Vibrotactile rendering for uniform sound power on haptic display with minimum number of actuators

Haptic display devices offer vibrotactile feedback to the user when touched. Typically, the vibrating touch surface generates different sound powers depending on the touch position. Because the radiated sound power acts as an auditory stimulus that influences the user's tactile perception, it must be uniformized to ensure consistent perception for the user. However, controlling the sound power radiated from a touchscreen requires a large number of actuators, which leads to a cumbersome structure and elevated costs. Therefore, this study introduces a novel method to uniformize the radiated sound power while maintaining the vibrotactile rendering performance with minimum number of actuators. To this end, depending on the number and positions of the actuators, the modified system dynamics were calculated using frequency response function-based substructuring. Then, an optimization problem was defined with the actuator driving signals and actuator positions as the design variables, which aims to minimize the number of actuators while radiating uniform sound power. To validate the proposed method, experiments were conducted on an automotive haptic display. Based on the results, satisfactory vibrotactile rendering was achieved for all touch positions, and the radiated sound powers were highly uniform, with standard deviations of only about 0.54 dB.