A global continuous control scheme for the finite-time or (local) exponential stabilization of mechanical systems with constrained inputs is proposed. The approach is formally developed within the theoretical framework of local homogeneity. This has permitted to solve the formulated problem not only guaranteeing input saturation avoidance but also giving a wide range of design flexibility. The proposed scheme is characterized by a Saturating-Proportional-Derivative type term with generalized saturating and locally-homogeneous structure that permits multiple design choices on both aspects. The work includes a simulation implementation section where the veracity of the so-cited argument claiming that finite-time stabilizers are faster than asymptotical ones is studied. In particular, a way to carry out the design so as to indeed guarantee faster stabilization through finite-time controllers (beyond their finite-time convergence) is shown.

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