On Finite Time Stability of Homogeneous P-PI Controller for Robot Manipulator Orientation Control

High precision control of robot manipulators is a fundamental and important problem in many robotic tasks. For the problem, finite time control, which guarantees the state convergence in finite time, is one of the effective approaches. In such a context, several finite-time position controllers based on nonlinear control theory such as higher order sliding mode control [1], or dilated homogeneity and homogeneous approximation [2]–[5], have been proposed. Moreover, its superior control performance is confirmed by experiments [4], [5].