Stabilization of Pseudoinverse Acceleration Control of Redundant Mechanisms

Resolved acceleration motion control using the pseudoinverse of the Jacobian matrix is a well-known algorithm for control of redundant robotic manipulators which is sometimes unstable. While the effects of this instability have been discussed in the literature, the cause has not. In this paper the cause of the instability is analyzed, and the unstable growth of joint velocities and accelerations is characterized in terms of the smallest singular value of the Jacobian matrix J of the kinematic function. New stabilizing modifications to the control scheme are derived which are not based on the simple addition of a kinematic component but rather attack the cause of the instability directly. Simulations which validate the new control laws are presented.