Bang-bang Control with Constant Thrust of a Spherical Blimp Propelled by Ultrasound Beam

Abstract

Ultrasound beam propulsion, a propulsion system that uses airborne ultrasound phased arrays (AUPAs) to propel a blimp in an indoor environment to propel a blimp, has advantages for operations near humans such as no audible noises and no risk of propeller strike. To achieve the high mobility with limited actuation force of AUPAs, the dynamics should be fully exploited. In this paper, we propose a two-degree-of-freedom controller specifically tailored for ultrasound beam propulsion. We investigate the trajectory of bang-bang control with constant thrust (BBCT control), where a blimp accelerates and then decelerates with constant thrust reaching the terminal point at rest, as one of the most basic trajectories. First, we analytically derive the trajectory of a blimp under aerodynamic drag. Then, we provide a trajectory generator that derives the maximum constant thrust for an arrangement of AUPAs and the constraints on the control input. Finally, we integrate the trajectory generator and a PID-based feedback controller in a physical setup. We evaluated the proposed controller in physical and numerical experiments. The results showed that the proposed method allows a blimp to reach the terminal point almost in expected time. We also showed that the flight time is shorter than a PID-based one-degree-of-freedom controller, which was typically used in previous studies, by 19.0 − 43.2 %.