Quasi-static shape control of soft, morphing structures

Eszter Fehér, András Árpád Sipos, Péter Várkonyi · arXiv · 2025

A general quasi-static shape-control framework for soft morphing structures is developed, analyzing how large deformations and compliance affect equilibrium topology and stability, illustrated with a snap-through-prone Kirchhoff rod.

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Plain English summary

The paper proposes a general framework for controlling the shapes of soft, morphing structures when external actions or requirements change slowly (quasi-statically). The goal is to move the structure through stable parts of its equilibrium set to satisfy predefined requirements or optimization criteria. Because the structures can undergo finite deformations, the equilibrium set can have complex (non-trivial) topology. The paper studies what this means for large shape changes and high compliance, including the emergence of unstable equilibria. It also discusses different “adaptivity scenarios,” such as inverse kinematics, optimization, and path planning, and how time-dependent loads and requirements influence the control behavior. The concepts are demonstrated using a curved Kirchhoff rod that can exhibit snap-through behavior.

Why this matters

The paper’s novelty is framed as a general framework for quasi-static shape control that explicitly accounts for equilibrium-set topology and stability effects arising from finite deformations in soft, high-compliance morphing structures. No information in the abstract indicates prototype development, field testing, or commercial deployment.

Key findings

  • Introduces a general framework for quasi-static shape control of soft, morphing structures under slowly varying actions/requirements.
  • Shows that finite deformations can lead to equilibrium sets with non-trivial topology, affecting shape-control behavior.
  • Analyzes how large shape changes and high compliance can produce unstable equilibria.
  • Identifies adaptivity scenarios spanning inverse kinematics, optimization, and path planning, including the role of time-dependent loads/requirements.
  • Demonstrates applicability with a curved Kirchhoff rod susceptible to snap-through.

Limitations

The abstract does not specify experimental validation, quantitative performance metrics, or comparisons to prior methods; it only states that applicability is demonstrated via an example (curved Kirchhoff rod).

Publication

Publisher
arXiv
Publication date
September 16, 2025
Research type
Preprint
arXiv
2509.12916
Access
open

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Method note: Summaries and ratings on this page are generated by AI from the abstract only. Read the original paper for full context. · Model: gpt-5.4-nano-2026-03-17