Optimal forward twisting pike somersault without self-collision

Abstract

In acrobatic sports, twisting fast before piking allows athletes to enlarge their scoring potential. Since planning the arm and hip movements to twist fast is unintuitive, optimal control appears as a powerful and risk-free tool. To our knowledge, predictive simulations of human motion did not include self-collision avoidance constraints resulting potentially in unrealistic solutions. Our objective was to generate innovative and realistic twisting techniques for forward somersaults ending in pike position by solving an optimal control problem including non-collision constraints. Optimal techniques for one, two, or three twists before piking were generated by minimising the duration of the twisting and piking phases. The model was composed of five segments with one degree of freedom at the chest and two at the hips and shoulders. We explored local minima using a multi-start approach. Solutions were further analysed to assess the impact of non-collision constraints, the segments’ contribution to twist creation, and their stability. For each desired number of twists, one relevant solution was chosen. Optimisation showed that trampolinists could attempt new acrobatics: forward triple twisting somersault ending in pike position. This research also shows that non-collision constraints strongly modify the optimal techniques without impairing significantly their performance.