Predicting the drift motion for kinematically redundant robots

Redundant robots that are kinematically controlled by using Jacobian pseudoinverses 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) analyzed this problem using a differential geometric approach. Both studies arrived at conditions under which a cyclic path in the work space does not result in a cyclic path in the joint space. It is shown that these criteria are equivalent. A measure for the drift motion of planar kinematically redundant manipulators is presented. A mathematical analysis that determines the predictable properties of drift motion for planar manipulators operating under pseudoinverse control is presented. In fact, it is shown that the Lyapunov stability analysis and phase portrait techniques can be used to predict the stability behavior of drift utilizing the drift density measure. The information-such as how much drift will occur and which configurations are drift stable-can be obtained from the analysis.>