Stabilization Control of Underactuated Spring-Coupled Three-Link Horizontal Manipulator Based on Energy Absorption Idea

Abstract

A spring-coupled three-link horizontal manipulator (STHM) is an underactuated mechanical system that possesses two control inputs and three degrees of freedom (DOF). This paper discusses the stabilization control problem for this multi-DOF underactuated system. By using an energy-absorbing idea, we design two types of virtual friction controllers: PsD controller and PD controller. Additionally, the stability of the control system is analyzed based on Lyapunov theory and LaSalle’s invariance principle. The design of the stabilizing controller in this paper makes good use of the physical characteristics of the STHM system. The design process of the whole control system is simple. Numerical examples demonstrate the validity and superiority of our developed control strategy.

Keywords

• underactuated manipulator
• stabilization control
• virtual friction
• Lyapunov function
• LaSalle’s invariance principle