Continuous rolling motion control for the Acrobot composed of rounded links

This paper describes the modeling of the Acrobot composed of 2 links with a curved contour and the continuous rolling motion control for this Acrobot. The outer contour of each link is shaped from the arc whose radius is different by the tip and the sidepiece of the link. The model differs according to the contact point between the Acrobot and the ground. Therefore, it is difficult to control the whole motion via common control strategy. From an intuitive analysis based on the Acrobot¿s energy while the Acrobot rolls with a certain constant relative angle, control strategy is constructed in two phases. The phases are when the Acrobot rolls with lowering( downward phase) and raising(upward phase) the center of the gravity. As the control in upward phase needs to lower the COG of the Acrobot, a collision between the Acrobot and the ground becomes unavoidable. Therefore, analysis of this collision phenomenon is also conducted. At last, by selecting the output functions that can achieve the control objective at each phase and applying Output Zeroing control, continuous rolling motion is realized in numerical simulation.