Phase Optimization for Multipoint Haptic Feedback Based on Ultrasound Array

Ultrasound-based haptic feedback is a potential technology for human–computer interaction (HCI) with the advantages of a low cost, low power consumption and a controlled force. In this paper, phase optimization for multipoint haptic feedback based on an ultrasound array was investigated, and the corresponding experimental verification is provided. A mathematical model of acoustic pressure was established for the ultrasound array, and then a phase-optimization model for an ultrasound transducer was constructed. We propose a pseudo-inverse (PINV) algorithm to accurately determine the phase contribution of each transducer in the ultrasound array. By controlling the phase difference of the ultrasound array, the multipoint focusing forces were formed, leading to various shapes such as geometries and letters, which can be visualized. Because the unconstrained PINV solution results in unequal amplitudes for each transducer, a weighted amplitude iterative optimization was deployed to further optimize the phase solution, by which the uniform amplitude distributions of each transducer were obtained. For the purpose of experimental verification, a platform of ultrasound haptic feedback consisting of a Field Programmable Gate Array (FPGA), an electrical circuit and an ultrasound transducer array was prototyped. The haptic performances of a single point, multiple points and dynamic trajectory were verified by controlling the ultrasound force exerted on the liquid surface. The experimental results demonstrate that the proposed phase-optimization model and theoretical results are effective and feasible, and the acoustic pressure distribution is consistent with the simulation results.