Generating optimal dynamic motions for closed-chain robotic systems

Chettibi, Taha; Haddad, Moussa; Labed, Abdenour; Hanchi, S.

doi:10.1016/j.euromechsol.2005.01.005

Cited by 10 publications

(5 citation statements)

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“…From the point of view of robotics science, the problem of performing movements with the least expenditure of energy is known as the Optimal Free Motion Planning Problem (OFMPP). 8 Although the first papers dealing with OFMPP for robots appeared about 30 years ago, 13 it remains an active and attractive research area in robotics. This interest can be justified by two main factors.…”

Section: Introductionmentioning

confidence: 99%

“…Authors highlighted the difficulty in computing the C-space since a system of nonlinear equations, inherent to closure constraints, must be solved at each iteration of the search process. 8 The optimization criteria commonly employed in robotics are based on physical criteria involving energy, control effort, jerk, or time. 6,9,14,17,25 A minimum energy formulation may thus be an interesting approach for mobile robots, particularly in applications in which the battery weight is a critical issue.…”

Section: Introductionmentioning

confidence: 99%

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Optimal power loss motion planning in legged robots

Potts

Cruz

2014

Robotica

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SUMMARYAn iterative algorithm to minimize energy loss in kinematic chains is proposed. This algorithm is designed to low level of control where variables such as terminal states, runtime, and physical and electrical parameters of the movement are given by higher levels of control. An original complex problem of optimization is transformed into a simple quadratic programming problem subject to linear constraints by discretizing all dynamic system variables. The whole system is then converted into a recursive matrix equation that is solved iteratively. A proof of convergence is suggested. The performance of the algorithm is illustrated by using it in the motion planning of a quadruped robot.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal power loss motion planning in legged robots

Potts

Cruz

2014

Robotica

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“…Na literatura existe reportada uma grande quantidade de robôs com pernas (Abderrahim et al, 1999;Choi et al, 2000;Brown e Huissoon, 2000;Galvez et al, 2001;Armada et al, 2003;Weingartent et al, 2004;Tokhi et al, 2005;Choi e Park, 2006) (Stryk e Bulirsch, 1992;Hull, 1997;Betts, 1998). Os métodos indiretos são baseados no cálculo das variações ou Princípio do Máximo de Pontryagin (Bryson e Ho, 1975 (Chettibi et al, 2005).…”

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“…Existem relatados na literatura alguns exemplos que mostram a aplicação de tais métodos, aplicados a robôs paralelos ou seriais, encontram-se assim técnicas de controle para otimizar a trajetória de manipuladores minimizando determinados parâmetros físicos tais como, energia mecânica, esforço de controle, jerk ou tempo (Facchinei, 1997;Guo e Zhang, 2001;Bobrow et al, 2004;Luo et al, 2004;Chettibi et al, 2005)…”

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“…Chettibi et al, 2005).Diferentemente dos métodos indiretos, os diretos são baseados em transformações do sistema original em problemas de programação não-linear por meio da discretização de algumas ou de todas as variáveis dinâmicas do sistema. Esta nova forma de abordagem tem-se mostrado robusta e simples em muitas aplicações.A aplicação de técnicas de controleótimo a robôs de cadeia fechada, tais como, manipuladores, robôs antropomórficos e robôs paralelos em geralé uma técnica relativamente recente, istoé devidoà complexidade do seu movimento,à grande quantidade de ligamentos e corpos que interagem no mecanismo eà dificuldade de fazer uma modelagem exata do sistema.…”

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Modelagem e controle ótimo de um robô quadrúpede.

Potts¹

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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 d'Alembert 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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