Way Point Tracking of a Spherical Inverted Pendulum

The paper addresses the problem of way-point tracking for the spherical inverted pendulum under the influence of a planar force. A nonlinear controller is proposed that drives the pendulum to track an ordered sequence of desired translational positions (x_ri,y_ri) by visiting their neighborhood N_mui in an inertial reference frame while stabilizing the pendulum about the upper equilibrium. The way-point tracking controller incorporates two parts: a nonlinear control law (we choose from our previous "global" or "semi-global" nonlinear controllers); a reference signal. The stability analysis is carried out. The effectiveness of the proposed strategy is evaluated in computer simulation.