Augmenting Self-Stability: Height Control of a Bernoulli Ball via Bang-Bang Control

Abstract

Mechanical self-stability is often useful for controlling systems in uncertain and unstructured environments because it can regulate processes without explicit state observation or feedback computation. However, the performance of such systems is often not optimised, which begs the question how their dynamics can be naturally augmented by a control law to improve performance metrics. We propose a minimalistic approach to controlling mechanically self-stabilising systems by utilising model-based, feedforward bang-bang control at a global level and self-stabilizing dynamics at a local level. We demonstrate the approach in the height control problem of a sphere hovering in a vertical air jet - the so-called Bernoulli Ball. After developing a model to study the system and theoretically proving global asymptotic stability, we present the augmented controller and show how to enhance performance measures and plan behaviour. Our physical experiments show that the proposed control approach has a reduced time-to-target compared to the uncontrolled system without loss of stability (ranging from a 2.4 to 4.4 fold improvement) and that we can plan sequences of target positions at will.