Measure of joint path drift for kinematically redundant robots

Redundant robots which are kinematically controlled by using Jacobian pseudo-inverses may not have repeatable joint motions. This problem was initially observed and analyzed by C.A. Klein and C.H. Huang (1983). T. Shamir and Y. Yomdin (1988) recently analyzed this problem using a differential geometric approach. The above papers arrived at conditions under which a cyclic path in the work space does not result in a cyclic path in the joint space. However, it was not clear that these conditions were equivalent. It is presently shown that these two criteria are indeed equivalent. A measure for the drift motion is presented. The mathematical analysis given in the present paper can determine these predictable properties of drift motion. It is shown that the Lyapunov analysis and phase portrait techniques can be used to predict the stability behavior of drift utilizing the drift density measure described here. Information about how much drift will occur and which configurations are stable can be obtained from the analysis