Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. In various tasks that the real world systems have to perform, the execution time is critical, and thus, it is important to enforce that the system trajectories that converge to a desired state do so 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. Specifically, we develop feedback controllers using sliding mode approach that guarantee finite-time tracking. The approach is based on designing 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. 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.

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