Motion Modeling and Trajectory Tracking Control for a Soft Robotic Table

In this article, the development of a control framework for a soft robotic table is presented. The framework aims to enable the soft table to effectively manipulate an object to track a reference trajectory. The table system has been modeled using empirical methods via experiments and finite-element analysis simulations. A closed-loop trajectory tracking system, including a trajectory controller, a vision feedback, and a reference trajectory, has been designed. An algorithm to allocate actuation has been developed to implement the tracking system into the existing soft table system. Finally, simulations and experiments using different tracking controllers of an object tracking a circular trajectory have been conducted to validate the proposed trajectory tracking system. The experimental result shows that the tracking error remains within 3.4 mm for the
$X$
-axis and 4 mm for the
$Y$
-axis. The error in orientation remains within 12.8
$^\circ$
. All the errors are bounded in the acceptable margin, which proves the effectiveness of the proposed trajectory tracking control method.