Nonlinear Swing down Control of the Acrobot

Abstract

In this paper, we concern swing down control of the Acrobot which is a 2-link planar robot with a single actuator driving the second joint, whose control objective is to stabilize the Acrobot to the downward equilibrium point with the two links in the downward position for all initial states of the Acrobot with the exception of a set of Lebesgue measure zero. To achieve this control objective, we design a nonlinear controller by using nonnegative linear feedback of the sine function of the angle of the second joint in addition to the negative linear feedback of its angular velocity. By analyzing globally the solution of the closed-loop system consisting of the Acrobot and the presented controller and focusing on the equilibrium points of the closed-loop system and their stability, we prove that the control objective is achieved provided that some conditions on two control gains are satisfied. We design the two control gains such that the real parts of the dominant poles of the linearized model of the closed-loop system around the downward equilibrium point are minimized. We provide simulation results for two Acrobots to show the effectiveness of the presented controller.