Exploration of Redundancy Underlying High Bar Movements

Abstract

This paper deals with two gymnastic maneuvers on the high bar, the kip movement and the giant swing backward movement, as a task under a second-order nonholonomic constraint. Since the movements in such a system are highly restricted by the constraint, imagining to what extent redundancy exists between an initial and a final configuration that defines the task is difficult. Thus, we study the redundancy underlying high bar movement tasks by constructing a simple dynamical model of the high bar movement. The time histories of the angles of the actuated joints are parameterized by a spline function or a Fourier series, whose movements are confirmed to be approximately consistent with the measured movement of an expert gymnast.Using this model, we propose a systematic method to calculate a set of spline/Fourier parameters that achieves a task. The redundancy part underlying the kip and giant swing backward movements is concretely illustrated. Moreover, we discuss the possible optimization criteria that explain the high bar movements of the expert gymnast using the calculated parameter set.