Semidefinite programming for manipulating acoustic traps in real time (SMART)

Sound waves can be used for trapping and manipulating objects immersed in liquids or air. However, most acoustic levitation techniques are limited to particles with diameters much smaller than the acoustic wavelength or require time-consuming optimisation-based methods that hinder the dynamic manipulation of objects. Here, we present an approach based on semidefinite programming to manipulate levitated objects in real time. To demonstrate this technique, a phased array consisting of 256 ultrasonic transducers operating at 40 kHz is used for rotating a non-spherical Rayleigh object or to translate Mie spheres along various trajectories. In contrast to previous optimisation-based approaches, the proposed method can determine the emission phases of each transducer in real time, strongly facilitating the implementation of a model-based closed-loop control in future acoustic levitation systems. This is a fundamental step for manipulating levitated objects precisely and at high speeds.