Optimal control of multi-input SMA actuator arrays using graph theory: Expanding wavefront & simultaneous operations

Shape memory alloy (SMA) actuators are compact and have high force-to-weight ratios, making them strong candidates to actuate robots, exoskeletons, and prosthetics. However, these actuators are thermomechanical in nature and slow cooling rates can limit their performance. To improve the convective cooling, SMA wires have been embedded in vascular networks allowing cold fluid to pass across the actuators to cool/extend them. The vascular network can also deliver hot fluid to heat and contract the wire. In addition to the fluidic network, an electrical network operating in parallel can resistively heat the SMA to produce contraction. To minimize the weight and size of the vascular and electrical networks, a scalable N[N architecture has been implemented that allows for 2N control devices (valves, transistors) to be shared amongst N
²
actuators. This Network Array Architecture (NAA) allows each actuator to be controlled individually or in discrete subarrays. However, this architecture does not allow all combinations of actuators to be activated simultaneously; therefore in general a sequence of control commands will need to be executed in order to achieve the complete actuation. In order to find an optimal sequence of control commands, graph theory algorithms have been implemented. By treating each actuator's state as binary (fully contracted or extended), the collected states of an actuator array can be represented as nodes of the graph and the control commands as the graph edges. By properly weighting the costs of the graph edges, search algorithms can be used to find an optimal set of control commands for desired state changes. NAA results in a multi-graph that has 2
^NA—N
nodes and is highly interconnected. While initial work in this area established the basic validity of a graph search approach for NAA control, this article presents a scalable method of determining the optimal set of controls to minimize the operating cost (time and energy) and computational search cost.