Modeling constraints to redundancy in bimanual force coordination.

This study investigated the interactive influence of organismic, environmental, and task constraints on the organization of redundant force coordination patterns and the hypothesis that each of the three categories of constraints is weighted based on their relative influence on coordination patterns and the realization of the task goal. In the bimanual isometric force experiment, the task constraint was manipulated via different coefficients imposed on the finger forces such that the weighted sum of the finger forces matched the target force. We examined three models of task constraints based on the criteria of task variance (minimum variance model) and efficiency of muscle force output (coefficient-independent and coefficient-dependent efficiency models). The environmental constraint was quantified by the perceived performance error, and the organismic constraint was quantified by the bilateral coupling effect (i.e., symmetric force production) between hands. The satisficing approach was used in the models to quantify the constraint weightings that reflect the interactive influence of different categories of constraints on force coordination. The findings showed that the coefficient-dependent efficiency model best predicted the redundant force coordination patterns across trials. However, the within-trial variability structure revealed that there was not a consistent coordination strategy in the online control of the individual trial. The experimental findings and model tests show that the force coordination patterns are adapted based on the principle of minimizing muscle force output that is coefficient dependent rather than on the principle of minimizing signal-dependent variance. Overall, the results support the proposition that redundant force coordination patterns are organized by the interactive influence of different categories of constraints.