Body-Goal Variability Mapping: the Interaction Between Geometry and Sensitivity in an Aiming Task
- Department of Engineering Science & MechanicsPennsylvania State University
martedì 17 maggio 2005
caffe`, te` & C. ore 17.00
The execution of every directed movement requires that the individual solve the problem of interaction between the body, the environment, and the requirements of the task. We approach this problem using the concept of a goal function that encodes this interaction in terms of body variables, goal variables, and the relevant geometry and physics that specify the environmental requirements of the task. Given a goal function, an excess of body degrees of freedom necessarily leads to a Goal Equivalent Manifold (GEMs) that contains all possible solutions to a given task. We also define the sensitivity along the GEM, which characterizes how error in the body variables gets mapped onto the goal variables and thus directly effects performance. In general, these sensitivity properties will vary as one moves along the GEM, and thus different task strategies that may seem equivalent have very different performance characteristics. After discussing a simple theoretical model of aiming that illustrates the key concepts, we apply these ideas to the analysis of redundant kinematic data in an aiming task carried out with and without a laser pointer. We use the data to estimate a linear mapping relating body to goal variables. It is shown that in order to characterize performance one must consider two factors: (1) the geometrical structure of body variability along the GEM; and (2) the sensitivity parameters that control the degree to which task-relevant body variability is amplified at the target. Both of these factors can be computed using the estimated linear mapping. Using this approach, we show that the performance for a 2 X 2 test matrix with two different nominal postures and two different sensory conditions (laser/no laser) can be classified using by examination of the clustering of data in the GEM orientation-sensitivity plane.
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