WITHDRAWN: Design and control of a mobile robot following the desired Trajectory using an adaptive sliding mode approach

Abstract

This paper presents a design for a control system that will ensure the stability and proper operation of a mobile four-wheeled robot. As a result of the nonlinear dynamics, structural and parametric uncertainty of this robot, various control approaches are used to achieve stability and proper performance and minimize modeling errors and uncertainties. Two control approaches are applied to ensure that this robot is stable, that its performance is appropriate, and that modeling errors and uncertainties are minimized. In the presence of external disturbances and parametric uncertainty, this algorithm uses the signals provided by the sensor from the trajectory to follow the predetermined trajectory. It was assumed in previous articles that the upper bound of uncertainty was known. In this paper, we assume the upper bound of uncertainty and disturbance in the robotic system is unknown since, in many cases, we cannot know the extent of these uncertainties. In this paper, we generalized the sliding mode control law and proved its effectiveness so that by including an adaptive part to the control law, we make it into a robust-adaptive sliding mode control, and we could estimate the upper bound uncertainties online based on these adaptive laws. The control objective is to follow a predefined trajectory by regulating the linear and angular velocities in the presence of external disturbance and parametric uncertainty. The Adaptive Super Twisting (AST) algorithm is designed to build a robust controller with neglected chattering in a steady state. The proposed controller is validated experimentally. The results show that the proposed controller guarantees the performance of the conventional SOSMC under external disturbance and parametric uncertainty with less chattering. This typology can be expressed as a distinct theorem with stable results. Simulations with MATLAB software demonstrate that the controller ensures optimal performance under external disturbances and parametric uncertainty with fewer fluctuations.