INVERSE ORIGAMI DESIGN FOR SOFT ROBOTIC DEVELOPMENT

Inverse origami design for soft robotic development is described herein. A method as described herein can include determining, by a system comprising a processor, shape parameters corresponding to an input shape; generating, by the system based on the shape parameters, an origami crease pattern representative of the input shape, wherein the origami crease pattern comprises respective origami cell units, and wherein the origami crease pattern is defined by a group of vector size parameters corresponding to relative fold lengths associated with the respective origami cell units, a vector angle parameter corresponding to fold angles associated with the respective origami cell units, and a scalar cell height parameter; and imprinting, by the system, the origami crease pattern onto a tangible medium.

BACKGROUND

Origami, originally from the ancient art of paper folding, can be used to construct various three-dimensional (3D) structures with different shapes and sizes from a flat sheet. The resulting 3D structures can have selective compliance and reversible features between the flat and 3D forms. Three-dimensional origami structures can be made from a wide range of materials and enable functional folds, with stiffness ranging from soft to rigid, by processing a flat sheet with specific crease patterns.

SUMMARY

The following summary is a general overview of various embodiments disclosed herein and is not intended to be exhaustive or limiting upon the disclosed embodiments. Embodiments are better understood upon consideration of the detailed description below in conjunction with the accompanying drawings and claims.

In an implementation, a method is described herein. The method can include determining, by a system including a processor, shape parameters corresponding to an input shape. The method can further include generating, by the system based on the shape parameters, an origami crease pattern representative of the input shape. The origami crease pattern can include respective origami cell units, and the origami crease pattern can be defined by a group of vector size parameters corresponding to relative fold lengths associated with the respective origami cell units, a vector angle parameter corresponding to fold angles associated with the respective origami cell units, and a scalar cell height parameter. The method can additionally include imprinting, by the system, the origami crease pattern onto a tangible medium.

In another implementation, a system is described herein. The system can include a processor and a memory that stores executable instructions that, when executed by the processor, facilitate performance of operations. The operations can include determining properties of a target shape; generating, based on the properties, an origami crease pattern representative of the target shape, the origami crease pattern including respective origami cell units and being defined by a group of first vector parameters corresponding to relative fold lengths of the origami cell units, a second vector parameter corresponding to fold angles of the origami cell units, and a scalar parameter corresponding to a height of the origami cell units; and rendering the origami crease pattern onto a tangible sheet.

In an additional implementation, a non-transitory machine-readable medium including computer executable instructions is described herein. The instructions, when executed by a processor, can facilitate performance of operations including generating, based on properties of an input shape, an origami crease pattern representative of the input shape, where the origami crease pattern includes respective origami cell units, and where the origami crease pattern is defined by parameters including a group of vector length parameters corresponding to relative fold lengths of the respective origami cell units, a vector angle parameter corresponding to fold angles associated with the respective origami cell units, and a scalar cell dimension parameter that defines a spatial dimension of the respective origami cell units; and imprinting the origami crease pattern onto a tangible sheet.

DETAILED DESCRIPTION

Various specific details of the disclosed embodiments are provided in the description below. One skilled in the art will recognize, however, that the techniques described herein can in some cases be practiced without one or more of the specific details, or with other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring subject matter. In addition, it is noted that the drawings provided herein are not drawn to scale, either within the same drawing or between different drawings, unless explicitly stated otherwise.

Described herein are techniques that facilitate inverse origami design for soft robot development. Traditionally, developing a robot involves the design of 3D functional structures and finding suitable 3D manufacturing methods. These manufacturing methods are usually bottom-up, with complicated steps and limited scale in implementation. In contrast, origami facilitates a top-down manufacturing method, e.g., in which a 3D structure can be deployed to a 2D plane. This can remarkably decrease manufacturing complexity, shorten the production cycle of origami-inspired robots, and allow the use of mechanical meta-materials with different features of drivability, tunable stiffness, and bi-stability, among other benefits.

Difficulties in developing soft origami robots lie in the design of flat crease patterns to achieve desired 3D origami structures. Existing origami design techniques typically involve manual iterative modification of a crease pattern until the final desired folded shape is obtained, which increases the complexity of origami design and hinders the mass production of corresponding designed robots. As a result, traditional 3D model design, e.g., that utilizes software to generate desired solid structures by inputting simple commands, are generally used in practice. Various aspects described herein facilitate automatic generation of flat crease patterns based on a desired folded shape, which significantly mitigates and/or removes these difficulties.

With reference now to the drawings,FIG.1illustrates a block diagram of a system100that facilitates inverse origami design for soft robotic development. As shown inFIG.1, system100includes a parameter extraction component110, a pattern generator component120, and a fabrication component130, which can operate as described in further detail below. In an implementation, the components110,120,130of system100can be implemented in hardware, software, or a combination of hardware and software. By way of example, the components110,120,130can be at least partially implemented as computer-executable components, e.g., components stored on a memory and executed by a processor. An example of a computer architecture including a processor and a memory that can be used to implement the components110,120,130, as well as other components as will be described herein, is shown and described in further detail below with respect toFIG.29.

Based on shape parameters as generated by the parameter extraction component110, the pattern generator component120of system100can produce an origami crease pattern that is representative of the input shape associated with the shape parameters. An origami crease pattern as generated by the pattern generator component120can be expressed as, or otherwise include, a group of origami cell units, e.g., Miura cell units as described below with respect toFIG.3. Additionally, an origami crease pattern as created by the pattern generator component120can be based on an inverse origami design model that defines the crease pattern based on a group of parameters. These parameters can include, e.g., a group of vector length or size parameters that correspond to respective fold lengths associated with the respective origami cell units, a vector angle parameter that corresponds to fold angles associated with the respective origami cell units, and a scalar cell height or cell dimension parameter that is based on a desired final size of the folded origami shape. These parameters and their derivation are described in further detail below, e.g., with respect toFIG.6.

In response to generation of an origami crease pattern by the pattern generator component120, the fabrication component130of system100can imprint and/or otherwise render the origami crease pattern onto a tangible medium10, e.g., a flat sheet composed of one or more materials, a layered group of flat sheets, etc. By way of non-limiting example, the fabrication component130can print the origami crease pattern onto a paper sheet, etch the origami crease pattern into a sheet composed of polyethylene terephthalate (PET) and/or other plastics, and/or facilitate transferal of the pattern onto the tangible medium10in any other suitable manner Techniques that can be utilized by the fabrication component130are described in further detail below, e.g., with respect toFIG.11.

Various implementations presented herein utilize an inverse origami design model using standard patterns, e.g., Miura origami patterns, with widespread robotic applications to promote the development of soft origami robots. With this model, desired origami structures and corresponding crease patterns can be generated simply on the basis of input shape parameters or 2D shape graphics. Additionally, users can easily process resulting origami designs to obtain the flat crease patterns of desired folded shapes. Furthermore, this model can be incorporated into a user-friendly software platform for easy implementation, e.g., as will be described in further detail below with respect toFIG.27. With this platform, various soft origami robots with crawling, actuation, and grasping functions can be constructed by integrating with soft smart actuators.

The design model presented herein can be used to construct origami structures with various cross sectional shapes in a simple manner while allowing the generated origami structures to be axially foldable by stacking layers, as shown in diagram200ofFIG.2. In contrast to traditional 3D modeling, which obtains solid structures by extruding from desired shape graphics, inverse origami modeling as provided herein can generate 3D foldable structures from graphics corresponding to a desired shape. The resulting foldable structures can be utilized, e.g., in developing soft functional robots by integrating with soft smart actuators.

Inverse Origami Design Model

Turning now toFIG.3, a multilayer Miura origami pattern300with a uniform cell structure is shown. The pattern300is composed of respective layers310, and each of the layers310are in turn composed of respective origami cells (cell units)320. The pattern300shown inFIG.3presents a planar shape with mountain and valley folds, which can be axially compressed with a negative Poisson ratio. As used herein, solid and dotted lines represent the mountain and valley folds of a crease pattern, respectively. Origami with other nonplanar shapes can be made by modifying the flat crease pattern consisting of mountain and valley folds.

FIG.3further depicts a flat crease pattern330corresponding to a Miura cell unit as well as a folded shape340resulting from application of the crease pattern. In an implementation, an inverse origami design model can determine how to combine different crease patterns for given desired folded shapes. As used herein, a general cell can be abstracted with five basic parameters [h, a, b, d, θ] by generalizing the structure of a single cell320of the pattern300, where a, b, d, and θ are vector parameters that define the sizes and angles of the mountain and valley folds, and h is a scalar that defines the half-height of the cell, as shown by the flat pattern330inFIG.3. Each general cell can have an axisymmetric crease pattern with a constant h to maintain the axial compressibility of the multilayer origami.

Turning next toFIG.4, diagram400shows the possible configurations (folded shapes) of a general cell, e.g., a cell320, based on the flat crease patterns. In accordance with the difference among three adjacent angles θ (e.g., θ1, θ2, and θ3), a general cell can have four types of basic crease patterns, resulting in different shape morphing. Only half of the crease pattern is shown in diagram400due to the symmetry of the general cell. A 3D reference system for each of the crease patterns is established in the lower-left corner, and the right-hand rule is used to describe the orientation of the final folded shape. Additionally, the arcs shown with each of the crease patterns represent the limited variation range of angles θ2and θ3, respectively from left to right.

For crease pattern I, where θ1, θ2, and θ3are less than 90°, three possible folded shapes rely on the value of θ1+θ3−2θ2. These shapes have different folded directions, such as counter-clockwise fold (I-1), parallel fold (I-2), and clockwise fold (I-3). The counter-clockwise fold is defined to be positive in accordance with the right-hand rule, and the parallel fold is considered zero. Crease pattern II, where θ1, θ2<90° and θ3>90°, has a positive folded direction, and crease patterns III (θ1<90° and θ2, θ3>90° and IV (θ1, θ3<90°, and θ2>90° have a negative folded direction.

On the basis of the four basic crease patterns shown in diagram400, the single general cell can also have two categories of transformative crease patterns, e.g., mutual replacement of mountain and valley folds and inverse crease patterns symmetrical about the y-axis. The former has no change in folded direction, and the latter has a folded direction opposite the non-transformative crease patterns. An origami with a nonplanar shape can be produced by combining these crease patterns in series.

Referring next toFIG.5, a nonplanar origami example including multiple crease patterns is illustrated. More particularly,FIG.5illustrates a final folded shape510resulting from a flat crease pattern520based on folding operations shown by530and540. As shown inFIG.5, the difference in the folded direction of respective crease patterns can greatly affect the growth direction of the final folded shape510, following the analysis results described above with respect toFIG.4. The used types of crease patterns are marked in the flat origami pattern520and the final folded origami510. Two folds, namely, the first shaping fold that produces the initial folded shape and the second functional fold that allows the origami to fold and unfold with a stiffness between the initial and final folded shapes, are usually found in the origami morphing. An origami structure with five layers based on the flat origami pattern520is shown by530and540.

In an implementation, different crease patterns can automatically be combined to form a final desired folded shape, e.g., after determining the possible crease patterns and folded directions of each cell. As described above with respect toFIGS.3-5, a model can be used in which basic parameters [h, a, b, d, θ] can uniquely define a flat origami pattern. As a result, a desired folded shape can be constructed using only the corresponding parameters [h, a, b, d, θ] of the origami pattern in the inverse design model. As described below, mathematical parameters can be used to describe the desired folded shape in the inverse design model, thereby providing parametrical inputs for calculating the corresponding [h, a, b, d,0].

Diagram600inFIG.6illustrates an example framework of an inverse origami design model that can be used to solve the above problem. As shown in diagram600, two different routes can be used for designing desired regular and custom folded shapes. For regular shapes, shape parameters [n, L, W]can be used to define a regular desired folded shapes directly, where n is the number of sides, W is the width or thickness of each side, and L is the side length. When n=3, a positive integer q rather than L can be used as an input parameter to define the side length of the desired shape for easy use of the model, where L=1.15W(q+1). This derivation is described in further detail below with respect toFIG.7.

Further in the example of a regular shape, the parameters [h, ν] can be calculated from [n, L, W]based on geometric properties or constraints, such as P and E coincidence, e.g., corresponding to the points P and E shown in the folded shape340inFIG.3, and equal thickness of the sides. The parameter θ can be based on the growth orientation of the desired folded shape and determine type(s) of crease patterns used, e.g., based on diagram400inFIG.4. Subsequently, a first algorithm, shown in Table 1 below, can be used to solve [a, b, d] to well match the size of the desired shape.

Alternatively, for an irregular custom folded shape such as a spiral or wave, continuous line segments can initially be used to divide and fit the curve shape. The length Lsof line segments and the angles Δ between adjacent line segments are generated as the vectoring parameters of [Ls, Δ] to define such a nonregular shape. A second algorithm, shown in Table 2 below, can be used to optimize the combination of different crease patterns and solve θ on the basis of the adjustable built-in parameters of β1and β2. When Δ>β1or <β2, different crease patterns, such as II or III as shown in diagram400, can be used to better construct the origami shape. Here, the algorithm shown in Table 1 below can be used to calculate other parameters [a, b, d].

A universal shape folding model with parametrical input of [h, a, b, d, θ] can then be established, e.g., as described below with respect toFIG.9, after obtaining the five basic parameters to generate a corresponding flat crease pattern. This flat crease pattern can include mountain and valley folds for subsequent fabrication. The shape folding model can also simulate the origami morphing that guides the actual fold of the fabricated origami pattern. On the basis of the inverse origami design model, a user-friendly software interface can also be used to assist users with or without origami experiences in using this model to design the origami with desired shapes and sizes, e.g., as described below with respect toFIG.27.

In an implementation, flat crease patterns of desired folded shapes can be generated based on simple shape parameters or 2D shape graphics. The basic parameters [h, a, b, d, θ] of the crease pattern can first be calculated from different desired folded shapes, including three regular shapes as shown inFIG.7and a general custom shape as shown inFIG.8. A universal shape folding model is then shown inFIG.9to present the flat crease pattern and origami morphing process based on the calculated parameters.

As shown by diagram700inFIG.7, a regular polygon can be defined with the number of sides (n), the side length (L), and the side thickness (W), which can be constructed by one type of crease pattern, such as I-3(FIG.2). Each crease pattern I can include two adjacent facets. On the basis of the ithcrease pattern I-3, the line segments d2i−1(i=1˜n) construct the final folded shape of the origami, and the angle αibetween the line d2i−1and d2i+1can change the shape, which is constrained by the three adjacent angles θ.

A constraint that point P coincides with E is used to make the final folded shape regular, which requires that line segment d2ibisects the line PE vertically. L corresponds to the value of d2i−1, n determines the angle αi, and the height h can be calculated as follows:

where the input shape parameters are [n, L, W], and the origami has n groups of crease patterns and 2n facets. In accordance with Equations (1) and (2), the parameters h and 0 can be calculated. Next, the algorithm shown in Table 1 above can be used to calculate other size parameters [a, b, d] based on geometrical constraints.
CASE 2: Rectangle (n=4)

As shown by diagram702inFIG.7, for a rectangle (n=4), the desired shape can be defined with the side length L and the side width W. The shape can be constructed by four type of crease patterns of I-2, III, inverse I-2, and inverse II. The shape has four intersection angles of 90°, and L and W can consist of odd numbers of facets for closing the shape. Under satisfying the constraint that P coincides with E, θican be 45° or 135° to ensure that the rectangle has the same thickness of T in the length and width direction. θihas the same values when using the crease pattern I-2or inverse I-2. T is a passive parameter and equal to W cos 45° in this case. Assuming that the rectangle has 2m+1 and 2k+1 facets in the length and width direction, respectively, L and W restrict the value of positive integers m and k due to the same h, which can be expressed as follows:

where m usually has many solutions, and the minimum value is taken by default to obtain the maximum h for easy fabrication. The parameter θ can be defined as follows:

where Iiis a unit matrix of 1×i. Here, the algorithm shown in Table 1 above is still used to calculate other size parameters [a; b; d], where the invalid situation that P cannot coincide with E is considered when the facets experience crease patterns except I. An additional constraint that adjacent facets must have no interference after complete folding can also be added.
CASE 3: Regular triangle (n=3)

As shown in diagram704ofFIG.7, a regular triangle (n=3) can be defined with the side length L and side thickness W. In the triangle, each interior angle is 60°, and each side has the same L and number of facets. The shape can be also constructed by four types of crease patterns of I-2, III, inverse I-2, and inverse II. Under satisfying the condition that P coincides with E, θican be 60° or 120° to ensure the same Won each side. Each side can include odd numbers of facets (2q+1) for forming a closing shape, where q is a positive integer. L and W restrict the value of h and q, which can be expressed as follows:

where (L tan θi/2W) is a positive integer to ensure that q is meaningful. The values of α2q+1, α2(2q+1), and α3(2q+1)at the three corners can be increased to prevent interference during folding, which is considered in the algorithm shown in Table 1 above. The actual perimeter of the triangle can be equal to 3L(q+2)/(q+1). For ease of use, q can be used rather than L to control the desired shape. Therefore, the shape parameters of this case are [n, q, W], and the actual L can be calculated by 1.15W(q+1). The size parameter θ is defined as follows.

where I2q+1is a unit matrix of 1×(2q+1). Other size parameters a, b, and d can be further produced by the algorithm shown in Table 1 above.
Case 4: Custom shape

The above three cases illustrate how to obtain the basic parameters of regular shapes based on [n, L, W]. However, for an irregular shape, such as that shown by diagram800inFIG.8, the shape parameters can be difficult to be given directly. Therefore, the shape parameters of the irregular shapes for calculation can be abstracted as follows. As shown in diagram800, a series of linear segments, e.g., line segments Ls, can be used to fit the desired folded shape. Additionally, the angular differentials Δ between adjacent line segments can be determined, where Δ∈[0, 360°]. A larger number of line segments can make the approximate shape closer to the desired shape. The value of Lscorresponds to the value of d2i−1; therefore, the angle θ2i−1can be obtained once h is given. θ2ican be first calculated by the angle Δ and Equation (1) as given above under the crease pattern I, where Δ is equal to a. However, the crease pattern I has limited performance on constructing the shape with a small intersection angle. The algorithm shown in Table 2 above can be used to combine multiple configurations of crease patterns for better shape construction, where thresholds defined by tuning parameters β1and β2are used. When Δ<β2or Δ>β1, the pattern I can be replaced with the crease patterns II or III, and the corresponding θ will be updated. The algorithm shown in Table 1 above can then be employed after obtaining the angle θ to produce other size parameters a, b, and d.

The algorithm shown in Table 1 above can be configured to preferentially satisfy the constraint that P coincides with E and h=2W cos θ2i, precisely constructing the desired shapes. Therefore, the generated origami with the irregular folded shape may have a variable width, especially at small Δ, as shown in diagram800. This condition can be due to the origami pattern having the same h but variable θ. If equal width is preferentially considered, the generated origami can exhibit discontinuous or superimposed lines Ls, as further shown in diagram800, which may not follow the desired shape well. When the folded shape is divided by dense and uniform lines Ls, the width difference can be minimized under the constraint that P coincides with E.

Origami Shape Folding Model

An example shape folding process for a general origami with basic parameters [h, a, b, d, θ] is modeled in diagram900inFIG.9. Only half of one layer is used to describe the folding relationship due to the symmetry of the origami pattern. As shown in diagram900, the flat pattern can be composited of N adjacent rigid facets with the same height h. The facet i has six additional parameters (ai, bi, di, di+1, θi, θi+1) to define its shape, where i=1˜N. The line segment dican be given as follows:

Two adjacent facets rotate around the intersection line (di) during the shape folding. For example, facet2can rotate an angle p2clockwise around the line d2relative to facet1, whereas facet3can rotates an angle p3counter-clockwise around the line d3relative to facet2. The lines bican be coplanar due to the symmetric origami pattern when the facets are considered rigid. Therefore, facet1can rotate an angle p1counter-clockwise around line b1to meet the coplanar constraint. In accordance with space geometry calculation, the coplanar constraint can be represented as follows:

where i>1, and the value of angle pican be calculated by the angles θiand p1. p1has a range of [0 °, 90°] and determines the shape folding degree. The pattern is flat when p1=0° and folded completely when p1=90°. pi=180° or −180° when p1=90°, which is based on θi. piis negative with a range of [−180°, 0°] and positive with a range of [0°, 180°] when θi>90° and θi<90°, respectively.

A sub-coordinate system Oi(xi, yi, zi) can then be established on each facet i, where the origin Oiis located at the intersection of lines diand bi, and the axis yicoincides with line diand points from bottom to top. A base coordinate system O0(x0, y0, z0) can be established to illustrate the folding motion, where the origin O0coincides with O1, and axis y0coincides with line b1and points from left to right. When the rotation direction of p1is defined to be positive, the other rotation angles Pican be made in accordance with the right-hand rule and the calculated results of Equation (8).

where i>1 and P1=p1. pimay be positive or negative in accordance with Equation (8). This equation is universal for all types of crease patterns and determines the mountain or valley folds.

In the shape folding motion, facet i can be considered rigid; therefore, the relative positions of the four vertexes of the facet can be unchangeable. The homogeneous position matrix of the facet i can be given in coordinate system Oi.

The basic functions of the 3D rotation matrix used are defined as follows:

where Ry(x) represents a rotation of x degrees around the y axis, Rz(x) represents a rotation of x degrees around the z axis, and Ty(x) represents a translation of x along the y axis.

The origin O0-Nis always in the plane of x=0 due to the existence of the coplanar constraint. Facet1has a rotation of P1around the y0axis, and the coordinate system O1has a definite relationship with O0(O10=Ry(P1)·Rz(θ1)). The other coordinate systems Oi(xi, yi, zi) are further inferred relative to the coordinate system O0, as follows:

Therefore, the position of each facet in the base coordinate system can be calculated by using Equations (10) and (12).

The origami shape can be displayed by drawing all the facets in the base coordinate system. The folded motion of the origami can be simulated by changing the value of p1. The solved vertex coordinates of these facets can be used to produce the crease pattern of the origami with different line styles. Mountain and valley folds are periodic in lines a and b, whereas the fold styles depend on the rotation direction of p around lines d. Given the coplanar constraint, this model can also process the origami patterns with any number of layers by adding some simple commands

With reference now toFIG.10, origami examples generated by the inverse origami design model described above are illustrated. As shown byFIG.10, three regular shapes, i.e., a decagon1000, rectangle1002, and triangle1004, are generated via the shape parameters of [10, 6, 2.5], [4, 20, 10], and [3, 5, 2.5], respectively. The stretched height of the origami can be adjusted by setting the value of layers in the model, e.g., as described above with respect toFIG.6. Two multi-curvature shapes1010,1020and their respective corresponding origami1012,1022can be constructed on the basis of provided graphic files of the desired folded shapes. As further shown by1030and1032, the model can also generate origami with complex geometries, such as the letter T, showing its good adaptability.

Design and Construction Platform for Soft Origami Robots

Turning now toFIG.11, diagram1100illustrates an example integrated platform that can guide the design and construction of soft origami robots. As shown in diagram1100, the platform can include three parts, namely geometry design1110, 2D fabrication1120, and 3D actuation1130.

In the geometry design1110, a desired origami shape can be defined in accordance with corresponding robot design parameters. The associated origami morphing can be simulated in the proposed inverse design model, and the corresponding flat crease pattern can be obtained.

In the 2D fabrication1120, the sheet material, such as paper, PET films, etc., is chosen for producing a flat crease pattern. A matched 2D fabricated method (e.g., paper printing, laser engraving, laminate manufacturing, etc.) can then be used to write the crease pattern on the sheet. In an implementation, choice of the fabrication method can depend on the material(s) of the sheet and the desired folding stiffness. For instance, paper printing is usually used on soft and thin sheets, such as common A4 papers, to produce low-stiffness origami. Laser engraving can be used on stiffer sheets, such as PET, to produce origami with different folding stiffness by adjusting the laser power. Laminate manufacturing is used to produce thick origami with a large stiffness difference between sheet facets and creases.

In some implementations, the crease pattern generated during the 2D fabrication1120can include openings, and/or other suitable indicators, at respective positions relative to the crease pattern. These openings and/or indicators can then be utilized to facilitate the placement of actuators and/or other items into the resulting 3D origami structure(s)1122during the 3D actuation1130.

The 3D origami structure(s)1122with the desired folded shapes and sizes can made by using the above operations combined with pre-folding. In the 3D actuation1130, the origami structure(s)1122can integrate with various soft actuators, such as shape memory alloy (SMA), pneumatic, and electrostatic actuators, to achieve 3D actuation based on robot functional specifications. With this platform, soft origami robots with different functions can be constructed easily.

Soft Crawling Origami Robots

Turning toFIGS.12-14, respective aspects of an example soft crawling robot using origami structures are illustrated. Referring first toFIG.12, a robot body1200, e.g., that can be designed with desired regular shapes and sizes based on the inverse origami design model described above, is illustrated. Following the design and construction platform described above with respect toFIG.11, the used origami body1210can be made of PET films, e.g., by laser engraving and pre-folding, and three shape memory alloy (SMA) coil actuators1220can be inserted into the robot body1200to achieve 3D actuation. Two flexible electrostatic actuators1230can also be incorporated into the robot as electro-adhesive feet, which can made by sputter coating (e.g., as described in further detail below with respect toFIGS.18-19) and provide reversible and robust electrostatic adhesion on large-range surfaces. As shown inFIG.13, an example flexible electrostatic actuator1230can be composed of an electrode1310positioned between two layers1320,1322of polyimide film.

Returning toFIG.12, a soft air tube1240can be introduced into the origami body1210for accelerating airiness. In accordance with the exploded view1400of A-A as shown byFIG.14, each SMA coil actuator1410can be compacted with a soft wire by using a hollow aluminum tube1420and attaching to the origami body1210after passing through a location plate1430and cap1440. In a non-limiting implementation, the location plate1430can be composed of carbon fiber and have a thickness of approximately 0.2 mm, and the cap1440can be composed of polylactic acid (PLA) materials. As further shown byFIG.14, the location plate1430can have three small holes for distributing three actuators radially.

An origami hinge1450, shown in further detail byFIG.15, can be constructed by a multilayer composition that includes two PET films1510,1512and one middle adhesive layer1520. In a non-limiting implementation, the adhesive layer1520can have a thickness of approximately 0.2 mm. The hinge1450connects the body with the electro-adhesive feet while allowing a low relative rotational stiffness between them.

The actuation schematic of the robot described above with respect toFIGS.12-15is shown by diagram1600inFIG.16. As shown in diagram1600, Two steps are performed in each cycle. The robot can achieve two forward-motion modes by activating different combinations of muscle actuators. Motion mode I requires three actuators to be activated simultaneously (as shown in diagram1600via unfilled circles), similar to an earthworm, to achieve peristalsis that can pass through a narrow height. In contrast, motion mode II only requires two muscle actuators to realize the extension and flexion movement, similar to an inchworm, moving at a relatively fast speed and low power consumption.

As further shown by diagram1700inFIG.17, a soft origami robot can turn by activating one side of the SMA muscle described above. When the right side of the muscle is activated periodically, e.g., as shown by1702, the robot can turn left at a substantially constant speed. When the left side of the muscle was activated periodically, e.g., as shown by1704, the robot turned right with a similar speed, resulting in a return to its previous orientation, e.g., as shown by1706.

Referring next toFIG.18, a diagram1800depicting an example process for fabricating a flexible electrostatic actuator, e.g., an actuator1230, is provided. As shown at1802, a mask1810for sputter coating can be 3D-printed on the basis of a desired geometry and transferred on a polyimide film1820with adhesive1830. Next, as shown at1804, a sputter coater can be utilized to apply sputter coated copper1840from a copper target material1850onto the polyimide film1820. As shown at1806, the mask1810can be removed, and two soft wires can be attached to the two poles of the electrode. Finally, as shown at1808, the electrode layer can be sandwiched by two polyimide films1820with adhesive1830, and the sample can be cut at locations1860into the desired shape.

FIG.19is an overhead view of an example pattern that can be used for the electrode1310of the electrostatic actuator1230shown inFIG.12. The produced electrostatic actuator1230is flexible and can deform under a light load, thereby adapting to different environments well. For instance, as additionally shown by diagram2000inFIG.20, the flexible electrostatic actuator1230can deform under the action of electrostatic force, thereby adapting to flat, convex, and concave substrates.

Soft origami robots as described above can use an origami structure with SMA muscle actuators to achieve multimodal motions in a compact structure, including peristalsis, crawling, turning, and climbing. The soft origami robot can climb on flat and curved surfaces without any adjustment by integrating with a flexible electrostatic actuator, significantly expanding the environmental adaptability of current soft crawling robots. Its shape and size are easy to reconfigure and can be rapidly prototyped for new applications by using the inverse origami design model provided herein.

Turning now toFIG.21, diagram2100illustrates the use of origami structures to develop a soft VAOM that can achieve linear reciprocating actuation similar to human muscles. On the basis of the inverse origami design model, origami structures with desired regular shapes and sizes are made and then sealed up with a wrapping film2110to construct the VAOM, as shown in diagram2100. An air tube2120is placed into the origami structure and facilitates formation of a vacuum that compresses the structure, as shown by the change in the structure from state2102to state2104.

Diagram2200inFIG.22depicts a VAOM with improved stiffness by using a PET film to fabricate the origami structure. The VAOM works well under a lateral pressure, showing its unique properties, including axial compliance and radial stability. In a high-pressure environment, the VAOM still maintains its actuation capacity, which can greatly promote its application. Diagram2200further shows that when a defect2210is designed to occur in particular positions of a nonstandard origami, the original axial folding may transfer to a bend folding under the vacuum actuation, as shown by the change in the structure from state2202to state2204. These reversible defects can be made by popping the valley fold into another mechanically stable state, and they provide a possibility of customizing the folding motion of the origami.

FIG.23illustrates the use of defects2310to modify the folding motion of two VAOMs2320to construct a soft gripper. Diagram2302illustrates an initial state of the gripper, while diagram2304illustrates a state of the gripper subsequent to activation of the VAOMs2320. As further shown by diagram2306, the gripper can be closed under the combined actuation of the VAOMs2320and a middle VAOM2330, thereby enabling the gripper to grasp objects of different sizes.

Compared with conventional vacuum-actuated muscles, the VAOM-based design described above has advantages in structure stability, programmable design, and no twisting motion involved. On the basis of the inverse design platform, the VAOM can be easily constructed with different materials, shapes, and sizes, thereby allowing the development of various VAOM-based robots for new applications.

Miniature Soft Origami Gripper

Referring next toFIGS.24-25, the use of shaping origami folds in developing a miniature soft gripper for compliant grasping is illustrated. With reference toFIG.24, patterns associated with an origami hinge2400and origami gripper2402are provided. The hinge2400and gripper2402are designed in accordance with the desired curved shapes using the proposed inverse origami design model. As shown byFIG.24, the hinge2400and gripper2402include adhesion areas2410to facilitate adhesion of the hinge2400to the gripper2402.

The origami structure of the gripper2402uses laminate manufacturing in 2D fabrication, which is a multilayer composition, including two PET films2420,2422cut by the same crease pattern and one double-side polyimide adhesive2430. The origami shape of the gripper2402can be changed by rotating any of its facets because of movement transmission.

FIG.25illustrates an example opening operation of the origami structures shown inFIG.24over three states2500,2502,2504. As shown at stage2504, four rubber bands2510are attached to the origami structure to enable the gripper to keep its initial closed state. An origami hinge2520is designed to provide compliant support for the gripper and to connect with other places easily. An SMA coil actuator2530is then used to open the gripper for grasping. When the SMA coil2530is de-energized, the gripper trends to the initial closed state under the restoring force of the rubber bands2510, thereby grasping objects without consuming power.

In an implementation, an origami gripper as shown byFIG.25can be assembled to a soft crawling robot, e.g., as described above with respect toFIGS.12-17, to endow the crawling robot with manipulative capabilities. For instance, short-time activation of the SMA coil can open the gripper and let an object enter a capture range when the robot approaches an object. The gripper closes and grasps the object without power consumption after the SMA coil is de-energized. The robot can then continue to push forward or drag the object backward. When the robot arrives at a suitable position, the object can be released by activating the SMA coil again.

Compared to conventional soft grippers that are mostly fabricated by complicated steps and careful assembly, manufacturing of the origami gripper is simple and easy of scale. The origami gripper is also easy for storage and transportation due to unique advantages of ultralight weight and reversible morphing between flat and 3D forms, and can grasp objects by simple folding. The bi-stability exhibited by the origami structure can reduce the requirement for external continuous actuation. With the aid of the inverse design model, the shape and size of the gripper are easily reconfigured for applications at different scales.

Inverse Origami Design Platform

Turning now toFIG.26, a block diagram of a system2600that facilitates inverse origami design via parameters provided via a user interface is illustrated. As shown inFIG.26, system2600includes a parameter extraction component110, a pattern generator component120, and a fabrication component130that can operate as described above with respect toFIG.1. Additionally, system2600includes a user interface component2610that can enable a user to provide an input shape and/or shape properties to the parameter extraction component110, e.g., via a graphical user interface (GUI).

FIG.27depicts a non-limiting example of a GUI2700that can be utilized by the user interface component2610of system2600. As shown inFIG.27, the GUI2700includes four display areas2710,2720,2730,2740. Display area2710facilitates the entry of shape parameters [n, L, W], e.g., for a desired origami corresponding to a regular shape as described above. For an irregular shape, a user can provide a graphic file with the desired shape, e.g., consisting of a continuous line, and load the file into the GUI2700via the button in display area2720. In response to loading a shape file in display area2720, the GUI2700can display the loaded graphic and enable the user to divide the graphic with any density of line segments. After setting the number of layers in display area2730, users can save the corresponding flat pattern as a file for subsequent fabrication.

In response to generation of a pattern, the calculated origami shape can be displayed in display area2740. Users can adjust this origami shape, e.g., by changing the value of h and thresholds of β1and β2in display area2720. The value of L/h can ensure size matching between the calculated and desired origami. As additionally shown in visual area2720, users can check the morphing of the desired origami by changing the shape folding ratio to observe corresponding changes to the crease patterns.

As described above with respect toFIG.27, the flat crease pattern of a desired origami structure is saved as an independent file in the inverse origami design platform. A non-exhaustive listing of fabrication methods that can be used to write the pattern on a flat sheet are provided below.

Paper printing: In this method, the flat crease pattern can be printed directly on paper (e.g., an A4 paper sheet) and then cut from the paper. The paper can be folded manually, and the pattern can guide paper folding to produce the desired origami shape. For a regular folded shape, the two ends of the origami can be connected by a double-sided adhesive. The method is accessible and low-cost, and the generated origami has low folding stiffness.

Laser writing: In this method, a PET film with a thickness of approximately 0.2 mm can be used for laser writing of the flat crease patterns, due to the mechanical properties and heat resistance of PET film. When hard materials are used to fabricate the origami pattern, stress concentration can be considered at the intersection of creases during folding. Accordingly, adding hole patterns into the flat origami pattern can effectively eliminate stress concentration. For a regular folded shape, locking patterns can be added into the flat crease pattern to connect the two ends of the origami with solid mechanical interlocking. A laser cutting device can be used to engrave the mountain and valley creases on the front and back of a PET film. The cut creases (edge, hole, and locking patterns) can be completely cut off from the PET film. From the resulting flat origami pattern, the desired origami structure can be formed after pre-folding. The generated origami stiffness can be adjusted by changing the film thickness or laser engraving power.

Laminate manufacturing: In this method, two PET films with a thickness of approximately 0.2 mm can be laser cut in accordance with the same flat crease pattern. Several openings (holes, apertures, etc.) can be added to the flat crease pattern for installing SMA actuators. A polyimide double-sided adhesive can be used as the middle layer to bond the two PET films together, thereby forming a sandwiched structure. The desired origami shape can be obtained by folding the flat sheet. This method can enlarge the stiffness difference between facets and creases, thereby allowing the generated origami to have a good transferability of motion among facets.

Flexible Electrostatic Actuator

An electrostatic actuator can be used to provide reversible and robust adhesion. As described above with respect toFIG.13, it can be composed of a concentric circular copper electrode1310sandwiched between two polyimide films1320,1322with adhesive. The electrode generates an electric field under high voltage, changes the charge distribution on the working surface by electrostatic induction, and then utilizes Coulomb force to generate electrostatic adhesion. The concentric circular electrode can generate stronger electrostatic adhesion than other electrode geometries. Returning toFIG.18, the copper electrode can be sputter-coated on the bottom polyimide film to minimize its thickness, e.g., to approximately 270 nm. The bottom polyimide film can act as a dielectric layer to separate the electrode from working surfaces. The top polyimide film can cover and fill the gaps among the interdigitate electrodes together with the bottom film. The flexible electrostatic pad, with a thickness of approximately 35 μm, has low deformation resistance so that it can adapt to the working surfaces with moderate curvatures under the action of Coulomb force, as described above with respect toFIG.20.

Referring next toFIG.28, a flow diagram of a method2800that facilitates inverse origami design for soft robotic development is illustrated. At2802, a system comprising a processor can determine (e.g., by a parameter extraction component110) shape parameters corresponding to an input shape.

At2804, the system can generate (e.g., by a pattern generator component120) an origami crease pattern representative of the input shape. The origami crease pattern can comprise respective origami cell units (e.g., origami cells230), and can be defined by a group of vector size parameters corresponding to relative fold lengths associated with the respective origami cell units, a vector angle parameter corresponding to fold angles associated with the respective origami cell units, and a scalar cell height parameter.

At2806, the system can imprint (e.g., by a fabrication component130) the origami crease pattern onto a tangible medium (e.g., a paper sheet, one or more PET sheets, etc.).

FIG.28as described above illustrates a method in accordance with certain embodiments of this disclosure. While, for purposes of simplicity of explanation, the method has been shown and described as series of acts, it is to be understood and appreciated that this disclosure is not limited by the order of acts, as some acts may occur in different orders and/or concurrently with other acts from that shown and described herein. For example, those skilled in the art will understand and appreciate that methods can alternatively be represented as a series of interrelated states or events, such as in a state diagram. Moreover, not all illustrated acts may be required to implement methods in accordance with certain embodiments of this disclosure.

With reference again toFIG.29, the example environment2900for implementing various embodiments described herein includes a computer2902, the computer2902including a processing unit2904, a system memory2906and a system bus2908. The system bus2908couples system components including, but not limited to, the system memory2906to the processing unit2904. The processing unit2904can be any of various commercially available processors. Dual microprocessors and other multi-processor architectures can also be employed as the processing unit2904.

The system bus2908can be any of several types of bus structure that can further interconnect to a memory bus (with or without a memory controller), a peripheral bus, and a local bus using any of a variety of commercially available bus architectures. The system memory2906includes ROM2910and RAM2912. A basic input/output system (BIOS) can be stored in a non-volatile memory such as ROM, erasable programmable read only memory (EPROM), EEPROM, which BIOS contains the basic routines that help to transfer information between elements within the computer2902, such as during startup. The RAM2912can also include a high-speed RAM such as static RAM for caching data.

The computer2902further includes an internal hard disk drive (HDD)2914(e.g., EIDE, SATA), one or more external storage devices2916(e.g., a magnetic floppy disk drive (FDD), a memory stick or flash drive reader, a memory card reader, etc.) and an optical disk drive2920(e.g., which can read or write from a CD-ROM disc, a DVD, a BD, etc.). While the internal HDD2914is illustrated as located within the computer2902, the internal HDD2914can also be configured for external use in a suitable chassis (not shown). Additionally, while not shown in environment2900, a solid state drive (SSD) could be used in addition to, or in place of, an HDD2914. The HDD2914, external storage device(s)2916and optical disk drive2920can be connected to the system bus2908by an HDD interface2924, an external storage interface2926and an optical drive interface2928, respectively. The interface2924for external drive implementations can include at least one or both of Universal Serial Bus (USB) and Institute of Electrical and Electronics Engineers (IEEE) 1394 interface technologies. Other external drive connection technologies are within contemplation of the embodiments described herein.

A number of program modules can be stored in the drives and RAM2912, including an operating system2930, one or more application programs2932, other program modules2934and program data2936. All or portions of the operating system, applications, modules, and/or data can also be cached in the RAM2912. The systems and methods described herein can be implemented utilizing various commercially available operating systems or combinations of operating systems.

Computer2902can optionally comprise emulation technologies. For example, a hypervisor (not shown) or other intermediary can emulate a hardware environment for operating system2930, and the emulated hardware can optionally be different from the hardware illustrated inFIG.29. In such an embodiment, operating system2930can comprise one virtual machine (VM) of multiple VMs hosted at computer2902. Furthermore, operating system2930can provide runtime environments, such as the Java runtime environment or the .NET framework, for applications2932. Runtime environments are consistent execution environments that allow applications2932to run on any operating system that includes the runtime environment. Similarly, operating system2930can support containers, and applications2932can be in the form of containers, which are lightweight, standalone, executable packages of software that include, e.g., code, runtime, system tools, system libraries and settings for an application.

A user can enter commands and information into the computer2902through one or more wired/wireless input devices, e.g., a keyboard2938and/or a pointing device such as a mouse2940. Other input devices (not shown) can include a touch screen, a microphone, an infrared (IR) remote control, a radio frequency (RF) remote control, or other remote control, a joystick, a virtual reality controller and/or virtual reality headset, a game pad, a stylus pen, an image input device, e.g., camera(s), a gesture sensor input device, a vision movement sensor input device, an emotion or facial detection device, a biometric input device, e.g., fingerprint or iris scanner, or the like. These and other input devices are often connected to the processing unit2904through an input device interface2944that can be coupled to the system bus2908, but can be connected by other interfaces, such as a parallel port, an IEEE 1394 serial port, a game port, a USB port, an IR interface, a BLUETOOTH® interface, etc.

A monitor2946or other type of display device can be also connected to the system bus2908via an interface, such as a video adapter2948. In addition to the monitor2946, a computer typically includes other peripheral output devices (not shown), such as speakers, printers, etc.

The computer2902can operate in a networked environment using logical connections via wired and/or wireless communications to one or more remote computers, such as a remote computer(s)2950. The remote computer(s)2950can be a workstation, a server computer, a router, a personal computer, portable computer, microprocessor-based entertainment appliance, a peer device or other common network node, and typically includes many or all of the elements described relative to the computer2902, although, for purposes of brevity, only a memory/storage device2952is illustrated. The logical connections depicted include wired/wireless connectivity to a local area network (LAN)2954and/or larger networks, e.g., a wide area network (WAN)2956. Such LAN and WAN networking environments are commonplace in offices and companies, and facilitate enterprise-wide computer networks, such as intranets, all of which can connect to a global communications network, e.g., the Internet.

When used in a LAN networking environment, the computer2902can be connected to the local network2954through a wired and/or wireless communication network interface or adapter2958. The adapter2958can facilitate wired or wireless communication to the LAN2954, which can also include a wireless access point (AP) disposed thereon for communicating with the adapter2958in a wireless mode.

When used in a WAN networking environment, the computer2902can include a modem2960or can be connected to a communications server on the WAN2956via other means for establishing communications over the WAN2956, such as by way of the Internet. The modem2960, which can be internal or external and a wired or wireless device, can be connected to the system bus2908via the input device interface2944. In a networked environment, program modules depicted relative to the computer2902or portions thereof, can be stored in the remote memory/storage device2952. It will be appreciated that the network connections shown are example and other means of establishing a communications link between the computers can be used.

When used in either a LAN or WAN networking environment, the computer2902can access cloud storage systems or other network-based storage systems in addition to, or in place of, external storage devices2916as described above. Generally, a connection between the computer2902and a cloud storage system can be established over a LAN2954or WAN2956e.g., by the adapter2958or modem2960, respectively. Upon connecting the computer2902to an associated cloud storage system, the external storage interface2926can, with the aid of the adapter2958and/or modem2960, manage storage provided by the cloud storage system as it would other types of external storage. For instance, the external storage interface2926can be configured to provide access to cloud storage sources as if those sources were physically connected to the computer2902.