Uncontrolled manifold and Juggling: Retrieving a set of Controlled Variables from Data

In this paper we analyze the concept of UnControlled Manifold (UCM), that consists in the kinematic variables that are not controlled by the user, being not relevant to the task. We proceed testing a set of controlled variables inspired by the literature about tracking task, then we propose a procedure to identify them on the basis of captured data. We are interested in the analysis of behavior in a Virtual Environment and in the real world. In particular we analyze the three ball cascade juggling and its simulation through a platform named Light Weight Juggling focusing on the task of ball tossing. Users arm kinematics is represented as a robotic manipulator with 7 degrees of freedom. Joint angles are retrieved through an optical tracking system. The variables controlled in the virtual environment are a subset of the ones controlled in the real world, that leads to an UM that differs from the one in the real world. A comparison between the statistics computed in the two cases is performed to explore behavioral differences in the two cases