Imperfect Dynamic Modeling of Parallel Robots Eases the Crossing of Type-II Singularities

Parallel robots must cross Type-II singularities to take full advantage of their workspace. However, since the inverse dynamic model of parallel robots degenerates at these singularities, crossing them requires infinite actuation forces. Previous approaches to crossing singularities with finite forces use Computed Torque Controllers that track a trajectory specifically designed to meet a consistency condition that avoids the degeneracy of the dynamic model. Alternatively, this paper presents an adaptive Computed Torque Controller to cross singularities with finite forces without constraining the trajectory. The proposed controller exploits the modeling errors that prevent an exact vanishing of the tracking errors. These errors multiply the controller gains that intervene in the dynamic model that degenerates at singularities. This allows our controller to adaptively adjust these gains to ensure the consistency condition at all times, avoiding the degeneracy of the dynamic model.