A robust control approach to the swing up control problem for the Acrobot

Studies the swing up control for the Acrobot, i.e., to move the Acrobot from its stable downward position to its unstable inverted position and balance it about the vertical. The combination of the partial linearization control for the swing up phase proposed by Spong (1995) and the robust control for the capture and balance phase is utilized in this paper. The key idea is first to treat the speed of the second link when it rotates across the vertical as an uncertainty, and then to design a robust controller based on the quadratic stabilization method to cope with such uncertainty. It is shown that that the robust controller is generally superior to the LQR controller in capturing and balancing the Acrobot, and the difficulty of tuning the gains in the swing up phase can be ameliorated.