Nonlinear Analysis and Control of a Reaction-Wheel-Based 3-D Inverted Pendulum

This paper presents control and learning algorithms for a reaction wheel-based 3-D inverted pendulum. The inverted pendulum system has two main features: the ability to balance on its edge or corner and to jump from lying flat to its corner by suddenly braking its reaction wheels. Algorithms that address both features are presented. For balancing, a backstepping-based controller providing global stability (almost everywhere) is derived, together with a simple tuning method based on the analysis of the resulting closed-loop system. For jump-up, a computationally efficient gradient-based learning algorithm is provided, which is shown experimentally to converge to the correct angular velocities enabling a successful jump-up. Moreover, a controller based on feedback linearization is derived and used to track an ideal trajectory during jump-up, increasing robustness and reliability.