Control algorithms for stabilizing underactuated robots

Three control algorithms are developed to stabilize an underactuated two-link robot at its unstable inverted position. The well-known linear quadratic regulator is described first. Next, a stabilization control law using partial feedback linearization is developed where the reference trajectories for the linearized degrees of freedom are designed by analyzing the zero dynamics. The linear quadratic regulator and partial feedback linearization control algorithms both assume an exact dynamic model. To deal with modeling inaccuracies, a robust controller using sliding mode concepts is supplied. Numerical simulations are presented.