Shape memory alloy (SMA) actuators are compact and have high force-to-weight ratios, making them strong candidates to actuate robots, exoskeletons, and prosthetics. To optimize speed and energy consumption, SMA actuators have been embedded in an N×N vascular network that can deliver electric and thermofluidic energy to the each actuator. The scalable architecture of the vascular network allows for 2N control devices (valves, transistors) to be shared amongst N² actuators, so that as the number of actuators increases, the number of required control devices scales at a smaller rate. This Network Array Architecture (NAA) allows for each actuator to be controlled individually or in discrete subarrays. However, not all combinations of actuators can be activated simultaneously; therefore in general, a sequence of control commands will be need to be executed in order to achieve the desired actuation. By treating each actuator as having a binary state, the combined states of the actuator array can be represented by graph theory, where states are nodes and the transitions between states are graph edges. By properly weighting the costs of the transitions, graph search techniques can be used to find optimal sets of control commands for desired state changes. This paper formulates the control of NAA actuators systems as a graph theory problem, and characterizes the ability of search algorithms to optimize a weighted combination of speed and energy usage, while minimizing computational cost.

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