New results of angular momentum based stabilizing control of the Acrobot

Abstract

For the Acrobot (a two-link planar robot moving in the vertical plane with a single actuator at the second joint), this paper studies how to design angular momentum based stabilizing controllers with a large region of attraction for its upright equilibrium point, where all the links are upright. First, in addition to the angular momentum of the Acrobot about the first joint, its first-time derivative, and its second-time derivative, this paper shows how to design a variable from the non-singularity of the Jacobian matrix of these four variables. This paper presents a necessary and sufficient condition such that the Jacobian matrix is nonsingular regardless of all the mechanical parameters, and proposes two parameterizations of the variable to be designed and two types of stabilizing controllers using these four variables. Finally, the simulation results are presented to show that the regions of attraction of the proposed controllers are much bigger than those of the linear state-feedback controllers having the same poles of the linearized system of the closed-loop system.