Tracking Control of a Miniature 2-DOF Manipulator with Hydrogel Actuators

Due to the nature of the complex spatiotemporal dynamics of stimuli-responsive soft materials, closed-loop control of hydrogel-actuated mechanisms has remained a challenge. This letter demonstrates, for the first time, closed-loop trajectory tracking control in real-time of a millimeter-scale, two degree-of-freedom manipulator via independently-controllable , temperature-responsive hydrogel actuators. A linear state-space model of the manipulator is developed from input-output measurement data, enabling the straightforward application of control techniques to the system. The Normalized Mean Absolute Error (NMAE) between the modeled and measured displacement of the manipulator's tip is below 10%. We propose an Observer-based controller and a robust $H_{\infty }$ -optimal controller and evaluate their performance in a trajectory tracking output-feedback framework, compared with and without sinusoidal disturbances and noise. We demonstrate in simulation that the $H_\infty$ -optimal controller, which is computed using Linear Matrix Inequality (LMI) methods, tracks an elliptical trajectory more accurately than the Observer controller and is more robust to disturbances and noise. We also show experimentally that the $H_\infty$ -optimal controller can be used to track different trajectories with an NMAE below 15 $\%$ , even when the manipulator is subject to a 3 g load, 12.5 times an actuator's weight. Finally, a payload transport scenario is presented as an exemplar application; we demonstrate that an array of four manipulators is capable of moving a payload horizontally by applying the proposed $H_\infty$ -optimal trajectory-tracking controller to each manipulator in a decoupled manner.