Dynamic modelling and mass matrix evaluation of the DELTA parallel robot for axes decoupling control

The recent development of the direct drive DELTA, a 3 to 4 degree-of-freedom parallel robot dedicated to pick and place operations, opened a number of new perspectives in the domain of fast and accurate handling of light objects. The elimination of reduction gearing in these designs although improving acceleration capabilities has the disadvantage of increasing mechanical couplings between robot axes and reflects the full varying inertias directly onto each motor axis. To resolve this problem, the computed-torque control method has been applied to many serial robots over the past few years. Its application to parallel robots has however been restrained by the difficulty in establishing a simple dynamic model that can easily be calculated in real time. In this paper, an efficient method based on the direct application of the virtual work principle is proposed. Contrarily to the other methods developed up to now, it has the advantage of providing explicitly the mass matrix of the robot, which can be used in the control algorithm for axes decoupling. The use of the dynamic model in a feedforward control strategy leads to an improvement of trajectory tracking by a factor 6.