Mixed $\mathcal{H}_{\infty}/\mathcal{H}_{2}$ Control of a Soft Robotic Structure Actuated by Dielectric Elastomers

Dielectric Elastomer Actuators (DEAs) are an efficient and compact solution to build soft robotic structures. Due to their non-conventional characteristics, soft robots bring new challenges in terms of control design. Closed-loop control is essential in high-precision tracking tasks. In this paper, we propose a mixed $\mathcal{H}_{\infty}/\mathcal{H}_{2}$ control using a formulation based on Linear Matrix Inequalities (LMIs) for a soft robotic structure actuated by two DEAs. The objective is to provide a feedback law which guarantees stability when tracking time-variant references. The design presented allows to easily tune the resulting closed-loop bandwidth ( $\mathcal{H}_{\infty}$ performance), while minimizing the control action ( $\mathcal{H}_{2}$ performance). The effectiveness of the proposed approach is validated through extensive simulation studies using a physics-based nonlinear model of the soft robot.