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Computación y Sistemas

On-line version ISSN 2007-9737Print version ISSN 1405-5546

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




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.;;


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



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.



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.





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



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