Finite-time tracking using sliding mode control

Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. In this paper, we consider a general class of fully actuated mechanical systems described by Euler-Lagrange dynamics and the class of underactuated systems represented by mobile robot dynamics that are required to reach and maintain the desired trajectory in finite time. An approach known as the terminal sliding mode control (TSMC) involves non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time thus ensuring finite-time tracking. The main advantage of this control scheme is in fast converging times without excessive control effort. Such controllers are known to have singularities in some parts of the state space and, in this paper, we propose a method of partitioning the state space into two regions where the TSMC is bounded and its complement. We show that the region of bounded TSMC is invariant and design an auxiliary sliding mode controller predicated on linear smooth sliding surface for the initial conditions outside this region. Furthermore, we extend these results to address TSMC for underactuated systems characterized by the mobile robot dynamics. We demonstrate the efficacy of our approach by implementing it for a scenario when multiple dynamic agents are required to move in a fixed formation with respect to the formation leader. Finally, we validate our results experimentally using a wheeled mobile robot platform.