Nonlinear Coordinate Transformation and Trajectory Tracking Control of an Underactuated Soft Robot Driven by Dielectric Elastomers

In this paper, we investigate model-based trajectory tracking position control of an articulated soft robotic system driven by rolled dielectric elastomer actuators. The system's features, including underactuation with a configuration-dependent actuation matrix, open-loop bi-stable behavior, and significant elastic as well as kinematic nonlinearities, make the design of a tracking controller a highly challenging task. Starting from an accurate Euler-Lagrange dynamic model of the soft robot, we propose a nonlinear coordinate transformation to achieve the so-called collocated form. Conditions for the existence of such change of coordinates are investigated using a geometric argument, which in turn provides an analytical expression for the inverse transformation as well as a characterization of the region in which such inverse exist. Next, a partial state feedback linearization law is designed for trajectory tracking, and the zero dynamics stability is analyzed. The effectiveness of the approach is finally verified via numerical simulation based on an accurate physical model.