Energy-based Swing-up Control and Motion Analysis for Pendubot with Damping

Abstract

This paper analyzes an energy-based swing-up control for use with a Pendubot robot with damping at the passive joint. The Pendubot uses a two-link manipulator with a single actuator at first revolute joint, and no actuator at the second(passive) joint. This system is a representative type of underactuated mechanical system(UMS). In order to “swing-up” the system, control is performed as follows. First, the energy-based control is used to move the Pendubot with damping attached to the passive joint from various arbitrary positions to near its upright equilibrium point. The controller is then changed to a linear quadratic regulator(LQR) to balance the system. We then analyzed the system to achieve swing-up; We analyzed the conditions that did not fall into the singularity when designing the energy-based controller; we also analyzed cases in which swing-up was reached(or not reached) if the Pendubot with damping began to stand still. We simulated the swing-up control using MATLAB in order to check the validity of the analysis. Our reasoning for adding a damper at the passive joint of the Pendubot is as follows. Flexible links are modeled with multiple virtual rigid links and revolute joints that consist of springs and dampers. Until now, a few swing-up studies have been conducted on the Pendubot with a spring at the passive joint, but none have examined the Pendubot with damping at the passive joint. As such, an examination of the swing-up of the Pendubot with damping will be helpful for future researchers when studying flexible links.