Stabilization of the spatial double inverted pendulum using stochastic programming seen as a model of standing postural control

The stabilization of a double inverted pendulum actuated at the hip only and moving in a three dimensional space may be considered to be a model of a human - and of other animals - postural control. Here, we show that postural control is possible by minimization of the system Lagrangian. A stochastic programming procedure proves to be able to find oscillatory inputs that bring the system close to the unstable upright equilibrium position. Our study shows that steering complex mechanical systems may in certain cases be actually be simpler than expected.