Optimal Control Algorithm for Multi-Input Binary-Segmented SMA Actuators Applied to a Multi-DOF Robot Manipulator

In this paper, we present an optimal design and control algorithm for multi-input binary-segmented Shape Memory Alloy (SMA) actuator arrays applied to a multi-degree-of-freedom (DOF) robot manipulator as it tracks a desired trajectory. The multi-DOF manipulator used for this paper is a 3-DOF-robot finger. A multi-input binary-segmented SMA actuator drives each DOF. SMA wires are embedded into a compliant vessel, such that both electric and fluidic (hot/cold) input can be applied to the actuators. By segmenting the SMA actuators, each segment can be controlled in a binary fashion (fully contracted/extended) to create a set of discrete displacements for each joint of the manipulator. To design the number of segments and length of each segment, an algorithm is developed to optimize the workspace. To optimize the workspace, it is desired to have a uniform distribution of reachable points in Cartesian space. Moreover, the number of neighbors (points that can be reached just by one control command from the current configuration) and the computational cost are important in workspace optimization. Graph theory search techniques based on the A* algorithm are employed to develop the control algorithm. A path-cost function is proposed to optimize the cost, which is a combination of actuation time, energy usage, and kinematic error. The kinematic error is estimated as the deviation between the actual and desired trajectory. The performance of the search algorithm and cost function are validated through simulation.