Mathematical Analysis of the Joint Motion of Redundant Robots Under Pseudo-Inverse Control

Redundant robots that are kinematically controlled using Jacobian pseudo-inverses may not have repeatable joint motions, when the end-effector traces a closed path in the workspace. This phenomenon is known as joint drift. The joint drift problem was initially observed and analyzed by Klein and Huang[lO]. Shamir and Yomdin(l5J also analyzed this problem using differential geometric approach. Klein and Kee[ll.] observed through numerical experiments that the drift had predictable properties. In this paper we present a measure of the drift motion, we show this measure is useful for predicting the stability properties of drifts. We further show that this measure of drift does indeed exhibit the properties numerically observed by Klein and Kee.