Mechanical Engineering Journal (Feb 2016)
Mathematical model for simulating human squat movements based on sequential optimization
Abstract
This study formulates a three-link and three-joint optimal control model for simulating human squat movements, clarifies its performance, and examines the strategy for generating squat movements from a computational viewpoint. The model is characterized by sequentially minimizing its two criterion functions for the crouching-down and rising-up processes of the squat movements and predicting the desired value of the state-variable vector in the crouching-down process and the overall movement duration necessary for optimization. Each criterion function consists of three kinds of energy costs, a center-of-gravity cost, and a torque-change cost. The model is applied to reproduction or generation of trajectories of human squat movements, and the following results are obtained: (1) the desired value of the state-variable vector and the overall movement duration can be predicted as linear functions of the minimum height of the center of gravity at the switching time when the mode of motion switches from the crouching-down process to the rising-up one; (2) there exists an optimal switching time to minimize the sum of the two criterion functions; (3) the reproduced squat movement trajectories agree well with the measured ones; and (4) the reproduced trajectories are hardly affected by which one of the criterion function’s costs is minimized. These results suggest that the formulated model can be effective in simulating human squat movements and that three kinds of strategies-which individually minimize the energy, center-of-gravity, and torque-change costs-can be equivalent to one another in terms of the reproduced trajectories as far as human squat movements are concerned. The results also suggest that the minimum height of the center of gravity can be minimum information indispensable for generating squat movements.
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