On the Drift Rate in Pseudo-Inverse Control of Redundant Robots

Redundant robots which are kinematically controlled using Jacobian pseudo-inverses may not have repeatable joint motions. This problem has been observed and analysed by Klein and Huang[4]. Shamir and Yomdin[8] also analysed this problem using differential geometric approach. Klein and Kee[5] observed through numerical experiments that the drift had predictable properties. Previously Ahmad and Luo[7] presented a measure for the manipulator drift motion (in planar work spaces), which proved useful for drift stability analysis. The mathematical method developed in Luo and Ahmad's paper[7] can predict the properties observed by Klein and Kee. This paper presents a generalisation of the measure of drift in [6] and [7] into arbitrary dimensional workspace and joint space for redundant robots.