Robust dynamic backstepping averaged sub-gradient integral sliding mode control for navigation of mobile robots

The main goal of the current investigation is to present an output feedback robust control that regulates the motion of mobile robotic autonomous devices based on the application of the dual averaged sub-gradient descendant method. Sub-gradient realization aims to solve the design of a proposed extremum seeking control to stabilize the trajectory tracking error between the three-dimensional position of mobile robotic autonomous devices and some attainable reference trajectories in the same spatial domain. The controller belongs to a class of sliding mode controller with variable gain based on a sliding surface depending on the tracking error and its time derivative. This derivative is estimated with the application of a distributed time-dependent super-twisting robust differentiator. The proposed mobile robotic autonomous device dynamics considers the dynamics of actuators (direct current motors) which drives the mobilization of mobile robotic autonomous devices. The dynamic nature of the mobile robotic autonomous devices regulated by motor actuators induces a backstepping-like controller design based on a two-stage sequential application of the sub-gradient strategy, one for the mobile robotic autonomous devices and the second for the motor dynamics. The mixed strategy appears as a novel formulation to solve the path track for reference trajectories of mobile robotic systems. The proposed control considers the optimization of the tracking error dependent functional without the full knowledge of the mobile robotic autonomous device dynamics. With the aim of proving the effectiveness of the suggested design, two numerical examples are developed. In these examples, the tracking performance, minimization of the proposed functional as well as control evolution are evaluated. The controlled tracking outcomes of the proposed integral sliding mode control are contrasted with the outcomes produced by a set of proportional–derivative and selected sliding mode (first-order type) controllers. The suggested controller shows a superior tracking of the reference trajectory than the other two comparative controllers, using quality measures such as least mean square error and its integral.