Vision based control of a 3D inverted pendulum

This paper presents a stabilization control system of a 3D inverted pendulum. The challenge is to realize a control via remote sensing based on a low cost CCD camera. The proposed method transforms the 3D problem into a 2D one by choosing a new balancing plane for the pendulum at each camera's sampling instant. For a given plane, two feedback loops are considered. The first one, which is an observation loop, processes the delayed and sampled angle information delivered by the artificial vision system so as to set up a linear and stable model of the pendulum (without any approximations) and to reconstitute its continuous state by means of a specific observer called Piecewise Continuous reduced-order Luenberger Observer (PCO). The second loop, which is a stabilisation loop, makes use of a Lyapunov function based control in order to stabilise the cart-pendulum system. Simulations and experimental results illustrate the method's performance. © 2009 Lavoisier, Paris.