Bilinear system approximation-based inverted pendulum stabilization in three dimensions

Abstract

This paper considers inverse optimal control design for an inverted pendulum with three-dimensional movements. We show that the inverted pendulum model can be transformed into the bilinear system via a quadratic approximation and coordinate/input transformations. Then, the inverse optimal controller proposed in one of our previous works is applied to the resulting bilinear system. We next show that the present scheme has a better performance than traditional linear optimal control for linearly approximated systems by effectively utilizing the vertical movement of the pendulum system. This result is confirmed by conducting numerical simulations.

Vision-based control of a flying spherical inverted pendulum on a Quadrotor

“…In order to achieve this goal, this paper proposes an inverted pendulum that is attached by a ball joint to a Quadrotor such that this last enables to control the Spherical Inverted Pendulum in its unstable equilibrium upright position. The thing that has already attracted many attentions [6][7][8][9][10][11][12]. However, most of these research were discussed either in terms of decoupling or they considered a simple inverted pendulum with different initial conditions of the angle and angular velocity of the pendulum.…”