Dielectric Elastomers Actuators (DEAs) represent a valid alternative to traditional actuators used in soft robots, thanks to their extreme flexibility, large deformation, high energy efficiency, lightweight, silent operations, and self-sensing capabilities. In this work, we present recent advances on model-based design and control of an articulated soft robot module driven by rolled DEAs. The considered module exhibits a T-shaped structure made by two plates connected by a soft flexible backbone, which is compressed by two pre-tensioned rolled DEAs. When actuated via high voltage, the DEAs expand and the soft structure bends toward the desired direction. The developed module can serve as a building block for tentacle-like soft robotic structures. Initially, we focused on a bi-dimensional version of the robot, which is capable of generating in-plane bending and displacements upon DEA electrical activation. By optimizing the system geometry via a model-based design approach, we can cause the buckling instability of the backbone to be triggered by the DEA activation, resulting in turn in a bi-stable actuation with large bending angles up to 25°. Despite bi-stability substantially improves the range of motion of the system, proportionality of regulation is lost. To recover proportional regulation, motion control strategies based on a passivity framework are adopted. The control method is here validated experimentally on a real-life prototype based on a real-time camera feedback. Experimental results confirm the effectiveness of the stabilizing control approach. While the adoption of a camera feedback choice is an acceptable choice for initial controller validation, it is not a suitable sensing method if the aim is to integrate the soft robot in an unstructured environment. To overcome this limitation, a real-time self-sensing scheme is proposed. Based on a real-time processing of DEA voltage and current measured during high voltage actuation, the proposed architecture allows estimating the mechanical state of the DE soft structure without requiring additional electro-mechanical sensors. Finally, first steps towards the model-based design and validations of a three-dimensional version of the DE soft robotic system are presented.