A geometric approach to the Uncontrolled Manifold analysis

In this work we extend the classical Uncontrolled Manifold (UCM) analysis to the case of micro-manipulation via hand-held tools. A major contribution of this paper is that our algorithm is independent of the choice of coordinates. This is made possible by the explicit choice of a geometric structure which is suggested by the specific application, i.e. manipulation via hand-held tools. Based on the properties of rigid body motions, available from the robotics literature, we implemented the crucial steps of UCM analysis based on the intrinsic notions of geodesics. In particular, this allowed defining a mean posture and deviations from it which are coordinate independent. We applied our geometric, coordinate-independent UCM analysis to experimental data acquired from healthy subjects performing static pointing tasks with a hand-held tool. All subjects display much larger variability on the nullspace of the Jacobian, i.e. the UCM. In other words, variability is tremor and subjects seem to project more tremor along motions which do not directly affect the task. We thus have a tool to analyze the control of accurate motion, e.g. where/how older and experienced surgeons perform better than young novices, despite larger tremor.