Redundancy of the giant swing backward movement on the high bar

Extent of redundancy in human movements under nonholonomic constraints can be an important factor to determine a resulting movement. However, the redundancy has seldom been examined concretely in previous studies concerning optimality of human movements under such constraints. This study focuses on a gymnastic movements on the high bar, called `giant swing backward' as an almost periodic task under a second order nonholonomic constraint, and reveals a part of redundancy of the task by extending our previous study. To this end, a simple dynamical model of an expert gymnast performing the giant swing backward is constructed with parameterization of time histories of actuated joint angles by Fourier series, and is confirmed to approximately reproduce a measured movement of the gymnast. The redundancy is calculated in various parameter spaces composed of lower order Fourier coefficients. The results illustrate restricted but considerable redundancy underlying the giant swing backward. Moreover, within the set of the redundant movements, four kinds of optimization criteria are examined to explain the movement performed by the gymnast.