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19274/PI/14 21996/PI/22 Analysis Applied Mathematics Computational Mathematics Computational Mechanics Computer Graphics and Computer-Aided Design Computer Science Applications Control and Optimization Control and Systems Engineering DICOPMA Dielectric elastomer Dielectric elastomers Electro-active polymer Energy–momentum scheme Evolutionary topology optimization Fail-safe design Finite element method General Engineering General Mathematics Mechanical Engineering Nonlinear electro-elasticity Numerical Analysis Ocean Engineering Phase-field PID2022-141957OA-C22 Polyconvexity Rank-one laminates Software Topology optimisation 
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2020
 Martínez-Frutos, Jesus;  Ortigosa, Rogelio;  Pedregal, Pablo;  Periago, Francisco
Robust optimal control of stochastic hyperelastic materials Journal Article 
In: Applied Mathematical Modelling, vol. 88, pp. 888-904, 2020, ISSN: 0307-904X.
Abstract | BibTeX | Tags: Active fibers, DICOPMA, Hyperelasticity, Material uncertainty, Robust optimal control, Soft robotics, Turgor pressure | Links: 
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@article{MARTINEZFRUTOS2020888,

title = {Robust optimal control of stochastic hyperelastic materials},

author = {Jesus Martínez-Frutos and Rogelio Ortigosa and Pablo Pedregal and Francisco Periago},

url = {https://www.sciencedirect.com/science/article/pii/S0307904X20303772},

doi = {https://doi.org/10.1016/j.apm.2020.07.012},

issn = {0307-904X},

year  = {2020},

date = {2020-01-01},

urldate = {2020-01-01},

journal = {Applied Mathematical Modelling},

volume = {88},

pages = {888-904},

abstract = {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 L2-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.},

keywords = {Active fibers, DICOPMA, Hyperelasticity, Material uncertainty, Robust optimal control, Soft robotics, Turgor pressure},

pubstate = {published},

tppubtype = {article}

}

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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 L2-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.
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