Instability of pseudoinverse acceleration control of redundant mechanisms

Resolved acceleration motion control using the pseudoinverse or weighted pseudoinverse of the Jacobian matrix is a well-known algorithm for control of redundant robotic manipulators. Several authors have observed instabilities in simulations using this algorithm. In this paper the cause of the instability is determined, and the corresponding growth of joint velocities and acceleration is characterized in terms of the smallest singular value of the Jacobian matrix of the kinematic function, and a nearly-conserved quantity analogous to angular momentum. The analysis is supported by simulations. Based on the analysis, a stabilizing modification to the control scheme is derived that does not rely on the simple addition of a kinematic component, but rather addresses the cause of the instability directly. Simulations show that the new control algorithm stabilizes the motion in agreement with the analysis