An approximate Poincare return map for the dynamics of drifting manipulators under pseudoinverse control

Abstract

Redundant manipulators under pseudoinverse control will drift from an arbitrary initial condition to a stable limit cycle with the same period as the associated periodic workspace path. The geometric and dynamic properties of the intervening drift are examined. With the resulting framework and a prediction of the drift-free final configuration, an approximate Poincare return map is constructed. This map gives an accurate estimate of the configuration of the drifting manipulator at each return of the end effector to a particular location in the path. The intermediate positions of the manipulator and the settling time of the drift therefore allow quantitative analysis of the drift to determine possible obstacle collisions, repeatability bounds, etc