Body-goal variability mapping in an aiming task

Given the number of joints and muscles in the human body, there are typically an infinite number of ways to perform the same action, a feature of directed movements known as equifinality (Bernstein, The coordination and regulation of movements, Oxford, Pergamon, 1967). Here we present a new type of performance analysis based on the idea of a body-goal variability mapping. We show how this mapping arises naturally from the idea of a goal function that theoretically defines a task and, in the presence of equifinality, determines the set of all possible task solution strategies, the goal equivalent manifold (GEM). The approach also yields estimates of the sensitivity of goal-level errors to body-level perturbations, and we derive a general formula expressing the relationship between the two. We apply these ideas to the analysis of redundant kinematic data from subjects performing an aiming task carried out with and without a laser pointer. It is shown that in order to characterize performance one must consider two factors in addition to the body variability: first, the degree of alignment between body variability and the GEM; and second, the sensitivity parameters that control the degree to which goal-relevant body variability is amplified at the target. Both of these factors can be computed using the estimated body-goal mapping. We show that the performance for three conditions involving two different nominal postures and two different sensory conditions (laser/no laser) can be classified by examining the clustering of data in an orientation- sensitivity parameter plane associated with the map.