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Simulations of human movements through temporal discretization and optimization
KTH, School of Engineering Sciences (SCI), Mechanics.
2007 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

Study of physical phenomena by means of mathematical models is common in various branches of engineering and science. In biomechanics, modelling often involves studying human motion by treating the body as a mechanical system made of interconnected rigid links. Robotics deals with similar cases as robots are often designed to imitate human behavior. Modelling human movements is a complicated task and, therefore, requires several simplifications and assumptions. Available computational resources often dictate the nature and the complexity of the models. In spite of all these factors, several meaningful results are still obtained from the simulations.

One common problem form encountered in real life is the movement between known initial and final states in a pre-specified time. This presents a problem of dynamic redundancy as several different trajectories are possible to achieve the target state. Movements are mathematically described by differential equations. So modelling a movement involves solving these differential equations, along with optimization to find a cost effective trajectory and forces or moments required for this purpose.

In this study, an algorithm developed in Matlab is used to study dynamics of several common human movements. The main underlying idea is based upon temporal finite element discretization, together with optimization. The algorithm can deal with mechanical formulations of varying degrees of complexity and allows precise definitions of initial and target states and constraints. Optimization is carried out using different cost functions related to both kinematic and kinetic variables.

Simulations show that generally different optimization criteria give different results. To arrive on a definite conclusion on which criterion is superior over others it is necessary to include more detailed features in the models and incorporate more advanced anatomical and physiological knowledge. Nevertheless, the algorithm and the simplified models present a platform that can be built upon to study more complex and reliable models.

Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , vi, 52 p.
Trita-MEK, ISSN 0348-467X ; 2007:09
Keyword [en]
Forward dynamics, Biomechanics, Temporal discretization, Optimization
National Category
Mechanical Engineering
URN: urn:nbn:se:kth:diva-4585OAI: diva2:12992
2007-12-13, Sal E3, KTH, Osquars backe 14, Stockholm, 13:15
QC 20101110Available from: 2007-12-14 Created: 2007-12-14 Last updated: 2010-11-10Bibliographically approved
List of papers
1. Optimality in forward dynamics simulations
Open this publication in new window or tab >>Optimality in forward dynamics simulations
2008 (English)In: Journal of Biomechanics, ISSN 0021-9290, E-ISSN 1873-2380, Vol. 41, no 6, 1213-1221 p.Article in journal (Refereed) Published
Abstract [en]

This paper discusses a methodology and an algorithm for the analysis of dynamics of bio-mechanical systems, and in particular of optimal movement patterns between initial and target configurations. The basic formulation utilizes a finite element time discretization and establishes a large set of equations in displacements and forces. These are solved simultaneously for the whole time interval considered. The algorithm allows different optimization criteria for the movement, based on either the smoothness of the movement or the minimization of needed controls or control rates. It is primarily aimed at musculoskeletal simulations with either the joint resultant moments or the redundant muscular tensions as unknowns. Kinetic and kinematic constraints can be introduced for the obtained movement. Examples show that the obtained results are strongly dependent on the optimality criterion used. Systematic usage of the algorithm can improve knowledge about optimal motion planning.

Place, publisher, year, edition, pages
Elsevier, 2008
mechanisms, musculoskeletal system, forward dynamics, optimal movement, finite elements
National Category
Mechanical Engineering
urn:nbn:se:kth:diva-7849 (URN)10.1016/j.jbiomech.2008.01.021 (DOI)000255674700008 ()18342319 (PubMedID)2-s2.0-41549162337 (ScopusID)

uppdaterad från submitted till published(20101110) QC 20101110

Available from: 2007-12-14 Created: 2007-12-14 Last updated: 2016-07-19Bibliographically approved

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