Extremum seeking control for the trajectory tracking of a skid steering vehicle via averaged sub-gradient integral sliding-mode theory

This study introduces the development of a novel extremum-seeking controller designed to stabilize the tracking trajectory of a fully actuated four -wheeled skid steering vehicle. The controller design employs a class of averaged sub -gradient optimization strategies for a suitable convex function that depends on the enforced tracking trajectory achieved through an integral sliding mode implementation. The application of this controller necessitates a nonlinear coordinate transformation of the skid steering vehicle dynamics, resulting in a perturbed multi-input-multi-output linear system. Using the proposed controller, a multidimensional sliding surface remains remarkably stable despite tracking errors. The surface design defines a manifold that aligns with the sub -gradient of a convex function, contingent upon the integral of the tracking error. This connection establishes a link between the extremum-seeking problem and the sliding mode control design. Employing the cascade design strategy, commonly referred to as backstepping, enables the calculation of torques for the four wheels of the mobile vehicle using a sequence of auxiliary sliding surfaces, each with its corresponding complementary function for every stage. The dynamic formulation for the wheel torques is derived from the integral sliding mode methodology. A series of numerical evaluations are conducted to assess the controller's effectiveness in terms of functional performance. A comparison between the control action based on sliding mode and the traditional state feedback formulation validates the efficacy of the proposed design. This comparison demonstrates advancements in robustness in the face of modeling uncertainties and optimization of the performance function, which are theoretically supported by the suggested control design. Implementing the proposed controller in an experimental platform for a wheeled skid steering vehicle reaffirms the control design methodology presented in this study. This platform includes the application of an image processing algorithm to determine the non -inertial position of the autonomous vehicle using integral sliding mode control. This information completes the necessary data for implementing the on -site version of the proposed controller.