Adaptive hierarchical origami-based metastructures

Abstract

Shape-morphing capabilities are crucial for enabling multifunctionality in both biological and artificial systems. Various strategies for shape morphing have been proposed for applications in metamaterials and robotics. However, few of these approaches have achieved the ability to seamlessly transform into a multitude of volumetric shapes post-fabrication using a relatively simple actuation and control mechanism. Taking inspiration from thick origami and hierarchies in nature, we present a hierarchical construction method based on polyhedrons to create an extensive library of compact origami metastructures. We show that a single hierarchical origami structure can autonomously adapt to over 10³ versatile architectural configurations, achieved with the utilization of fewer than 3 actuation degrees of freedom and employing simple transition kinematics. We uncover the fundamental principles governing theses shape transformation through theoretical models. Furthermore, we also demonstrate the wide-ranging potential applications of these transformable hierarchical structures. These include their uses as untethered and autonomous robotic transformers capable of various gait-shifting and multidirectional locomotion, as well as rapidly self-deployable and self-reconfigurable architecture, exemplifying its scalability up to the meter scale. Lastly, we introduce the concept of multitask reconfigurable and deployable space robots and habitats, showcasing the adaptability and versatility of these metastructures.

Fig. 1. Overview of the construction and advantages of hierarchical origami-based shape-morphing metastructures.

Schematic illustrations of a level-1 metastructure composed of an nR spatial looped mechanism with n rotary hinges and n rigid linkages (a) and a level-2 metastructure composed of a “kR” spatial looped mechanism at level 2 and nR looped mechanisms at level 1 (b). c The designs of rotary hinges and rigid linkages in the forms of respective origami line fold and different polyhedrons. d Illustration of two types of reconfigurable metastructures using planar and spatial tessellation of thin plates and prims, respectively. Examples of 3D-printed prototypes of self-reconfigurable level-1 (e) and level-2 (f) origami-based robotic metastructures actuated by electrical servomotors. Scale bar: 3 cm. The level-1 and level-2 metastructures are composed of closed-loop connections of 8 and 32 cubes, respectively. g Demonstration of the advantages of hierarchical looped mechanism in creating self-reconfigurable metastructures with versatile shape morphing under fewer reconfiguration DOFs (actuated servomotors) than 3.

Fig. 2. Design of hierarchical origami-based shape-morphing metastructures.

a–c Schematics of constructing level-1 (a), level-2 (b), and level-3 (c) reconfigurable and deployable structures using hierarchical closed-loop rigid bar (line hinges)-linkage (cubes) mechanisms (column ii) as different-leveled structural motifs (column iii). The representative morphed architectures with internal structural loops (ISLs) are shown in column iv. d Schematics of selected combinatorial designs by either combinatorically hinging two adjacent cubes at one of the four cube edge pairs at level 1 (i) and level 2 (ii) or flipping any level-1 structure with asymmetric hinge locations on top and bottom surfaces (ii) or combined. e Comparison of the maximum initial structural DOFs of different hierarchical structures composed of 4, 6, and 8 cubes at level 1. f Comparison of the combinatorically designed four categories of level-2 structures in (b) (insets and Supplementary Fig. 6) on the number of combinatorial level-2 hinge connections, reconfiguration modes, and morphed configurations with ISLs.

Fig. 3. Continuous shape morphing of an optimal level-2 structure.

a Shape-morphing configurations diagram in the 3D-printed prototype exhibiting hierarchical transition tree-like features. The branches in the transition tree of represent the bifurcated configurations. Scale bar: 3 cm. b The variation of flexible level-2 link length with the opening angle of hinges during the shape transition from node M_D to M_E, and node M_E to M_F in reconfiguration loop 1 in (a). Inset shows the eigenvalues v_kk as a function of the rotating angle in both level-1 and level-2 structures. c The relationship between the number of reconfiguration paths and the number of kinematic bifurcation configuration states for the combinatorically designed category I–III level-2 systems. d One selected combinatorial design of the shape-morphing level-2 structures by rearranging the level-1 hinges (i), and some of its representative reconfigured shapes (ii–v). Scale bar: 3 cm. e Comparison among the total number of hinges, the number of rotated joints, and the number of reconfiguration DOFs during the reconfiguration loop from node M_A to M_F and back to M_A in (a).

Fig. 4. Angle relationships during the shape morphing.

a Schematics of level-2 structures with labeled hinge connections on top and bottom surface. b Schematics of the opening angles γ_kj (k, j are integers with 1 ≤ k ≤ 4 and 1 ≤ j ≤ 8 denote the link and hinges opening angles, respectively) between adjacent cubes in level-1 structure. c Construction of eight local coordinate systems for the 8 hinges of level-1 structure. d The reconfiguration kinematics from node M₇ (i) to node M₁₃ (iii) in Fig. 3a, b: the involved shape-changing details of level-1 link #1 and #3 (ii) and variations of the rotating angles for all folds (iv). Scale bar: 3 cm. e The reconfiguration kinematics from node M₁₅ (i) to node M₂₁ (v) by bypassing node M₂₅ (iii) in Fig. 3a, b: the involved shape-changing links #1 and #2 for the process from node M₁₅ to M₂₅ (ii) and links #2 and #4 for the process from node M₂₅ to M₂₁ (iv) and variations of all folds during these two processes (vi). Scale bar: 3 cm. f Low reconfiguration DOFs for the reconfiguration process in (d) (1 DOF) and (e) (1 or 2 DOF(s)).

Fig. 5. Application in autonomous robotic transformer for multigait locomotion.

a Schematics of untethered actuation design details for the level 1 eight-cube-based structure: 5 electrically powered servomotors for active hinge rotation (i), onboard power system and Bluetooth wireless receiver to conduct reconfiguration order (ii) from customized remote control software (iii). b Demonstrated untethered shape morphing in the level-1 structure through looped mechanisms. c–e Shape transformation in level-1 structure for multigait locomotion. Scale bar: 3 cm. c Forward (i) and sideway locomotion (ii). d Locomotion gait switch from reconfiguration to legged walking; e Legged walking with carried payload on flat surface (i) and 10°-sloped surface (ii). f Demonstration of the specific positions of 22 active servomotors and the rolling locomotion of level-2 structure. Scale bar: 3 cm. g Locomotion speeds of both level-1 and level-2 structures in (c–f).

Fig. 6. Application of level-2 structures in self-deployable architectures.

Self-deployment into bridge and/or shelter-frame-like (a) and fully open 4-story building-like structures (b) with high loading capacity of over 10 kg (c). Scale bar: 3 cm. d Comparison among the total number of hinges, the total number of servomotors, the rotated hinges, and the actively actuated servomotors during the shape transformation shown in (b).

Fig. 7. Multifunctional applications of level-2 structures in scalable architectures and space robots.

a Meter-scale demonstration of deployable, shape-morphing architectures using cubic packaging boxes (side length of 60 cm). Scale bar: 30 cm. b Schematics of potential conceptual applications in versatile reconfigurable space robots and habitats.