Origami Spring-Inspired Shape Morphing for Flexible Robotics

Abstract

Flexible robotics are capable of achieving various functionalities by shape morphing, benefiting from their compliant bodies and reconfigurable structures. In this study, we construct and study a class of origami springs generalized from the known interleaved origami spring, as promising candidates for shape morphing in flexible robotics. These springs are found to exhibit nonlinear stretch-twist coupling and linear/nonlinear mechanical response in the compression/tension region, analyzed by the demonstrated continuum mechanics models, experiments, and finite element simulations. To improve the mechanical performance such as the damage resistance, we establish an origami rigidization method by adding additional creases to the spring system. Guided by the theoretical framework, we experimentally realize three types of flexible robotics—origami spring ejectors, crawlers, and transformers. These robots show the desired functionality and outstanding mechanical performance. The proposed concept of origami-aided design is expected to pave the way to facilitate the diverse shape morphing of flexible robotics.

Introduction

Flexible robotics possess compliant bodies and reconfigurable structures to achieve multiple functionalities, such as delivering different objects^1,2 and going through diverse environments.^3,4 The essential performance for functionality is the controllable shape morphing, based on materials or structural design or both. The material-based shape morphing can be classified into passive shape morphing with soft materials and active shape morphing with active materials. The emphasis of the former is to seek efficient actuation strategies like pneumatic, hydraulic, or chemical energy to drive the shape changing of robots,^1,4,5 while the latter is to explore advanced active materials to realize specific deformations in response to the external stimuli.^6–13

Shape-morphing strategies of flexible robotics based on structural design are focused on exploiting special structures with specific mechanical properties, such as negative Poisson's ratio,^14,15 multistability,^16–18 and buckling.¹⁹ These structures can provide various and programmable deformation modes and, thus, have many advantages and great potential prospects.²⁰ Among various structural design strategies, origami made of thin paper is a promising candidate.^2,21–27 First, origami is constructed by folding the paper along the prescribed creases on an easy-to-manufacture two-dimensional sheet. The distribution of creases can be designed to provide desired geometrical constraints, leading to different degrees of freedom of motion and potentially simple control systems.^23,28–30 Second, the bending effect usually dominates in the origami system, introducing generically nonlinear effective mechanical response, which can be utilized to design origami springs,^24,28,31 origami cantilevers,^32,33 etc. Despite having various designs of origami actuators/robotics in the literature, these applications usually suffer from difficulties: (1) The models to capture the shape morphing rules and the mechanical response are usually sophisticated (e.g., computationally expensive truss model^34,35), which enhance the difficulties of the rational design; (2) There usually exists inevitable stress concentration at the corner of the crease (e.g., Kresling pattern²²), which results in undesired damage to the structure. Therefore, it is necessary to develop new theoretical methods to overcome these difficulties and guide the further use of origami in flexible robotics.

In this work, we consider the generalized origami springs as a template for the application of flexible robotics, which also overcomes the abovementioned difficulties to some extent. To this end, we first introduce a series of origami springs by alternately folding multiple regular-polygon-array paper ribbons, known as the interleaved origami spring (IOS). IOSs exhibit stretch-twist-coupling shape morphing when stretching. We demonstrate a continuum model to simplify the analysis of the shape morphing and the mechanical response of IOSs. The theoretical model is validated by experiments and finite element simulations. Moreover, to optimize the mechanical response and improve the damage resistance, we propose an origami rigidization method by predesigning additional creases on the facets to transform the buckled facets into rigidly foldable facets. The simulation shows that the origami rigidization significantly lowers the stress concentration and enhances the damage resistance of the structure. Then, the shape-morphing performances and mechanical responses of IOSs are further applied to construct flexible robotics, including origami spring ejectors, crawlers, and transformers, which demonstrate the feasibility of the origami-aided-design concept. Finally, we anticipate that the design framework can be generalized and applied to other systems such as stimuli-sensitive and nonperiodic origami.

Construction of the Origami Spring

The zigzag origami (ZO) is the simplest origami structure to provide elasticity of a rectangular paper ribbon through the alternate mountain-valley folding. Applying the uniaxial force F, the ZO behaves as a nonlinear spring with no twist involved (Fig. 1a). Inspired by the ZO, we construct an IOS by alternately folding two perpendicularly arranged rectangular paper ribbons of the same size (Fig. 1b). In addition to elasticity, the IOS also exhibits a coupled twist along the central axis (Fig. 1c) when stretching, due to the interactions between these two paper ribbons. To enrich the class of IOS, we systematically fold ribbons consisting of chains of different polygons. These IOSs are named as IOS-6 and IOS-8, respectively, depending on the shapes of the facets (Fig. 2; Supplementary Note S1 and Figs. S1 and S2). They are expected to have distinct stretch-twist couplings and mechanical responses due to the different interactions of facets, which will be analyzed later.

FIG. 1.

Geometry of the ZO and IOS. (a) The uniform-stretching configuration of ZO under uniaxial tension. (b) The folding process of IOS-4. (c) The stretch-twist-coupling shape morphing of IOS under uniaxial tension. IOS, interleaved origami spring; ZO, zigzag origami. Color images are available online.

FIG. 2.

Schematics of the stretch-twist-coupling performance of IOSs and continuum analysis diagrams. (a) The configurations of IOS-4 and the corresponding simplified equivalent continuum diagrams in extension ratio $\tilde{z} =$ 0.10, 0.25, and 0.50, respectively. Light-, sky-, and dark-blue solid lines indicate the large-pitch helices, while yellow dashed lines the small pitch. (b) The shape-morphing model of the IOS-4 unit cell on 3D and top view, respectively. (c) The dependences of $\tilde{θ}$ upon $\tilde{z}$ for IOS-4. The data were obtained from experiments, FEA, and the proposed theoretical model. The thumbnail exhibits z/l_f as a function of $\tilde{z}$ , showing an approximately linear relationship. (d–i) Similar analyses for IOS-6 and IOS-8. The results reveal the different stretch-twist couplings in IOS-4, IOS-6, and IOS-8. 3D, three-dimensional; FEA, finite element analysis. Color images are available online.

Shape Morphing Modeling

In this section, we aim to analyze the stretch-twist coupling of IOSs, by replacing the origami structure with an analogous continuum having the same effective response. This method makes the shape-morphing analysis easier and more intuitive and also can be used for other kinds of origami structures. Figure 2a shows the IOS-4 configurations and the corresponding analogous continuum diagrams in different extension ratios with eight unit cells. The continuum consists of a cylinder with four helices winded on the surface. Three assumptions are satisfied in the simplified model. First, all the sides keep straight with a constant side length a; second, the process is quasi-static, while all the unit cells keep the same configuration; and third, all the origami vertices land on the corresponding helices. The stretch-twist performance is characterized by two dimensionless parameters, that is, the twisting angle of each cell $\tilde{θ}$ and the extension ratio $\tilde{z}$ , which are defined as $\tilde{θ} = \frac{θ}{n}$ (1)

\tilde{z} = \frac{z}{l_{L P H} (a, n, z)} = sin φ

(2)

where $θ$ and z are the twisting angle and the extension length of the whole structure, respectively. n is the number of the unit cells, $l_{L P H} (a, n, z)$ is the arc length of the large-pitch helix, which is a function of a, n, and z, and $φ$ is its helix angle.

We intercept four adjacent facets of an IOS-4 as the unit cell, which contains two square facets in each paper ribbon (Fig. 2b). Projecting the vertices of the unit cell onto the plane perpendicular to the cylindrical axis and passing through A, one can obtain the projected vertices B′, …, G′ and the sum of the projected arcs $\hat{A B'} + \hat{B' C'} + \hat{C' D'} + \hat{D' A} = 2 π r$ , where r is the radius of the cylinder. The expression of r is further deduced as a function of $\tilde{z}$ (see Note S2 in Supplementary Data for the details) $r = \frac{a N_{4}}{6} \sqrt{\frac{N_{4} (N_{4} + M_{4})}{6}}$ (3)

by calculating the projected arcs, where $M_{4} = \sqrt{1 - {\tilde{z}}^{2}}$ , $N_{4} = \sqrt{9 - {\tilde{z}}^{2}}$ . The twisting angle of each unit cell $\tilde{θ}$ is also given as a function of $\tilde{z}$ $\tilde{θ} (\tilde{z}) = \frac{4 (\hat{E' B'} - \hat{A B'})}{r} = 4 a r c c o s (P_{4} Q_{4} + \sqrt{1 - P_{4}^{2}} \sqrt{1 - Q_{4}^{2}})$ (4)

where $P_{4} = 1 - 108 M_{4}^{2} ∕ [N_{4}^{3} (M_{4} + N_{4})]$ , $Q_{4} = 1 - 12 ∕ [N_{4} (M_{4} + N_{4})]$ . We obtain the twisting angle $θ$ and the corresponding extension length z through the finite element analysis (FEA) and experiments. $\tilde{θ}$ and $\tilde{z}$ can be further calculated by Eqs. (1) and (4), respectively. The relationship between z and $\tilde{z}$ is approximately linear (Fig. 2c, inset), implying that $l_{L P H} (a, n, z)$ can be regarded as a constant independent of z. We thus assume $\tilde{z} = \frac{z}{λ l_{f}}, λ \geq 1$ (5)

where $λ l_{f} = l_{L P H}$ , $λ$ is a constant coefficient, and $l_{f}$ is the extension length of the IOS when $φ = π ∕ 2$ ( $l_{f} = 2 a n$ in IOS-4s). In Figure 2c, the dependences of $\tilde{θ}$ upon $\tilde{z}$ (i.e., the stretch-twist coupling) from experiments, FEA, and our proposed model are plotted, which are in great agreements.

Similar analyses are also performed for IOS-6 and IOS-8. The geometric parameters of IOSs with differently shaped facets but the same circumradius r₀ are listed in Supplementary Table S1 (derivation process see Note S2 in Supplementary Data). The theoretical, FEA, and experimental results in Figure 2h and i reveal that similar stretch-twist couplings also exist in IOS-6 and IOS-8, with slight discrepancies. It is noted that $λ$ tends to 1 when increasing the number of the regular-polygon edges, which means, as the number of the edges increases, the length of the large-pitch helix is close to the extension length when $φ = π ∕ 2$ .

Structural Optimization

We observe that the IOSs undergo more and more significant buckling with the progress of stretching in both experiments and simulations. The buckling results in the increase of elastic energy and, hence, the increase of tensile force. Moreover, stress concentrations mostly appear near the corners of creases (Fig. 3b) and cause undesired damages. To resolve these, we propose a predesign-crease strategy, that is, setting additional creases (namely secondary creases, red lines in Fig. 3a) along the diagonals of facets in addition to the primary creases (black lines in Fig. 3a) along the sides to guide the predictable folding rather than buckling. Similar buckling-control strategies were reported but with different purposes and effects.^29,36–38 By setting these secondary creases, the overwhelmed buckling is released and the buckling conflicts between adjacent facets are relieved, resulting in great improvements of mechanical performances. This strategy essentially transforms the buckled facets into rigidly foldable facets and, therefore, is named origami rigidization method. Accordingly, the name of the IOS optimized by this method is thus updated as rigidized interleaved origami spring (RIOS).

FIG. 3.

Demonstration of the origami rigidization method. (a) Diagrams of the crease distributions. Black (red) lines represent primary (secondary) creases. Solid (dashed) lines are mountain (valley) creases. (b) Shape-morphing configurations ( $\tilde{z} =$ 0.8) obtained by FEA, colored by the Mises stress nephogram. (c) Uniaxial force $\tilde{F}$ applied on origami springs versus extension ratio $\tilde{z}$ . The theoretical models match the experimental data well. Color images are available online.

Figure 3b shows the FEA results of the shape-morphing configurations of IOSs and RIOSs ( $r_{0} = 10$ mm, $n = 8$ ) colored by the Mises stress nephogram. One can observe that RIOSs exhibit rigidity or approximate rigidity on the facets without or with less buckling, compared to the corresponding IOS cases, especially in the square-facet cases (IOS-4 and RIOS-4). More importantly, the values of the maximal stress decrease in RIOSs compared to those in IOSs, indicating that the stress concentrations are relieved.

Next, we analyze the mechanical response of IOSs and RIOSs. Figure 3c illustrates the force-extension curves of IOSs and RIOSs. $\tilde{F}$ is defined as $\tilde{F} = F ∕ (2 a n n_{p r})$ , where $2 a n n_{p r}$ is the total length of the primary creases with $n_{p r}$ the number of paper ribbons. Overall, the forces required to stretch the springs follow IOS-4 < IOS-6 < IOS-8, RIOS-4 < RIOS-6 < RIOS-8, and RIOS < IOS under the same facet shape, while the square-facet case has the maximal difference. The force increases monotonically and continuously with respect to the uniaxial strain, which indicates that no multistability or other special mechanical responses occur. Since all the origami springs exhibit an initial free extension ${\tilde{z}}_{0}$ due to the residual strain in creases, we separate the force-extension curves into compression and tension regions.

Observed from the compression region, $\tilde{F}$ and $\tilde{z}$ are in an approximately linear relationship, we thus assume $\tilde{F} = k_{c} (\tilde{z} - {\tilde{z}}_{0})$ (6)

where $k_{c}$ is the compression elastic constant with the unit $N \cdot m m^{- 1}$ and can be obtained by linear fitting with the experimental data. As illustrated in Figure 3c right, the regular-octagon-facet origami springs have the maximal $k_{c}$ both in IOS and RIOS. Moreover, RIOSs have smaller $k_{c}$ than IOSs, which illustrates that the rigidization optimization on RIOSs reduces the interaction among the facets to a certain extent.

In the tension region, the force-extension relationship is no longer linear (Fig. 3c, left), which could be attributed to the stronger and stronger interactions between the adjacent facets as the extension progresses. The total shape-morphing energy E is given by the sum of the folding energy of the primary creases $E_{F 1}$ , the folding energy of the secondary creases $E_{F 2}$ ( $E_{F 2} = 0$ in IOSs), and the buckling energy of the facets $E_{B}$ ( $E_{B} = 0$ in RIOSs) with the forms $\{\begin{matrix} E_{F 1} = \frac{1}{2} \cdot f_{k_{F}} (\tilde{z}) \cdot 2 a n n_{p r} \cdot ω_{1}^{2} \\ E_{B} = \frac{1}{2} \cdot f_{k_{B}} (\tilde{z}) \cdot 4 r_{0} n n_{p r} \cdot 2 ω_{B}^{2} \\ E_{F 2} = \frac{1}{2} \cdot f_{k_{F}} (\tilde{z}) \cdot 4 r_{0} n n_{p r} \cdot ω_{2}^{2} \end{matrix}$ (7)

where $f_{k_{F}} (\tilde{z})$ and $f_{k_{B}} (\tilde{z})$ are the unknown stiffness of the folding creases and the buckling, respectively. Here we assume $f_{k_{F}} (\tilde{z}) = k_{F} {\tilde{z}}^{ξ_{F}}$ and $f_{k_{B}} (\tilde{z}) = k_{B} {\tilde{z}}^{ξ_{B}}$ to fit the experimental data, where $k_{F}$ and $k_{B}$ are the stiffness constants with the unit $N \cdot r a d^{- 1}$ , $ξ_{F}$ and $ξ_{B}$ are dimensionless constant exponentials to capture the nonlinear behavior of $\tilde{F}$ upon $\tilde{z}$ . The folding angle of the primary crease $ω_{1}$ can be approximately expressed as $ω_{1} = φ + φ'$ (Supplementary Fig. S3). The buckling of the facets is simplified by two equal folding angles $ω_{B}$ along the diagonals, and the folding angle of the secondary creases is denoted by $ω_{2}$ . All the folding angles are functions of $\tilde{z}$ , obtained by evaluating coordinates (Note S2 in Supplementary Data). We use $Ẽ = E ∕ 2 a n n_{p r}$ to denote the energy per unit length of the primary crease; therefore, $\tilde{F}$ can be expressed as the partial derivative of $Ẽ$ with respect to $\tilde{z}$ , more specifically $\{\begin{matrix} {\tilde{F}}_{I O S} = \frac{\partial (Ẽ_{F 1} + Ẽ_{B})}{\partial z} = \frac{1}{λ l_{f} |_{n = 1}} [{\tilde{z}}^{ξ_{F}} k_{F} (A_{1} + A_{2} ξ_{F}) + {\tilde{z}}^{ξ_{B}} k_{B} (B_{1} + B_{2} ξ_{B})] \\ {\tilde{F}}_{R I O S} = \frac{\partial (Ẽ_{F 1} + Ẽ_{F 2})}{\partial z} = \frac{1}{λ l_{f} |_{n = 1}} [{\tilde{z}}^{ξ_{F}} k_{F} (A_{1} + A_{2} ξ_{F} + C_{1} + C_{2} ξ_{F})] \end{matrix}$ (8)

where A₁, A₂, B₁, B₂, C₁, and C₂ are the geometric correlation parameters related to $\tilde{z}$ . $ξ_{F}$ , $ξ_{B}$ , $k_{F}$ , and $k_{B}$ are undetermined coefficients. Substituting $\tilde{z} = {\tilde{z}}_{0}$ , ${\tilde{F}}_{I O S} = 0$ , and ${\tilde{F}}_{R I O S} = 0$ into Eq. (8), we have . Then the stiffness constants $k_{F}$ and $k_{B}$ can be further obtained by fitting with the experimental data using the least square method. Specific values and expressions above are listed in Supplementary Table S2. As shown in Figure 3c, the force-extension model we proposed matches well with the experimental data with acceptable minor deviations, indicating that the proposed models [Eqs. (6) and (8)] are able to capture the linear and nonlinear mechanical responses in the compression and tension regions. Moreover, the force-displacement curve of RIOS-8 (and IOS-8) has the biggest slope compared with the other types of RIOS (and IOS). This fact can be explained theoretically by Eqs. (7) and (8)—RIOS-8 has the longest crease per unit cell and, hence, the largest elastic energy density.

Performance in Flexible Robotics

Origami spring ejector

Since the origami springs have excellent compressing elasticity, they can be used as ejectors. We arrange two ZOs in parallel with the same size and number of creases as IOS-4, named parallel origami spring (POS), to be the control group. All origami springs were first compressed to the minimal length and rapidly released to push the origami hexagram for a distance ejecting. Several factors determine the ejecting performance, including z₀ and $k_{c}$ mentioned in the last section, the friction coefficient $μ$ with the substrate, the mass of the origami spring M, and the hexagram m (Supplementary Table S3). The ejecting distance can be deduced by the conservation of energy $x_{e j} = \frac{z_{0} (k_{c} z_{0} - μ M g)}{2 μ m g}$ (9)

where g is the gravitational acceleration constant. In this study, we ignore the small reciprocating motion of the origami spring for simplification. As seen from Eq. (9), it requires to increase the complete compression force of origami springs, that is, $k_{c} z_{0}$ and decrease M to obtain a good ejection ability. Owing to the origami rigidization method, the $k_{c} z_{0}$ of RIOSs improves to a certain extent, leading to a better ejecting ability compared with IOSs and POS (Fig. 4a). Among all, the RIOS-4 shows the best performance, which can push the origami hexagram forward over three times longer than its original length (Fig. 4b; Supplementary Video S1).

FIG. 4.

Performance of origami spring ejectors. (a) The ejecting performance $x_{e j} ∕ z_{0}$ of different origami springs. $x_{e j}$ and z₀ are the ejecting distance of the origami hexagram and the initial length of the origami spring, respectively. (b) The ejecting process of POS and RIOS-4. All involved origami springs are under $r_{0} =$ 10 mm and $n =$ 8. Scale bar: 50 mm. POS, parallel origami spring. Color images are available online.

Origami spring crawler

The origami spring crawler uses the outstanding recovery ability of the spring from its extended state to the free state. The elastic recovery performance was tested by repeatedly stretching the origami springs from their free extension states to $\tilde{z} = 0.8$ and recording the free extensions after unloading. Benefited from the mutual restraints and interactions between the paper ribbons, IOSs and RIOSs have both greatly better recovery performance than POS (Fig. 5a). Therefore, we used the IOS-8, which had the best elastic recoverability among, to mimic the crawl locomotion of earthworms. The two ends of the origami springs were dragged by rotary motors through two thin threads. The two threads stayed along the structure's central axis to obtain a controllable straight-line crawling. First, we made one of the motor work to stretch the origami spring until $\tilde{z} = 0.8$ . Then we stopped that motor and started the other motor to recover the stretching by relaxing the thread. The origami spring contracted to its free extension state with the head as the fixed point and finished an entire crawling cycle (Fig. 5b; Supplementary Video S2).

FIG. 5.

Performance of origami spring crawlers. (a) The elastic recovery performance of different origami springs under multiple stretching times. (b) The crawling performance $u ∕ z_{0}$ (u is the crawling distance) of the center of body (solid line), head (dashed line), and tail (dotted line) varying with number of crawling cycles. The thumbnail is five typical crawling moments of the IOS-8 throughout an entire crawling cycle. Crawling images of IOS-4 and IOS-6 can be seen in Supplementary Figure S12. (c) The process of the IOS-8 climbing over a cliff with 1.3-fold body length. (d) The process of the IOS-8 leaping over a cliff with 2.2-fold body length. All involved origami springs are under $r_{0} =$ 10 mm and $n =$ 8. Scale bar: 50 mm. Color images are available online.

Moreover, the origami spring crawlers have the ability to cross cliffs. Also using IOS-8 as the demonstration, the crawler climbed over a cliff step by step through properly stretching and contracting the body (Fig. 5c; Supplementary Video S3). When the width of the cliff increased to a considerable value, the crawler stored elastic potential energy by stretching the body and released it instantaneously to obtain enough initial velocity to leap over the cliff like an arrow (Fig. 5d; Supplementary Video S3).

Origami spring transformer

We demonstrate an origami spring transformer utilizing the deployability and the stretch-twist coupling. The fabrication process is exhibited in Figure 6a, which follows three steps sequentially: connecting two IOS-4s ( $r_{0} = 10$ mm, $n = 4$ ) with opposite chirality as the “muscle,” sealing the “muscle” by thin films as the skin, and mounting two wheels on both sides. The completed model is shown in Figure 6b. By slowly supplying gas through the tube, the transformer can transform into three configurations owing to the extensibility and flexibility of IOSs, including a closed box, an upright body, and a two-wheeled car (Fig. 6c; Supplementary Video S4). Furthermore, a rolling motion can be produced using the stretch-twist-coupling shape morphing of IOSs. As the shape morphing is symmetric with respect to the midplane, the rotation angle $θ$ varying with the extension length z can be calculated by Eq. (4) with $θ = 4 \tilde{θ} (r a d)$ and $z = 96.4 \tilde{z} (m m)$ . First, the transformer was in the closed box state, then the gas was rapidly supplied to stretch the “muscle,” and the two wheels were thus pushed away. Meanwhile, the middle of the “muscle,” namely the connection of two IOSs, underwent a twisting, leading the whole “car” to roll forward (Fig. 6d).

FIG. 6.

Design, fabrication, and resulting of an origami spring transformer. (a) The component introduction and fabrication process of the origami spring transformer. The process follows three steps, Steps 1, 2, and 3 are indicated by solid-line, dashed-line, and dotted-line two-way arrows, respectively. (b) The completed model. Gas is in or out through the tube to actuate the IOS. (c) The transforming process of origami spring transformer from a closed box to an upright body and then to a two-wheeled car by slowly stretching the “muscle.” (d) The rolling motion of the origami spring transformer by rapidly stretching the “muscle” and utilizing the stretch-twist-coupling performance. Scale bar: 30 mm. Color images are available online.

Conclusion

In this work, we demonstrate that the structural design of generalized origami spring with good shape-morphing performance is of benefit to the applications of flexible robotics. We first present a design strategy of generalized IOS, which exhibit stretch-twist coupling under uniaxial tension. We establish a continuum model and an origami rigidization method based on the experiments and finite element simulations to capture, analyze, and improve the shape-morphing performance of the IOSs. Guided by the theoretical framework, we propose ejectors and crawlers using the good elasticity of origami springs and devise an origami spring transformer that is capable of multiple transformations and a rolling motion. Besides the IOS, the stretch-twist coupling has also been observed in some deployable cylindrical origami systems and found in wide applications.^{22,39,40,41,42} However, comparing with them, IOS exhibits significant advantages in the simple and fast folding process, controllable buckling-folding transformation on facets, excellent stretch-twist-coupling characteristic, smooth and continuous folding/unfolding motions, and good maintaining of the central axis during shape morphing. These abovementioned advantages indicate that IOSs are good candidates for structural designs of robotics.

The framework can be potentially and naturally generalized using paper ribbons with different polygons or combining IOSs and RIOSs, so as to break the axially symmetric stretch-twist-coupling and achieve various shape-morphing performance. Alternatively, active materials can be used to design stimuli-sensitive origami springs. Taken together, we expect that our framework of origami-aided design will pave the way to facilitate the diverse shape morphing of flexible robotics.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported by the National Natural Science Foundation of China (NSFC) under grant nos. 91848201, 11988102, 11521202, 11872004, and 11802004 and Beijing Natural Science Foundation under grant no. L172002.

Supplementary Material

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