Stability analysis for prioritized closed-loop inverse kinematic algorithms for redundant robotic systems

A wide number of robotic applications makes use of priority-based kinematic control algorithms for redundant systems. Starting from the classical applications in position control of manipulators, the kinematic-based approaches were lately applied to, e.g., visual servoing or multi-robot coordination control. The basic approach consists in the definition of several tasks properly combined in priority. A rigorous stability analysis that ensures the possibility to effectively achieve the defined tasks, however, is missing. In this paper, by resorting to a Lyapunov-based stability discussion for the prioritized inverse kinematics algorithms, an effective condition is given to verify that the tasks are properly matched; moreover, minimum bound for the control gains are determined.