Dynamic Modelling of Flexible Payloads Manipulated by a Smart gripper in robotic assembly

During robotic assembly of flexible payloads, gravity and inertial forces acting on these payloads may induce both static shape deformation and vibration of the thin-walled payloads. Static deformations, which arise from deformation of the part due to its own weight under the influence of gravity, lead to misalignment of mating points of the part. Unwanted vibrations, arising from inertial forces acting on the part as it is positioned for assembly, must be damped out before it can be mated with other parts. This paper investigates the development of dynamic models of arbitrarily shaped flexible thin-walled payloads grasped by a smart gripper, comprised of multiple linearly actuated fingers with non-contact proximity sensors. Such an actuated gripper allows both partreshaping and active damping of unwanted vibrations of the part. Finite element modelling techniques are used to generate dynamic models of these arbitrarily shaped parts. Component mode synthesis methods are used to combine the dynamics of the actuated gripper with the dynamics of the thin-walled parts. The resultant dynamic model, developed with finite element modelling, is of high order, and hence model order reduction methods are employed to reduce the model order but retain the essential dynamics of the thinwalled payload gripper system. Using a two time-scale modelling technique, an integrated closed-loop modal truncation and control design procedure is used to design a shape and vibration controller for thin-walled payload. Simulation results modelling thin-walled sheet metal parts manipulated by an industrial robot confirm the validity of the proposed modelling approach.