A nonsingular fast terminal sliding mode control scheme for robust trajectory tracking of the underactuated EvoBot modular mobile robot in the vertical plane

Abstract

A robust control strategy for the vertical plane motion of an underactuated EvoBot mobile robot, modeled as a serial double inverted pendulum, is presented in this study. The control objectives include controlling both the directly actuated generalized coordinates and the non-actuated generalized coordinate, which is controllable through dynamic coupling with the actuated coordinates. In this regard, the system's dynamic equations are derived using the Lagrangian approach. A new nonlinear and nonsingular sliding manifold is introduced, based on which a nonsingular fast terminal sliding mode control scheme is proposed for the trajectory tracking control of the robot. This approach addresses the challenges posed by underactuation, system nonlinearities, instability, parameter uncertainties, and external disturbances. Through Lyapunov stability analysis, it is proven that finite-time asymptotic convergence of the tracking error to zero is ensured when the uncertainty upper bound is known, and convergence to a residual set is achieved when the upper bound is unavailable. The theoretical guarantees provided by the proposed control scheme are further validated through comprehensive MATLAB simulations, where its effectiveness is demonstrated under both low- and high-frequency disturbances as well as parameter uncertainties.