Object Manipulation under Hybrid Active/Passive Closure

In this paper, we discuss the manipulation of an object under hybrid active/passive closure. We show the orthogonality between the directions of active and passive force closures for general grasping systems. Based on the orthogonality, we decompose the dynamics of grasping system into the "active part" and the "passive part". By using the decomposition, we show that the grasped object can be manipulated only by considering the dynamics of the active part. We also consider how to determine the desired internal forces in order to satisfy frictional constraints during the manipulation. In order to verify the validity of our approach, some simulation results are shown