Swing-up control problem for a self-erecting double inverted pendulum

The paper presents a procedure to swing-up a double pendulum mounted on a cart. The aim of this problem is to take the system from its stable position to the inverted position by moving the cart. A technique to design controlled trajectories for nonlinear underactuated mechanisms is developed. The reference trajectory is obtained as a result of the optimisation of an initial trajectory defined through interpolation by splines. This reference is tracked using a gain scheduling linear quadratic optimal controller specifically designed for the reference trajectory. Simulation and the experimental results confirm the validity of this approach