Amirkabir Journal of Mechanical Engineering

Amirkabir Journal of Mechanical Engineering

Desired task space fixed time tracking by an uncertain robotic manipulator with an tunable convergence time independent of initial conditions

Document Type : Research Article

Authors
1 Department of Mechanical Engineering, Yazd University, Yazd, Iran
2 Department of Electrical Engineering, Yazd University, Yazd, Iran
Abstract
This paper proposes a novel nonlinear fixed time control structure for robotic manipulators in the presence of parametric uncertainties, modeling and parametric uncertainties, unknown, and friction torques. The control objective is to ensure accurate tracking of a prescribed task space trajectory. The proposed control framework is constructed by integrating the terminal sliding mode control method with two sets of nonlinear adaptation laws. One set of suggested adaptation laws estimates unknown physical parameters of the robotic manipulator’s dynamical model while the second set estimates unknown coefficients associated with joint friction torques. Applying the nonlinear control torques, generated by the proposed control framework, ensures that the end effector tracks the desired trajectory with exact zero steady state error after a predetermined fixed time which its independent of initial conditions. Using a collection of practical lemmas and well known inequalities, the paper analytically proves that the introduced control structure guarantees the global fixed time stability in the presence of all aforementioned uncertainties. The stability analysis also yields a nonlinear formula for calculating the convergence fixed time. The nonlinear relation reveals how the convergence fixed time depends on the proposed control structure’s arbitrary parameters. Finally, numerical simulations onto a 2-DOF robotic manipulator demonstrate that the end effector indeed reaches the desired trajectory within the fixed time.
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