Energy-based shape regulation of soft robots with unactuated dynamics dominated by elasticity

This paper proposes a model-based control design approach for a broad class of soft robots, having their elastic field dominating gravity in the unactuated coordinates. To this end, we consider finite-dimensional dynamic models obtained from approximations of the system's energy. Then, we propose a general control architecture that can stabilize soft robots based on potential energy shaping. We discuss three specializations of this general architecture: a PD with mixed feedback-feedforward gravity compensation, a PD with feedforward compensation, and a saturated version of the latter. We provide a physical interpretation of the controllers, and we illustrate their applicability through simulations.