Modeling of Dynamics and Model-Based Control of DELTA Direct-Drive Parallel Robot
Karol Miller* and Boris S. Stevens**
*Biomechanics Division, Mechanical Engineering Laboratory, MITI, Namiki 1-2, Tsukuba, Ibaraki, 305 Japan
(Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics, Nowowiejska 24, 00-665 Warsaw, Poland)
**Swiss Federal Institute of Technology (Ecole Polytechnique Fédérale de Lausanne), Institut de Microtechnique, 1015 Lausanne, Switzerland
The term “Extended Space” used in this article is hereby defined as a union of the operational and articulation spaces of a manipulator. The advantages in the use of such coordinates (extended space) in the description of DELTA robot is presented here and discussed in some detail. The emerging importance of parallel robots has necessitated an increased sophistication to achieve improved control. A method based on the direct application of the Hamilton’s Principle in extended space, has been applied efficiently to solving the inverse problem of dynamics and implemented for real time application in the control law of the direct-drive version of DELTA parallel robot.1-3) The full dynamic model of this robot has been developed herein. The numerical efficiency and other benefits of this approach over the more classical Lagrange and Newton-Euler methods for the inverse dynamics problem solving are also briefly discussed. For similar models, the version obtained by the direct application of Hamilton’s principle is found to possess 23% less mathematical operations than for the Lagrangebased model. Frictional effects. being very small in the direct-drive manipulator, are not included in the present Hamilton development but can be handled with a slight modification. Furthermore the acceleration information of the robot are not required as input states to the Hamilton model. The measurement of trajectory tracking performances for different controllers is conducted. The repeatability of the robot trajectory tracking is determined. The improvement obtained in the control algorithm’s performance after the Hamilton implementation is proven to be conclusive.