Robust PID sliding-surface control for nonholonomic pendulum-driven spherical robots in the presence of nonlinear perturbations and uncertainty shocks

This study is concerned with the control of spherical robots, which are an important benchmark in the field of robotic technology. Designing an effective controller for such a system requires considering factors such as disruptions and uncertainties. To address these challenges, we propose a practical type-2 fuzzy PID sliding surface technique that can stabilize and control the nonholonomic pendulum-driven spherical robot. This technique is specifically designed to account for uncertainties and disturbances in the system, making it suitable for real-world applications. The study begins by presenting the governing equations of the system and then outlines the design process of the proposed technique. To prove the reliability of the newly proposed controller and disturbance observer, the study employs the Lyapunov stability theorem. Ultimately, the study showcases the efficacy of the proposed approach via simulations and experiments, where it is shown to minimize the response time, reduce oscillations, and ensure stability under a range of operating conditions. This approach offers a promising solution for the control of nonholonomic robots, with potential applications in areas such as robotics, automation, and industrial control.