Modeling latching fluidic circuits to determine clocking limits for a refreshable braille display

Fluidic circuits made up of tiny chambers, conduits, and membranes can be fabricated in soft substrates to realize pressure-based sequential logic functions. Additional chambers in the same substrate covered with thin membranes can function as bubble-like tactile features. Sequential addressing of bubbles with fluidic logic enables just two external electronic valves to control of any number of tactile features by "clocking in" pressure states one at a time. But every additional actuator added to a shift register requires an additional clock pulse to address, so that the display refresh rate scales inversely with the number of actuators in an array. In this paper, we build a model of a fluidic logic circuit that can be used for sequential addressing of bubble actuators. The model takes the form of a hybrid automaton combining the discrete dynamics of valve switching and the continuous dynamics of compressible fluid flow through fluidic resistors (conduits) and capacitors (chambers). When parameters are set according to the results of system identification experiments on a physical prototype, pressure trajectories and propagation delays predicted by simulation of the hybrid automaton compare favorably to experiment. The propagation delay in turn determines the maximum clock rate and associated refresh rate for a refreshable braille display intended for rendering a full page of braille text or tactile graphics.