“…Examples include classic single pendulum on a cart (Åström et al, 2008;Åström & Furuta, 2000), Acrobot and Pendubot (Fantoni et al, 2000;Spong, 1994;1995;Graichen et al, 2007;Brown & Passino, 1997) and the rotary double inverted pendulum (Yamakita et al, 1993;1995). In addition to the stabilization and swing-up of different kinds of inverted pendulum robots, trajectory tracking of these underactuated systems has gained attention by researches (Cho & Jung, 2003;Chanchareon et al, 2006;Hung et al, 1997;Magana & Holzapfel, 1998). There are two major approaches to construct the trajectory tracking controller for such nonlinear systems.…”