Stabilization of a 2-DOF inverted pendulum by a low cost visual feedback

This paper presents a stabilization control system of a 2-DOF inverted pendulum. The challenge is to realize a control with a contact-less feedback including a low cost CCD camera. The global control system uses two feedback loops. The first one (inner loop) includes the delayed and sampled inverted pendulum´s top coordinates, obtained from the CCD camera and the second one (outer loop) concerns the cart´s position in continuous time (obtained from encoders). With this feedback scheme, we propose a specific control method by choosing an optimal balancing plane at each camera´s sampling instant, in view of transforming the 2-DOF pendulum problem to a 1-DOF one. Then in this balancing plane, we realize two control loops: The inner loop, relative to the pendulum´s angle, is controlled by a linearization and stabilization method based on an innovative observer called piecewise continuous reduced-order Luenberger observer (PCROLO). The outer loop uses a Lyapunov function based control scheme with slower internal dynamics compared to that of the pendulum, considering that the global controlled system (cart + pendulum) is an unstable non-minimum-phase system. Numerical simulations show that the stabilization control of the inverted pendulum on an x-y robot that are strongly non linear is successful.