A Strict Lyapunov Function for the Finite-Time Regulation of Robot Manipulators with Bounded Inputs

This paper proposes strict Lyapunov functions (SLFs) for the Saturated-Proportional-Saturated-Derivative with gravity cancellation controller for the case when the robot manipulator has non-ideal actuators and without taking into account the viscous friction in the model. The proposal of an SLF in this scenario has remained as an open problem in the regulation case. Here, we propose two different SLFs, one to ensure that the desired equilibrium is globally asymptotically stable and, the other, to ensure that such equilibrium is finite time stable. The comparison of the finite-time controller versus its linear implementation is illustrated via simulations, on a two degrees-of-freedom robot manipulator.