Robust optimal control of stochastic hyperelastic materials

J Martínez-Frutos , Rogelio Ortigosa (1) , P Pedregal , F Periago

1 Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena

Soft robots are highly nonlinear systems made of deformable materials such as elastomers, fluids and other soft matter, that often exhibit intrinsic uncertainty in their elastic responses under large strains due to microstructural inhomogeneity. These sources of uncertainty might cause a change in the dynamics of the system leading to a significant degree of complexity in its controllability. This issue poses theoretical and numerical challenges in the emerging field of optimal control of stochastic hyperelasticity. This paper states and solves the robust averaged control in stochastic hyperelasticity where the underlying state system corresponds to the minimization of a stochastic polyconvex strain energy function. Two bio-inspired optimal control problems under material uncertainty are addressed. The expected value of the L 2-norm to a given target configuration is minimized to reduce the sensitivity of the spatial configuration to variations in the material parameters. The existence of optimal solutions for the robust averaged control problem is proved. Then the problem is solved numerically by using a gradient-based method. Two numerical experiments illustrate both the performance of the proposed method to ensure the robustness of the system and the significant differences that may occur when uncertainty is incorporated in this type of control problems.

Mots clés: Robust optimal control; hyperelasticity; material uncertainty; turgor pressure; active fibers; soft robotics

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

J Martínez-Frutos, Rogelio Ortigosa, P Pedregal, F Periago. Robust optimal control of stochastic hyperelastic materials. Applied Mathematical Modelling, 2020. ⟨hal-02440704⟩