Redundancy underlying a gymnastic movement on the high bar

Stereotypic human movements observed in basic experimental tasks have been studied from the viewpoint of optimality with respect to some criteria. Recently, such framework is expected to be applied to understanding skilled realistic movements. This paper deals with a gymnastic maneuver on the high bar, called the kip movement, as a difficult goal-directed task under a nonholonomic constraint. The movements in such system are highly restricted by the constraint; however, it is difficult to imagine that to what extent redundancy remains for achieving the task. Thus, we study on the redundancy underlying the kip movement in this paper. To this end, a simple dynamical model of the kip movement is constructed, where the time histories of angles of actuated joints are parameterized by fifth spline functions. The movement of this model is confirmed to be approximately consistent with a measured movement of an expert gymnast. We propose a systematic method to numerically calculate a set of the spline parameters that achieve the task. A part of the redundancy underlying the kip movement is concretely illustrated. Moreover, we discuss what kind of criteria could be satisfied in the kip movement of expert gymnasts by using the set.