The Double Inverted Pendulum with Real Mass Distribution Stabilization

The stabilization of the real laboratory model of the underacuated double inverted pendulum having the actuator placed between its links and a realizable mass distribution adjustment is presented here. More specifically, this laboratory model is to be stabilized at its upper equilibrium with both links being stretched along a single line and pendulum achieving the maximal possible length. This paper presents various methods to design the stabilizing feedback for the double inverted pendulum actuated between its links and then performs optimization of the model with respect to masses distributions to minimize the controller torques. First, the open-loop control taking the double pendulum to the upper equilibrium is computed from various positions using the optimization tool FMINCON to minimize the torque energy with respect to the mass distribution parameters. Then the optimized parameters are used to test both the LQ feedback for local approximate linearization and the partial exact feedback linearization based nonlinear controller. Both simulations and laboratory experiments using a single leg of the walking-like four link experimental model are presented. The optimized mass distribution will be used in the future four-link development to facilitate its walking design.