

“…From equations(22) and(24), we deduce that the con-dition for system convergence is k xk 2 ! ffiffiffiffiffiffiffiffiffiffiffiffiffi e d 4l min ðQÞ q.…”

Trajectory tracking control for quad-rotor system in the presence of velocity constraint

“…To verify the utility of the proposed control method, this section has provided the simulation results. The main parameters for the quad-rotor are as follows: m ðkgÞ represents the total mass of quad-rotor and its value is 1:3424, g m=s 2 represents the acceleration of gravity and its value is 9:81, h m ð Þ represents the distance between the epicenter of the quad-rotor and the rotor axis and its value is 0:2, J pp kg Á m 2 ð Þrepresents the rotary inertia of p-axis and its value is 0:01175, J qq kg Á m 2 ð Þrepresents the rotary inertia of q-axis and its value is 0:01175, J rr kg Á m 2 ð Þrepresents the rotary inertia of r-axis and its value is 0:02229.…”

Finite-time trajectory control for a quadrotor aircraft using disturbance observer

“…To improve convergence rate, a novel nonlinear control method named finite-time control has been developed in the study by Bhat and Bernstein 23 and attracted the attention of many researchers. [24][25][26][27] The main feature of finite-time control lies in that the system state converges to the equilibrium point in finite time. Based on this, the problem of finite-time hovering control for a quadrotor aircraft was studied by Zhu et al 28 The attitude control algorithm was given using finitetime control technology.…”