Minimum-Energy State Determination of an Underactuated Suction Cup Gripper Grid

The use of pre-impregnated fiber plies for manufacturing composite components has a wide range of applications within e.g. aerospace, wind turbines and automotive. Automating the layup of these plies on complex moulds is an unsolved problem. In the Flexdraper project, we address this problem by a tool consisting of an underactuated array of suction cups mounted on linear actuators, interconnected with springs. This paper aims at developing a method to accurately predict the equilibrium configuration of the underactuated degrees of freedom for an arbitrary configuration of the extensions of the linear actuators. Our approach is to establish a model for the potential energy and minimize the value of this energy. The potential energy is due to gravity and the bending and stretching of the springs. We model the shape of the springs using cubic splines and derive expressions for the energies. The developed model is compared to measured data from the setup and the results have RMS errors on the positions around 1mm for four out of five test configurations and around 3mm for the fifth test configuration. Although we still need to further improve the accuracy, the cubic spline model shows the feasibility of the general approach, but a more precise shape approximation of the springs will be needed to achieve lower RMS errors.