SciELO - Scientific Electronic Library Online

 
vol.13 issue2Discrete-Time Modeling and Path-Tracking for a Wheeled Mobile Robot author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • Have no similar articlesSimilars in SciELO

Share


Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.13 n.2 México Oct./Dec. 2009

 

Artículos

 

On Line Optimal Control of Robots for Tracking without Inverse Kinematics

 

Control Optimo en Línea de Robot para Seguimiento sin Cinemática Inversa

 

Alejandro Rodríguez Ángeles, Carlos. A. Cruz Villar and David Muro Maldonado

 

Departamento de Ingeniería Eléctrica, Cinvestav, Av. Instituto Politécnico Nacional, San Pedro Zacatenco, C.P. 07360, A.P. 14–740, México, D.F. 07000, México. aangeles@cinvestav.mx; cacruz@cinvestav.mx; dmuro@cinvestav.mx

 

Article received on March 10, 2008
Accepted on September 04, 2008

 

Abstract

This article presents a novel on–line optimal control for tracking tasks on robot manipulators for which inverse kinematics is not required. The controller is composed by a stabilization Cartesian PID control plus a joint space optimal control, which is in charge of improving tracking performance. The joint space dynamic optimal control is based on the gradient flow approach with the robot dynamics as a constraint. The combination of both controllers is implemented in joint space, by considering the robot Jacobian, nonetheless for design of both controllers only direct kinematics and Cartesian errors are taken into account. Joint space controllers which are based on Cartesian errors commonly require the inverse kinematics of the robot, in this proposal the joint space optimal controller determines on line the required joint variables to achieve the Cartesian task, without using the inverse kinematics of the robot, thus an explicit inverse kinematics model of the robot is not needed. The paper presents experimental results with a two degree of freedom (dof) planar manipulator, showing that the optimal control part highly improves the tracking performance of the closed loop system.

Keywords: Gradient flow, direct kinematics, sensitivities, Cartesian control.

 

Resumen

Este trabajo presenta un control óptimo en línea para tareas de seguimiento de trayectoria en robots manipuladores, el cual no requiere de la cinemática inversa. El control está compuesto por un control PID Cartesiano para fines de estabilidad y un control optimizante en espacio articular para mejorar el desempeño en seguimiento. El control optimizante se basa en el flujo gradiente considerando la dinámica del robot como restricción. La combinación de ambas estrategias de control se implementa en espacio articular a través del Jacobiano del manipulador, sin embargo para el diseño de ambos controles no se requiere del modelo cinemático inverso del robot. El controlador propuesto considera errores Cartesianos, pero a diferencia de controladores en espacio articular que requieren del modelo cinemático inverso. El control aquí propuesto determina de forma implícita las variables articulares requeridas para la tarea cinemática, sin hacer usado del modelo cinemático inverso. El artículo presenta resultados experimentales con un robot planar de dos grados de libertad, donde se muestra que el control óptimo mejora el desempeño del robot en tareas de seguimiento.

Palabras clave: Flujo gradiente, cinemática directa, sensitividad, control Cartesiano.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgments

The authors acknowledge support from CONACYT through the projects 61838 and 84060.

 

References

1. Hwang, Y.K. and N. Ahuja "A potential field approach to path planning". IEEE Transactions on Robotics and Automation, 8, 1992, pp. 23–32.        [ Links ]

2. Abo–Hammour Z.S., N. M. Mirza, S.M. Mirza and M. Arif "Cartesian path generation of robot manipulators using continuous genetic algorithms". Robotics and Autonomous Systems, 41, 2002, pp. 179–223.        [ Links ]

3. Ata, A.A. and T. R. Myo "Optimal point–to–point trajectory tracking of redundant manipulators using generalized pattern search". International Journal of Advanced Robotic Systems, 2, 2005, pp. 239–244.        [ Links ]

4. Mcfarlane, S. and E. A.~Croft "Jerk–Bounded Manipulator Trajectory Planning: Design for Real–Time Applications". IEEE Transactions on Robotics and Automation, 19, 2003, pp. 42–52.        [ Links ]

5. Lee, S., J. Kim, F. C. Park, M. Kim, and J. E. Bobrow "Newton–type algorithms for dynamic–based robot movement optimization". IEEE transactions on robotics, 21, 2005, pp. 657–667.        [ Links ]

6. Ding, H., Y. F. Li, and S. K. Tso "Dynamic optimization of redundant manipulators in worse case using recurrent neural networks". Mechanism and Machine Theory, 35, 2000, pp. 55–70.        [ Links ]

7. Zhang, Y., S. S. Ge, and T. H. Lee "A unified quadratic–programming–based dynamical system approach to joint torque optimization of physically constrained redundant manipulators". IEEE Transactions on systems, man, and cybernetics – part B: cybernetics, 34, 2004, pp. 2126–2132.        [ Links ]

8. Helmke, U., and J.B. Moore, Optimization and Dynamical Systems, Springer–Verlag. London, 1996.        [ Links ]

9. Maly, T., and L. Petzold "Numerical methods and software for sensitivity analysis of differential–algebraic systems". Applied Numerical Mathematics, 20, 1996, pp. 57–79.        [ Links ]

10. Lewis, F.L., C.T. Abdallah, and D.M. Dawson, Control of Robot Manipulators, Macmillan Publishing. New York, 1993.        [ Links ]

11. M.W. Spong and M. Vidyasagar, Robot Dynamics and Control, John Wiley & Sons, Inc., New York, 1989.        [ Links ]

12. Craig, J.J., Introduction to Robotics Mechanics and Control, Pearson Prentice Hall. New Jersey, 1989.        [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License