Abstract
In this paper flatness based control is proposed and applied to stabilize the unstable equilibrium of a Inverted Double Pendulum (IDP) mounted on a cart integrating elasticity at joints. The flat output of the system serves as a point to be stabilized using vision feedback control. The proposed approach can be applied to a number of applications such as controlling a robot with feet, studying the characteristics of the human movement in the upright and modelling and controlling buildings subject to seismic excitations (movements resulting from an acceleration given to the cart). It is prove that the vision-based control is robust with a perturbing acceleration which excites the cart.