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arXiv · 2509.12916

Quasi-static shape control of soft, morphing structures

Eszter Fehér·András Árpád Sipos·Péter Várkonyi
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Abstract

Inspired by biological systems, we introduce a general framework for quasi-static shape control of human-scale structures under slowly varying external actions or requirements. In this setting, shape control aims to traverse the stable sub-manifolds of the equilibrium set to meet some predefined requirements or optimization criteria. As finite deformations are allowed, the equilibrium set may have a non-trivial topology. This paper explores the implications of large shape changes and high compliance, such as the emergence of unstable equilibria and equilibrium sets with non-trivial topology. We identify various adaptivity scenarios, ranging from inverse kinematics to optimization and path planning problems, and discuss the role of time-dependent loads and requirements. The applicability of the proposed concepts is demonstrated through the example of a curved Kirchhoff rod that is susceptible to snap-through behavior.

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Eszter Fehér, András Árpád Sipos, Péter Várkonyi. 2025-09-16. Quasi-static shape control of soft, morphing structures. https://arxiv.org/abs/2509.12916

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