Intrinsic bi-stability via thick-panel design in high-DoF Resch origami

Origami with high degrees of freedom (DoF), such as the Resch tessellation, offers a vast design space for complex morphing structures but poses significant control challenges. Embedding bistability is a promising strategy to simplify actuation, yet existing methods for creating intrinsic multi-stability are largely confined to kinematically simple, low-DoF patterns. This paper presents a systematic computational framework to design intrinsically bistable thick-panel structures from high-DOF Resch origami. Our decoupled, two-stage approach first employs a Stochastic Gradient Descent (SGD)-based kinematic simulation to discover a viable, complex folded configuration from the vast design space of a zero-thickness model. Subsequently, it formulates a set of bi-compatibility constraints for both the unfolded and the target folded states, which are then efficiently solved using linear programming to determine the thick-panel geometry. The efficacy of the framework is demonstrated through the design and verification of two Resch-ori units: one with bistability between fully-flat and fully-folded states, and another between the flat and an arbitrarily prescribed spatial state. The bistability is numerically verified by analyzing the kinematic degrees of freedom and the minimum energy path between stable states. This work provides a robust and computationally efficient pathway for harnessing the complexity of high-DOF origami to create functional, bistable systems.