Singularity-avoiding swing-up control for underactuated three-link gymnast robot using virtual coupling between control torques

An underactuated three-link gymnast robot (UTGR) is a simple model of a gymnast on a high bar. The control objective of a UTGR is to swing it up from a point near the straight-down position and to stabilize it at the straight-up position. To achieve this, we first divide the motion space into two subspaces, swing-up area and balancing area, and design a controller for each. The design of a swing-up control law that ensures that the UTGR enters the balancing area is crucial because the UTGR is subject to a nonholonomic constraint and is highly nonlinear during the swing-up motion. This study focused on how to design a swing-up control law that contains no singularities. The key concept is the introduction of a virtual coupling between control torques, which converts the problem of avoiding singularities to one of imposing constraints on the parameters of the control law and properly selecting those parameters. A swing-up control law thus designed ensures that the UTGR enters the balancing area in a natural stretched-out posture. This makes it easy to stabilize the UTGR in the balancing area. Copyright (c) 2013 John Wiley & Sons, Ltd.