Swing-up and Stabilizing Control of the Acrobot

We present a new approach for the swing-up and stabilizing control of the Acrobot, a planar, two-link, underactuated robot which is used for illustrating nonlinear control techniques. We develop a swing-up control stratgy based on a nonnegative function like the mechanical energy of the Acrobot. The swing-up controller is designed with a servo system that consists of a 2nd-order lag and a sinusoidal input obtained from the phase-plane trajectory of the center of mass of the Acrobot. The proposed balancing control law is a linear one designed by applying block control methods to the linearized model about an unstable equilibrium point, which can stabilize the whole system as keeping the amplitude of the 2nd joint angle small. Simulation results are given to show the performance of the controller.