Inter-trial dynamics of repeated skilled movements

In this paper, we develop a class of discrete dynamical systems for modeling repeated, goal-directed, kinematically redundant human movements. The approach is based on a mathematical definition of movement tasks in terms of goal functions. Each goal function can give rise to an associated goal equivalent manifold (GEM), which contains all body states that exactly satisfy the task requirements. A hierarchical control scheme involving in-trial action templates and inter-trial stochastic optimal error correction is included to generate a nonlinear map for the repeated execution of the task. A simple throwing task is used to illustrate the underlying concepts and to develop a model problem for further study. The performance at the goal level, as measured by the root mean square error, is shown to result from factors that are measures of passive sensitivity, the magnitude of body fluctuations, the orientation of fluctuations with the GEM, and the stability properties of the inter-trial controller. The action of the inter-trial controller developed for our model system is simulated and is shown to agree with the mathematically predicted performance.