Adjoint-based optimal control of contractile elastic bodies: application to limbless locomotion on frictional substrates
In nature, limbless locomotion is adopted by a wide range of organisms at various length scales. Interestingly, undulatory, crawling and inching/looping gait constitutes a fundamental class of limbless locomotion and is often observed in many species such as caterpillars, earthworms, leeches, larvae...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:upcommonspor::475e8f7b214e312dde12827c230c3457 |
| Acceso en línea: | https://hdl.handle.net/2117/462129 https://dx.doi.org/10.1016/j.cma.2023.116697 |
| Access Level: | acceso abierto |
| Palabra clave: | Strength of materials Elastic solids Calculus of variations Mathematical optimization Non-linear elasticity Growth model Soft robotics Limbless locomotion Optimal control Adjoint method Resistència de materials Elasticitat Càlcul de variacions Optimització matemàtica Classificació AMS::74 Mechanics of deformable solids::74B Elastic materials Classificació AMS::49 Calculus of variations and optimal control optimization::49M Methods of successive approximations Àrees temàtiques de la UPC::Física::Física de l'estat sòlid Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica |
| Sumario: | In nature, limbless locomotion is adopted by a wide range of organisms at various length scales. Interestingly, undulatory, crawling and inching/looping gait constitutes a fundamental class of limbless locomotion and is often observed in many species such as caterpillars, earthworms, leeches, larvae, and C. elegans. In this work, we developed a computationally efficient 3D Finite Element (FE) unified framework for the locomotion of limbless organisms on frictional substrates. Muscle activity is simulated with a multiplicative decomposition of the deformation gradient, which allows mimicking a broad range of locomotion patterns in 3D contractile elastic solids. We propose a two-field FE formulation based on positions and velocities. Governing partial differential equations are transformed into equivalent time-continuous differential–algebraic equations (DAEs). Next, the optimal locomotion strategies are studied in the framework of optimal control theory. We resort to adjoint-based methods and deduce the first-order optimality conditions, that yield a system of DAEs with two-point end conditions. Hidden symplectic structure is discussed, and Symplectic Euler time integration of optimality conditions are employed. The resulting discrete first-order optimality conditions form a non-linear programming problem that is solved efficiently with the Forward Backward Sweep Method. Finally, some numerical examples are provided to demonstrate the comprehensiveness of the proposed computational framework and investigate the energy-efficient optimal strategy out of distinct locomotion patterns adopted by limbless organisms. |
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