Backstepping Control of a Shape Memory Alloy Actuated Robotic Arm

Abstract

This paper investigates a nonlinear controller designed to stabilize a single-degree-of-freedom rotary shape memory alloy (SMA) actuated robotic arm. To this end, a bias-type robotic arm was built using 150 pm Flexinol SMA wire. This robot is designed to lift and position lightweight objects. Upon complete phase transformation, the SMA wire actuates the robot to rotate up to 1350. A linear spring is used to extend the wire to its original length because the SMA wire can only apply force in one direction. To measure the angular position of the robotic arm, an optical rotary encoder was used. To stabilize the robot, a model-based controller was developed. The controller incorporates the SMA actuated robot model with nonlinear control techniques. The model consists of three parts: the dynamics/kinematics of the arm, the thermoruechanical behavior of SMA wire, and the heat transfer model of the wire. The model-based backstepping controller determines the applied voltage to the SMA wire for positioning the arm at the desired angle by first calculating the wire's stress to stabilize the arm. The voltage to the SMA wire is then calculated based on the desired stress and the SMA's thermomechanical and heat transfer models. A series of simulations were performed to investigate stabilizing performance of the controller. Moreover, other issues such as robustness of the control design was evaluated. The results show that the control algorithms is able to globally and asymptotically stabilize the robot. The results further indicate that the sliding mode control has better robustness properties.