Mathematical model for simulating human squat movements based on sequential optimization

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 f...

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Autores principales:	Toshikazu MATSUI, Masayoshi MOTEGI, Natsuki TANI
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2016
Materias:	squat movement optimal control model sequential optimization desired state variable movement duration minimum height of center of gravity switching time Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/0cc87771f68f453b8e6cf99a15972621
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id	oai:doaj.org-article:0cc87771f68f453b8e6cf99a15972621
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spelling	oai:doaj.org-article:0cc87771f68f453b8e6cf99a159726212021-11-26T06:40:17ZMathematical model for simulating human squat movements based on sequential optimization2187-974510.1299/mej.15-00377https://doaj.org/article/0cc87771f68f453b8e6cf99a159726212016-02-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/3/2/3_15-00377/_pdf/-char/enhttps://doaj.org/toc/2187-9745This 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.Toshikazu MATSUIMasayoshi MOTEGINatsuki TANIThe Japan Society of Mechanical Engineersarticlesquat movementoptimal control modelsequential optimizationdesired state variablemovement durationminimum height of center of gravityswitching timeMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 3, Iss 2, Pp 15-00377-15-00377 (2016)
institution	DOAJ
collection	DOAJ
language	EN
topic	squat movement optimal control model sequential optimization desired state variable movement duration minimum height of center of gravity switching time Mechanical engineering and machinery TJ1-1570
spellingShingle	squat movement optimal control model sequential optimization desired state variable movement duration minimum height of center of gravity switching time Mechanical engineering and machinery TJ1-1570 Toshikazu MATSUI Masayoshi MOTEGI Natsuki TANI Mathematical model for simulating human squat movements based on sequential optimization
description	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.
format	article
author	Toshikazu MATSUI Masayoshi MOTEGI Natsuki TANI
author_facet	Toshikazu MATSUI Masayoshi MOTEGI Natsuki TANI
author_sort	Toshikazu MATSUI
title	Mathematical model for simulating human squat movements based on sequential optimization
title_short	Mathematical model for simulating human squat movements based on sequential optimization
title_full	Mathematical model for simulating human squat movements based on sequential optimization
title_fullStr	Mathematical model for simulating human squat movements based on sequential optimization
title_full_unstemmed	Mathematical model for simulating human squat movements based on sequential optimization
title_sort	mathematical model for simulating human squat movements based on sequential optimization
publisher	The Japan Society of Mechanical Engineers
publishDate	2016
url	https://doaj.org/article/0cc87771f68f453b8e6cf99a15972621
work_keys_str_mv	AT toshikazumatsui mathematicalmodelforsimulatinghumansquatmovementsbasedonsequentialoptimization AT masayoshimotegi mathematicalmodelforsimulatinghumansquatmovementsbasedonsequentialoptimization AT natsukitani mathematicalmodelforsimulatinghumansquatmovementsbasedonsequentialoptimization
_version_	1718409700572135424

Mathematical model for simulating human squat movements based on sequential optimization

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