Force control in a parallel manipulator through virtual foundations

An overwhelming controller provides robustness against uncertain parameters, disturbances and un-modelled dynamics. A simplified inverse dynamics model is used in this article to develop an overwhelming controller for a parallel manipulator (a Stewart platform), where the controller accommodates the modelling uncertainties such as the simplifications made for development of the inverse model in order to improve the computational efficiency. Such a control strategy leads to good trajectory tracking accuracy in presence of unknown disturbances. However, in addition to trajectory tracking performance, the controller for a Stewart platform should also be able to control or limit the interaction forces in applications such as robot assisted surgery and low-impact docking. The environmental forces can be accommodated during interaction period by modulating the impedance at the interface of manipulator and environment through virtual flexible foundations. The positional error induced during force control phase can be recovered during free flight or idle phase. While this approach has been successfully used in the past to control serial manipulators, the closed loop kinematic architecture in a parallel manipulator introduces many difficulties. This article proposes a modified overwhelming control scheme for parallel manipulators with compensations for interaction force control and positional error recovery. Bond graph modelling is used in this article as an integrated model and controller development tool. Force controlled machining on a spherical surface, which is akin to a surgical operation, is considered as an example application of the developed control strategy. The simulation results from the bond graph model of the controlled Stewart platform are presented to demonstrate the performance of the developed hybrid position force controller.