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 © 2013 John Wiley & Sons, Ltd.