Rendering Dynamic Source Motion in Surface Haptics via Wave Focusing

Emerging surface haptic technologies can display localized haptic feedback anywhere on a touch surface by focusing mechanical waves generated via sparse arrays of actuators. However, rendering complex haptic scenes with such displays is challenging due to the infinite number of physical degrees of freedom intrinsic to such continuum mechanical systems. Here, we present computational focusing methods for rendering dynamic tactile sources. They can be applied to a variety of surface haptic devices and media, including those that exploit flexural waves in thin plates and solid waves in elastic media. We describe an efficient rendering technique based on time-reversal of waves emitted from a moving source and motion path discretization. We combine these with intensity regularization methods that reduce focusing artifacts, improve power output, and increase dynamic range. We demonstrate the utility of this approach in experiments with a surface display that uses elastic wave focusing to render dynamic sources, achieving millimeter-scale resolution in experiments. Results of a behavioral experiment show that participants could readily feel and interpret rendered source motion, attaining 99% accuracy across a wide range of motion speeds.