Optimal Control of Multi-Input SMA Actuator Arrays on a Trajectory Using Graph Theory: Modified A-Star Search Algorithm

Abstract

It has been shown that a set of multi-input (electrothermal and thermofluidic inputs) Shape Memory Alloy (SMA) actuators implemented into a Network Array Architecture (NAA) and treated like binary actuators can be represented by graph theory, such that the actuator configurations are represented as graph nodes, and transitions between states as graph edges. However, to achieve a desired actuation, a set of sequential control commands is required. A search algorithm was originally developed to identify a set of sequential control commands to go from a start node to a destination node with minimum path cost, where the cost function is a weighted combination of actuation time and energy. The original algorithm only considered one destination at a time, optimizing the present cost with no regard to any future costs. The aim of the current work is to modify the existing algorithm to control these SMA actuator arrays over a trajectory (multi-destination search problem), and take advantage of future destination knowledge to optimize the path cost. To achieve this goal, a sub-search algorithm and modified performance function are developed. For each heating control command, the sub-search algorithm compiles required information from future nodes. Then, this information is used by the modified performance function to estimate the future path cost. The modified performance function is designed to estimate the future path cost, while computing the current path cost. Therefore, the modified performance function will identify the sequence of operations with a minimum total path cost. The results show that the modified algorithm has a total path cost that is up to 30% less than the original algorithm total cost.Copyright © 2012 by ASME