Stable Control Strategy for Planar Three-Link Underactuated Mechanical System

A stable-control strategy for a planar three-link passive-active-active underactuated mechanical system not subject to gravity constraints has been devised. The control objective is to move the end effector from any initial position to any target position. First, a dynamic model of the system is built, and its properties are analyzed. Next, based on the complete integrability of an underactuated planar acrobot (UPA), the control of a planar three-link system is divided into two stages. In each stage, keeping the angle of one active link constant reduces the planar three-link system to a UPA, thereby enabling the use of quadrature to obtain the angle constraint relationships between the passive and active links. Then, the target angles associated with the target position are calculated by particle swarm optimization based on the angle constraint relationships. Finally, a controller for each stage is designed, ensuring that the control objective will be reached. Simulation results demonstrate the validity of this control method.