ACTUATION AND MOTION CONTROL OF FLEXIBLE ROBOTS: SMALL DEFORMATION PROBLEM

Abstract

Abstract This paper introduces a new computational approach for the articulated joint/deformation actuation and motion control of robot manipulators with flexible components. Oscillations due to small deformations of relatively stiff robot components can negatively impact the precision and the robot functional operation. Such oscillations, which cannot be ignored, are modeled in this study using the finite element (FE) floating frame of reference (FFR) formulation which employs two coupled sets of coordinates; the reference and elastic coordinates. The inverse dynamics, based on the widely used FFR formulation, leads to driving forces associated with the deformation degrees of freedom. Because of the link flexibility, two approaches can be considered in order to determine the actuation forces required to achieve the desired motion trajectories. These two approaches are the partially-constrained inverse dynamics (PCID) and the fully-constrained inverse dynamics (FCID). The FCID approach, which will be considered in future investigations and allows for motion and shape control, can be used to achieve the desired motion trajectories and suppress undesirable oscillations. The new small-deformation PCID approach introduced in this study, on the other hand, allows for achieving the desired motion trajectories, determining systematically the actuation forces and moments associated with the robot joint and elastic degrees of freedom, and avoiding deteriorations in the vibration characteristics as measured by the differences between the inverse- and forward-dynamics solutions. To this end, a procedure for determining the actuation forces associated with the deformation degrees of freedom is proposed and is exemplified using piezoelectric actuators.