We address the challenge of engineering distributed haptic displays capable of reproducing multiple localized, independently addressable vibrations -- representing virtual tactile pixels -- at arbitrary locations on a surface. Our technique is based on the focusing of mechanical waves in a flexural plate using a sparse set of actuators. At tactile frequencies, wave diffraction prevents the formation of localized virtual tactile pixels at spatial scales relevant for multi-digit touch interactions. We overcome this limitation by augmenting the plate with a lattice of mechanical resonators, forming a locally resonant metamaterial plate. Coupling between the plate's dynamic modes and those of the resonators alters the dispersion relation governing wave transmission, introducing a slow-wave branch that enables focusing beyond the diffraction limit imposed by the unmodified plate. We use numerical simulations to engineer the dispersion relation of the metamaterial system for high-resolution focusing at tactile frequencies. We then fabricate a metamaterial tactile display and experimentally demonstrate virtual pixels that are far more localized than those generated on an otherwise identical plate without resonators, resulting in a tenfold reduction in virtual-pixel area. In behavioral experiments, we show that this system can deliver perceptually localized single- and multi-point tactile feedback and moving tactile sources while maintaining independent control over temporal waveforms at multiple display locations. The methods reported here can enable high-resolution haptic displays for widespread applications using a small number of actuated degrees of freedom.

翻译：我们解决了工程化分布式触觉显示器的挑战，该显示器能够在表面任意位置复制多个局部化、可独立寻址的振动——代表虚拟触觉像素。我们的技术基于使用稀疏致动器组在弯曲板中聚焦机械波。在触觉频率下，波衍射阻止了在多指触觉交互相关空间尺度上形成局部化虚拟触觉像素。我们通过在板上附加机械谐振子晶格，形成局部谐振超材料板，克服了这一限制。板的动态模式与谐振子模式之间的耦合改变了控制波传播的色散关系，引入慢波分支，使得能够超越未修改板所施加的衍射极限进行聚焦。我们使用数值模拟来设计超材料系统的色散关系，以实现触觉频率下的高分辨率聚焦。然后，我们制造了一个超材料触觉显示器，并通过实验演示了比相同但无谐振子的板产生的像素更局部化的虚拟像素，导致虚拟像素面积减少十倍。在行为实验中，我们展示了该系统能够提供可感知局部化的单点和多点触觉反馈以及移动触觉源，同时在多个显示位置保持对时间波形的独立控制。本文报道的方法可以利用少量驱动自由度实现高分辨率触觉显示器，适用于广泛的应用。