Introduction
Advances in soft robotics have presented the way robots interact with human or unstructured environments. In response to external stimuli, such as fluidic pressure, \cite{Marchese2015,Usevitch2020,Shah2021,Katzschmann2018,Heng_2021,Cianchetti_2014,Hawkes_2017}electric signals,\cite{Acome2018,Xing_2020,Li_2017} magnetic fields, \cite{Goudu_2020,Joyee_2019} and motor-tendon actuation,\cite{Manti_2015,Vikas_2016,In_2015} the architected soft matters, mostly elastomers, produce continuous and adaptive motions that allow delicate handling of fragile objects or shape adjusting to unstructured environments. By utilizing the inherent features of softness, soft robots are gradually being used for safety demanding applications or near human applications such as soft grippers,\cite{Goudu_2020,Joyee_2019,Brown_2010} soft manipulators,\cite{Xing_2020,Hawkes_2017} mobile robots,\cite{Hawkes_2017,Shah2021,Katzschmann2018,Li_2017,Joyee_2019,Vikas_2016} assistive wearable robots,\cite{Heng_2021,In_2015} and minimally invasive surgical tools.\cite{Cianchetti_2014,Runciman_2019} The established design method for soft fluidic robots is to embody anisotropic deformation in soft bodies by carving geometric patterns of extensible fluidic networks and embedding inextensible strain-limiting appendages (e.g., paper strips, fabrics, tendons).\cite{Polygerinos2017a,Ilievski2011} Consequently, the applied fluid causes asymmetric extension of fluidic networks and strain-limiting appendages, and the whole soft body produces pre-programmed motion such as bending,\cite{Ilievski2011,Mosadegh_2014,Tang2020,Yap2016} twisting,\cite{Connolly2015} and contraction.\cite{Yang2017,Koizumi2018} Researches to date have mainly focused on architecting fluidic networks and have achieved rapid actuation,\cite{Mosadegh_2014} high aspect ratio design,\cite{Becker2020} and high force generation.\cite{Tang2020,Yap2016} However, the current design method compels soft robots to be shaped as a long elastomeric beam or a cylinder because their form factors are subordinated to inextensible strain-limiting appendages, which may limit their spatial efficiency, and make it inconvenient for soft fluidic robots to be used with other mechanical elements due to physical interferences.
Origami deployable architectures have unique feature that are folded into compact forms when not in use, and be transformed into large shapes to be functional. This deployment combined functionality provides portability and mobility at the folded state while it can generate large motions at the deployed state. For example, in nature, flying insects such as ladybugs and earwigs fold and retract their hind wings for reduced inertia, and only deploy and flap them during flight.\cite{Deiters2016,Saito2017} With additional benefits such as desired shapes or motions which can be robustly guided by kinematics, and a large variety of constituting materials (from compliant paper to steel plate), the origami design has been considered as a promising method for deployable machines with possible applications in mobile robots, \cite{Baek2020,Lee2021,Lin2020} manipulators, \cite{Kim2018,Suzuki2020} space missions,\cite{Schenk2014,Pehrson2020} and biomedical tools.\cite{Suzuki2020,Johnson2017} Likewise, several researches of soft fluidic robots have adopted origami deployable architectures. Martinez et al developed paper-elastomer composite soft fluidic robots including Yoshimura origami cylinder structure (so-called bellows-like pattern) that grow or bend due to glued facets or an attached strip.\cite{Martinez2012} Li et al presented soft fluid robots in which an origami skeleton is sealed by flexible skin, and negative pressure is applied to fold the crease lines in a pre-programmed sequence.\cite{Li2017} Chen et al developed a hybrid actuator with a motor-driven tendon and a fluid-driven asymmetric Yoshimura origami cylinder, in which the effective length of the bending configuration can be changed.\cite{Chen2021} These existing works successfully imported origami deployable architectures’ large range of motion into fluidic networks, while they have not yet focused on designing or programming additional motions beyond kinematics of origami deployment.
Recently, implementation of soft and compliant materials widened the accessible regime of origami folding over origami kinematics.\cite{Faber2018,Mintchev2018,Kim2019} Our previous work, ‘a dual-morphing stretchable origami’, presented an entirely stretchable origami that deploys by unfolding and then produce additional motion by anisotropic stretching.\cite{Kim2019} Although this dual-morphing principle that utilizes both morphing principles of unfolding and stretching could achieve extreme shape morphing, there exist several limitations originating from the essential use of highly stretchable materials: i) low force due to incapability of holding high pressure, ii) poor reliability due to non-linearity of materials and Mullins effect, iii) slow response time due to heavy reliance on material response speed iv) difficulty in control due to difficulties in kinematics analysis of stretching behavior, and v) narrow material selection with only a few specific materials (expensive silicone elastomers or high-tech 3d printing materials) available. In addition, a complex fabrication process using sacrificial molds, as well as the need for deposition of multiple materials to achieve functional motion (e.g. bending) over deployment and balloon-like bloating, significantly increase fabrication cost. These drawbacks presented challenges for practical usage of dual-morphing principle in real-world applications, highlighting a need for a new design method of a different working principle that does not rely on stretching, broadens the range of applicable materials, and enables large deployment, high force, and low-cost/easy fabrication (the detailed comparison of the dual-morphing principle and the current work is shown in Table 1).