Stability Analysis for Prioritized Closed-Loop Inverse Kinematic Algorithms for Redundant Robotic Systems

Stability analysis of priority-based kinematic control algorithms for redundant robotic systems is approached in this paper. Starting from the classical applications in position control of manipulators, the kinematic-based approaches have lately been applied to, e.g., visual servoing and quadruped or multirobot coordination control. A common approach consists in the definition of several tasks properly combined in priority. In this paper, by resorting to a Lyapunov-based stability discussion for several prioritized inverse kinematics algorithms, sufficient conditions for the control gains and the tasks´ design are given for the regulation problem. Two case studies show the practical implementation of the results.