On the Stability of Closed-Loop Inverse Kinematics Algorithms for Redundant Robots

The purpose of this paper is to provide a convergence analysis of classical inverse kinematics algorithms for redundant robots, whose stability is usually proved only in the continuous-time domain, thus neglecting limits of the actual implementation in the discrete time, whereas the convergence analysis carried out in this paper in the discrete-time domain provides a method to find bounds on the gain of the closed-loop inverse kinematics algorithms in relation to the sampling time. It also provides an estimation of the region of attraction (without resorting to Lyapunov arguments), i.e., upper bounds on the initial task space error. Simulations on an 11-degree-of-freedom manipulator are performed to show how the found bounds on the gain are not too restrictive.