Optimization of Barbell Trajectory During The Snatch Lift Technique By Using Optimal Control Theory

Mathematical modeling and optimizing of snatch lift technique based on dynamic synthesis, is the aim of this study. The barbell trajectory is proposed as the performance index, evaluated experimentally by several researchers who have introduced some optimum trajectories according to the percentage of their owners' successes. Since none of the mechanical parameters were considered into the optimum trajectories, we develop a mechanical approach to fulfill this lack. Therefore, we use a biomechanical model comprised of five links to obtain the optimum trajectory of snatch weightlifting by means of minimizing a criterion function. To achieve this goal, we should solve the differential equations representing the model motion simultaneously with equations representing the performance criterion; therefore we use the optimal control approach via Pontryagin Maximum Principle (PMP) formulation. The performance criterion is defined as minimizing the sum of actuating torques of all joints during the whole snatch. The barbell trajectory of our optimized model is approximately similar to one which could be observed in experimental results. By comparing the results of this theoretical model with experimental observations of other researchers, it could be concluded that we have introduced a good predictive model. Using the biomechanical characteristics of any specific weightlifter as the input data to this model and comparing the results with the same weightlifter's experimental data can help the coaches to improve the performance of weightlifters.