## Optimization of strategy during locomotion using pseudospectral Chebyshev's method-competitive running as an example

### Piotr Samoraj

#### Abstract

Thesis contains the creation of computational algorithm for computer program Matlab using pseudospectral Chebyshev’s method to solve the minimal time problem. The main task was to find the optimal control in athletic run along the route with variable slope. Review of the literature was performed to describe and compare the methods previously used in the solutions of similar cases. Model of movement and energy model for runner was described. Publications which use pseudospectral Chebyshev’s method to solve other optimization problem were shown. There were no results of searching of human energy model with numeric data based on research. Assumptions, equations of motion, energy or equality constrains and inequality constraints are based on the available publications. Description of pseudospectral Chebyshev’s method was based on other articles. There were shown equations and constraints with using matrices. Function fmincon for the sequential quadratic programming was described. This function is epmloyed by Matlab to optimization process. Correctness of the optimization program was checked for problem of flat run (on a distance of 400 meters) and for task of swimming. For these problems,the analytical results were available in the publications based on the same data of energy model. After analyzing the results of flat run the number of nodes was determinded. For this number the solution is sufficiently accurate. Then, the calculations were done for the run with constant and variable slope over a distance of 400 meters. For these issues was exoutered how to define the length of run based on the horizontal axis. The results as a curves of velocity, energy resources per unit mass and the control variable are shown in the graphs. Calculations for the course with variable slope was performed for the four shapes of route with different altitudes. Graphs of time as function of level difference was created for each route profile. All results were analyzed and commented on. Conclusions were written. There were found general relations for various run cases. Also calculations were done for run over a distance 800 meters with a variable slope. For flat run on 400 meters the effect of different energy model data was tested to the final result - minimized time. For flat run on 400 meters influence on final result (minimum time) was tested by different data for energy model. On the end summarize was written with main conclusions. It was described in what way the thesis was realized
Diploma typeMaster of Science
Author Piotr Samoraj WMEiL
Piotr Samoraj,,
- Faculty of Power and Aeronautical Engineering
Title in PolishOptymalizacja strategii lokomocji metodą pseudospektralną Czebyszewa na przykładzie biegu lekkoatletycznego
Supervisor Ryszard Maroński ITLMS
Ryszard Maroński,,
- The Institute of Aeronautics and Applied Mechanics
Certifying unitFaculty of Power and Aeronautical Engineering (FPAE)
Affiliation unitThe Institute of Aeronautics and Applied Mechanics (IAAM)
Study subject / specializationMechanika i Budowa Maszyn
Languagepl polski
StatusFinished
Defense Date25-10-2013
Issue date (year)2013
Pages90
Internal identifierMEL; PD-2363
Reviewers Ryszard Maroński ITLMS
Ryszard Maroński,PhD, DSc,
WUT Professor - The Institute of Aeronautics and Applied Mechanics
, Franciszek Dul ITLMS
Franciszek Dul,PhD,
Assistant Professor - The Institute of Aeronautics and Applied Mechanics
Keywords in Polishoptymalizacja, zagadnienie minimalno-czasowe, pseudospektralna metoda Czebyszewa, Matlab, bieg lekkoatletyczny
Keywords in Englishxxx