Hybrid Control of Underactuated Manipulators with Frictional Joints

The stabilization of underactuated systems, forced by fewer actuators than DOFs, is more complex than that of fully actuated systems [67, 186]. As well known (see, e.g., [23, 249]), these systems possess nonholonomic properties, caused by nonintegrable differential constraints, and therefore, they cannot be stabilized by means of smooth feedback. Due to this, the present investigation is based on hybrid synthesis, which is recognized as an effective tool of controlling underactuated mechanical systems [250, 251]. Representative papers analyzing some control problems for underactuated systems include the study of accessibility [191], the stabilization of equilibria through passivity techniques [186] and energy shaping [27], stabilization and tracking via backstepping control [206], the use of virtual constraints to produce stable oscillations [209], path planning [37], and the control of mechanical systems with an unactuated cyclic variable [86], among others.