Quasi-static shape control of soft, morphing structures

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.