OptiTrap: Optimal Trap Trajectories for Acoustic Levitation Displays

Abstract: Acoustic levitation has recently demonstrated the ability to create volumetric content by trapping and quickly moving particles along reference paths to reveal shapes in mid-air. However, the problem of specifying physically feasible trap trajectories to display desired shapes remains unsolved. Even if only the final shape is of interest to the content creator, the trap trajectories need to determine where and when the traps need to be, for the particle to reveal the intended shape. We propose OptiTrap, the first structured numerical approach to compute trap trajectories for acoustic levitation displays. Our approach generates trap trajectories that are physically feasible and nearly time-optimal, and reveal generic mid-air shapes, given only a reference path (i.e., a shape with no time information). We provide a multi-dimensional model of the acoustic forces around a trap to model the trap-particle system dynamics and compute optimal trap trajectories by formulating and solving a non-linear path following problem. We formulate our approach and evaluate it, demonstrating how OptiTrap consistently produces feasible and nearly optimal paths, with increases in size, frequency, and accuracy of the shapes rendered, allowing us to demonstrate larger and more complex shapes than ever shown to date.