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Doctoral Thesis
DOI
10.11606/T.3.2011.tde-07032012-135641
Document
Author
Full name
Alain Segundo Potts
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Cruz, José Jaime da (President)
Coelho, Tarcisio Antonio Hess
Martins Filho, Luiz de Siqueira
Silva, Paulo Sérgio Pereira da
Terra, Marco Henrique
Title in Portuguese
Modelagem e controle ótimo de um robô quadrúpede.
Keywords in Portuguese
Controle ótimo
Modelagem cinemática
Modelagem dinâmica
Robô quadrúpede
Abstract in Portuguese
O presente trabalho visa à modelagem e ao controle ótimo de um robô quadrúpede autônomo. Devido a variações na topologia e nos graus de liberdade do robô ao longo do seu movimento, duas abordagens diferentes de modelagem foram consideradas: na primeira, foi considerado o robô com pelo menos duas pernas suportando seu corpo ou plataforma e, na segunda, considerou-se o modelo de uma perna no ar. Em ambos os casos, apresentou-se a solução dos problemas cinemáticos de posição direta e inversa por meio da parametrização de Denavit-Hartenberg. Analisaram-se também os problemas cinemáticos de velocidade e suas singularidades através da Matriz Jacobiana, e ainda obtiveram-se os modelos dinâmicos do sistema utilizando-se o Principio do Trabalho Virtual e o método iterativo de Newton-Euler para a plataforma e as pernas, respectivamente. A partir destes modelos dinâmicos, desenvolveu-se um algoritmo de otimização das perdas de energia elétrica dos motores das juntas. Neste sentido, utilizou-se a estratégia do controle independente por junta. Estratégia esta que, junto com a discretização no tempo do modelo do sistema, permitiu transformar o problema inicial de otimização para cada junta em outro de Programação Quadrática bem mais simples de ser resolvido. Depois de resolver estes problemas, para levar em conta as interações entre as dinâmicas das várias juntas, procedeu-se à busca de um ponto fixo ou mínimo global que caracterizasse a energia total gasta no movimento do sistema. Finalmente, realizada a demonstração e a análise de convergência do algoritmo, este foi testado no controle da andadura (gait) do robô Kamambaré. Como resultado do teste, observou-se o bom desempenho da formulação e a viabilidade de sua implementação em sistemas reais.
Title in English
Modelling and optimal control of a quadruped robot.
Keywords in English
Dynamical model
Kinematical model
Optimal control
Quadruped robot
Abstract in English
The present work aims the modeling and optimal control of an autonomous quadruped robot. Due to variations in the topology and the degree of freedom of the robot during its motion, two different modeling approaches were considered: firstly, the robot was considered with at least two legs supporting its body or platform and, second one, was considered the model of a leg in the air. In both cases, was presented the solution of the direct and inverse kinematic problem of position through the Denavit-Hartenberg parameterization. Were analyzed also, the kinematic problem of speed and the singularities through the Jacobian matrix, and was also obtained the dynamic model of the system using the Principle of Virtual Work or the dAlembert method and the iterative Newton-Euler method for the platform and legs, respectively. From these two dynamic model, were developed an algorithm for optimizing the power losses of the motors that driven the joints. In this sense, was used the strategy of independent control for each joint. Such a strategy, along with the discretization in time of the system model, has helped to change the initial optimization problem for each joint in a Quadratic Programming Problem, more simpler to solve. After solving these problems, and to take into account the interactions between the dynamics of various joints, was proceeded to search for a fixed point or a global minimum that would characterize the total energy spent in moving for the system. Finally, held the demonstration and analysis of convergence of the algorithm was tested in the control of gait of the Kamambaré robot. As a result of the test, we observed the good performance of the formulation and the feasibility of its implementation in real systems.
 
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Publishing Date
2012-04-11
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • BERNARDI, Reinaldo de, POTTS, Alain Segundo, and DA CRUZ, J.J. An automatic modelling approach to mobile robots. In MATHMOD 2009 - 6th Vienna International Conference on Mathematical Modelling, Viena, 2009. Proceedings MATHMOD 09 Vienna., 2009.
  • POTTS, Alain Segundo, and DA CRUZ, J.J. An Optimal Energy Control Algorithm for a Moving Paltform. In 18th IFAC World Congress, Milão, 2011. Preprints of the 18th IFAC World Congress., 2011.
  • POTTS, Alain Segundo, and DA CRUZ, J.J. Kinematics Analysis of a Quadruped Robot. In 5th IFAC Symposium on Mechatronic Systems, Cambridge, MA, 2010. Preprints of the 5th IFAC Symposium on Mechatronic Systems., 2010.
  • POTTS, Alain Segundo, DA CRUZ, J.J., and BERNARDI, Reinaldo de. A quadratic programming approach to the minimum energy problem of a mobile robot. In ICINCO 2008 - Fifth International Conference on Informatics in Control, Automation and Robotics, Funchal, Madeira, Portugal, 2008. Proceedings of ICINCO 2008., 2008.
  • POTTS, Alain Segundo, DA CRUZ, J.J., and BERNARDI, Reinaldo de. An iterative algorithm to minimize loss energy in mobile robot. In 9th International Symposium on Robot Control (SYROCO'09), Gifu, Japão, 2009. Preprints of the 9th International Symposium on Robot Control (SYROCO'09)., 2009.
  • POTTS, Alain Segundo, DA CRUZ, J.J., e BERNARDI, Reinaldo de. A first analysis of convergence for an iterative algorithm to minimize loss energy in mobile robots. In XVII Congresso Brasileiro de Automática, Juiz de Fora, MG, 2008. Anais do XVII Congresso Brasileiro de Automática., 2008.
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