Energetic Versus Sthenic Optimality Criteria for Gymnastic Movement Synthesis

Dynamic synthesis of human movements raises the question of the selection of a suitable performance criterion able to generate proper dynamic behaviors. Two quite different criteria are likely to be appropriate candidates: the minimum effort cost (or sthenic criterion) and the minimum energy cost. The paper is aimed at clarifying the dynamic effects of these two fundamental criteria when considering movements executed with liveliness as they are in gymnastic. It is well known that the former cost generates movements with smooth dynamics. A special attention is devoted to the latter. The optimal control theory shows that minimizing the energy consumption results in actuating inputs of bang-off-bang type producing momentum impulses. When achieving dynamic synthesis, this criterion makes necessary to account for bounds set on driving torques. Moreover, when dealing with one-sided contacts, as in floor handstands, the unilaterality of contact forces must be explicitly accounted for since it tends to be infringed by impulsive efforts. Numerical simulations of these formal properties are carried out using a parametric optimization technique, and considering the raising phase of floor handstands. It is shown that the energetic criterion tends to generate movements which exhibit similarities with their real counterpart performed by an expert gymnast. Conversely, the sthenic criterion produces movements quite different. But, a salient fact is that these ones proved to be easier to perform by young beginners. As a result, they could help to coach novice gymnasts.