Identification of Optimal Movement Patterns for Energy Pumping

Energy pumping is a way to gain kinetic energy based on an active vertical center of mass movement in rollers in sports like skateboarding, skicross, snowboard cross and BMX. While the principle of the energy transfer from the vertical movement to the horizontal movement is well understood, the question of how to achieve the optimal energy transfer is still unresolved. In this paper, we introduce an inverse pendulum model to describe the movement of the center of mass of an athlete performing energy pumping. On this basis, the problem of identifying the optimal movement pattern is formulated as an optimal control problem. We solve the discretized optimal control problem with the help of a SQP-algorithm. We uncover that the optimal movement pattern consists of a jumping, flying, and landing phase, which has to be timed precisely. We investigate how the maximal horizontal speed depends on parameters like rollers height and maximal normal force of the athlete. Additionally, we present a qualitative comparison of our results with measured results from BMX-racing. For athletes and coaches, we advice on the basis of our results that athlete's performance is optimized by using maximal force and adopt an exact and proper timing of the movement pattern.