Since the early 1940s, the field of robotics has evidenced a paradigm shift from conventional hard robotics to soft robotics, through the exploration of machines or components with biomimetic dexterous features capable of superseding the ability of humans whilst safely interacting with them. Soft robots are highly nonlinear systems made of highly deformable materials such as elastomers, polymers and other soft matter, that often exhibit intrinsic uncertainty in their elastic responses under large strains due to microstructural inhomogeneity. As a consequence, control of soft robots, potentially actuated by means of a wide spectrum of complex external stimuli (electric or magnetic field, mechanical pressure, osmotic pressure, etc.) is not a trivial task.
This presention will review on modelling, mathematical analysis, control and design of soft materials. The theoretical analysis and numerical modeling relies on the theory of hyperelasticity. In addition to the constitutive model, another aspect of paramount importance in optimal control of soft materials is the choice of the cost functional to be minimized. Tracking-type cost functionals based on distance functions, such as the Hausdorff distance, have been recently proposed as a natural choice in this field. The numerical treatment of uncertainty quantification is another difficulty due, among others, to the well-known phenomenon of the curse of dimensionality. All of these issues will be illustrated in the talk through several concrete examples. Finally, some mathematical challenges in this emergent field will be described.
The original results included in the presentation have been obtained in collaboration with Jesús Martínez-Frutos (UPCT), Carlos Mora-Corral (UAM), Rogelio Ortigosa-Martínez (UPCT) and Pablo Pedregal (UCM).