Multi-crease Self-folding by Global Heating

The remarkable capability of bio-entities in developing a morphology is called morphogenesis. As robots enter our daily life and become more ubiquitous, demands for the instant fabrication of robots that can morph and are adaptive to various environments increase. This is a challenge that has been tackled in modular robotics, where a robot's body consisting of multiple modules reconfigures and adapts to environmental changes [4, 16, 25, 26, 35], or in a similar effort but attempting to handle highly stochastic situations in a bottom-up manner [5, 15, 19, 22], or a folding manner [2]. A unique approach focusing on extending a robot's physical capabilities is taken by [1], where the robot can print and use a three-dimensional tool.

Recently, the folding-based creation of robot bodies from sheetlike materials has shown notable accomplishments [8, 9, 34]. The methods employed in these works make frequent use of origami-inspired foldings to create lightweight mechanisms. Complex bodies can be folded from a laser-cut single sheet of paper [27, 28].

This article makes the following contributions:

• 1. 

  a model, design, and method for designing flat origami structures that can self-fold in a controlled way, using global heating;

• 2. 

  an instantiation of this approach to create a self-folding cylindrical-shaped robot and extensive experimental characterization.

One of the requisite competencies for robots that morph from a sheet structure is self-folding capability. Various attempts at automating folding processes have been made [12], using shape memory alloys [7], a contraction sheet combined with Joule heating [3], light illumination for heat transfer [17, 31], pneumatic actuation coupled with an elastic body [18], or hydrogel expansion [6]. Nevertheless, few approaches have attempted to achieve the self-folding of large creased forms with a high degree of accuracy, or demonstrated a realistic fabrication time compared with the folding time.

The self-folding methodology described in this article, which is developed upon our previous work in [23, 24], consists of the following steps:

• 1. 

  We model and derive a method for causing a bend on one edge of a flat body structure created by layering a contraction sheet and structural sheets and using global heating (Section 2.1).

• 2. 

  We develop a method for designing 2D planar bridges and gaps in a layered sheet that enables multiple edges to be folded in parallel, using heat, to create different geometries.

• 3. 

  We compute and control the angles to be folded using steps 1 and 2; the material and geometry of the creases determine the size of the angle that can be folded (Section 2.2).

• 4. 

  We design a specific crease pattern to test the self-folding approach we advocate; this pattern can be folded reliably as a complete cylinder with patterned faces (Section 3.1).

• 5. 

  We integrate electronics and actuators in the self-folded cylindrical body to create a lightweight mobile robot and demonstrate and characterize its locomotion.

Our self-folding method is simple, it can be performed at low cost, and it is easily accessible using a home oven. Furthermore, the folding order could potentially be controlled by incorporating more than one contraction material that responds to different temperatures.

The folding method for a precise folding angle of a flat sheet as introduced in Section 2.1 is difficult in that we have two-dimensional material properties that have to be manipulated at the level of three-dimensional systems.¹ We focus on kinematically encodable folding angles that enable the control of a specific folding angle of a surface, which is inspired by a technique used for pop-up books. Figure 3 shows two major types of pop-up techniques: (a) parallel fold and (b) V-fold [14] (often called angle fold). The pop-up motion can be characterized with two kinematically coupled angles: the input angle (θ_in) and the output angle (θ_out). While θ_in and θ_out are linearly related in the case of parallel fold, they are nonlinearly proportional in the case of V-fold.

The transition from Figure 4a to 4c shows an example of our approach. We aim at a mountain fold and a valley fold as described in Figure 4a, respectively spanning θ_out1 and θ_out2 (θ_out ∈ (0 : π)). We segment the surfaces and deploy as a multi-pleat pattern (Figure 4b). When all creases are unfolded simultaneously (θ_in → 0), the attributed kinematics yield the sheet morphology shown in Figure 4b. Thus the geometries characterizing the surfaces in Figure 4a can be encoded in the parameters of creases in Figure 4c. The angles in Figure 4c, α₁ and α₂ (α ∈ (0 : 2π)), designate the output angles θ_out1 and θ_out2 at respective θ_in. Moreover, the edge lengths L_H∗ (∗ ∈ [1, 2, 3]) in Figure 4a can be encoded as the respective edge lengths in Figure 4c, and the widths along the x-axis in Figure 4a as the combination with L_V and the number of pleats, N ∈ ℕ. Namely, they are ∝ N × L_V. Finally, the thickness of the folded surfaces, D in Figure 4b, can be reduced by refining the resolution of pleats in accordance with D ∝ scale length. In summary, the methodology is to roughly control θ_in by the self-folding technique described in Section 2.1, and obtain θ_out in precision.

Figure 5a shows the relation between θ_in and completion with different α varying from α = 30° to α = 150° in five levels. It can be seen that the convergence of completion has good speeds: 80% of the folding angles are already accomplished at θ_in ≈ 90°, especially when α > 90°. Since actual convergence of θ_out when self-folding is determined by the physical factors (e.g., applied temperature, internal stress of PVC, and gap widths of hinges), it settles at θ_in < 90° (finely tunable). Figure 5a shows that the larger α becomes, the faster the folding is. By considering these physical tendencies, the actual folding angles can be preadjusted by setting wider α to obtain precise folding angles θ_out.

Figure 5b shows the angle θ_in required to gain a desired completion for different α. Attaining smaller θ_in requires more compression of the contraction layer and thus requires more heat input. The data shows that the larger α is, the less energy is required. Also, 70% completion can be attained for most α even if θ_in does not become less than 90°.

Manually folding a multi-crease structure is a time-consuming process. When the folding steps are on the order of dozens, or multiple creases need to be folded simultaneously, self-folding can greatly reduce the total fabrication time. In this subsection, we introduce a fabrication method for self-folding that is simple and fast, but also accurate and easily reproducible. The key insight is that the folding directions are determined by the gap width differences of the hinge parts (Section 2.1). The methodology is to sustain both the front and the back side of the structural materials' relative positions on a single supporting sheet, and sandwich a contraction layer by folding it in half, so that corresponding gaps come above and below the contraction layer (Figure 6).

First, the supporting layer (Post-it Sheet Labels and 3M Permanent Adhesive Full Sheet Labels) and the structural layer (Grafix Ink Jet Adhesive Film, thickness 0.12 mm) are laminated, so that the adhesive face of the structural layer faces out (Figure 6a). Using a laser cutting machine (VersaLASER, VLS 3.50) with regulated laser strength, we cut only through the structural layer and trim the front and back patterns (Figure 6b). The framelike segments of structural layers that cover the hinge parts are peeled off (Figure 6c). A contraction layer (PVC, thickness 0.03 mm) is inserted and sandwiched by folding the structural layer in half, so that the respective hinges overlap above and below the contraction layer (Figure 6d). We manually cut out the intersections of hinges using a cutter, where six creases are gathered. This process was incorporated on account of some bending direction errors we often encountered when heating up. However, further investigation is still required to conclude if this step is necessary. We peel off the supporting layer, and obtain the complete structure (Figure 6e). The complete structure has thickness 0.27 mm and size 70 × 125 mm². This fabrication method has an advantage with forms where large-scale shapes are formed by iterative crease accumulations.

In this section, we show how our self-folding method can be used to make a mobile robot. We show that a self-folded skeleton can function as a stabilizer of locomotion and perform basic locomotion when coupled with an easily implementable actuation unit (Figure 1).

The outer skeleton of the robot is a hollow cylindrical structure with symmetry, simplicity, and postural robustness. The pleat pattern, the X-form span, is one of the most complex foldings among V-folds, where intersections gather six creases, thus posing a significant self-folding challenge.

Instead of rhombus X-form spans, more general models of origami-inspired polygonal cylinders have been investigated in [10, 20]. The size of the body and the resolution of the pleats can vary. We selected a hexagonal shape because the resulting folded outer skeleton has sufficient volume to include all the robot's components, and at the same time the flat patches provide support and friction for locomotion. Our designed robot will use the flat areas to contact the ground and control slippage. The arrays of rhombuses are alternately redirected, so that when the sheet folds, zigzag-shaped edges naturally latch and thus the structure is stable (see Figure 2g). We set α = 60°, u = 20 mm, gap width = 2.5 mm, bridge width = 1 mm. The designed shape consists of 62 creases that must be folded simultaneously; thus, they are difficult to fold by hand.

Figure 8 shows the self-folding process performed in a heat oven. In order to transmit uniform heat to the sheet, the sheet was hung from the ceiling. This setting contributes to preventing direct physical contact with the heat source (generally the bottom of the oven). The oven we employed blows air from the side wall, and thus the sheet swings during the process.²

We ramped the temperature from room temperature (25°C) to 65°C (Figure 8a). When the temperature reached approximately 55°C, the crease pattern appeared on the sheet's surface, increasing the sculpture effect and forming a global curve (Figure 8d–g). When the temperature reached 65°C, the structure formed a complete cylindrical shape, automatically latching both sides via zigzag tooth-shaped edges (Figure 8h). The process was completed in approximately 5 min. The duration depends on the capability of the oven, as well as the size of the materials, and should be optimized according to conditions.

Note that the configured shape is made of 62 folds; that is, the failure rate of an individual build up fold must be at most . We have made four trials and encountered no error. As found in previous failure models, it is required that all 62 folds be completed without a failure. Should even one fold fail, the global structure becomes a distorted flat sheet.

A modularized actuation unit, which shapes the hexagonal cylinder to fit to the outer skeleton, is developed. The actuation unit features collaterally assigned vibration motors for locomotion. By alternating the movement of vibration motors, the robot can move to any planar configuration, according to [11, 21, 30] (Figure 9b). The controller board was developed on a printed flexible circuit, whose folded geometry fits into the actuation unit. Finally, the actuation unit is manually inserted and attached to the outer skeleton. The projecting nails cause the actuation unit to reside stably in the outer skeleton.

The circuit is printed onto a sheet layer and then folded. The circuit substrate is composed of three sheet materials: one with rigid stiffness, used as a backbone layer (polystyrene); another with heat-resistive properties (polyimide); and the third conductive (copper). After these layers are laminated into one sheet, coating material is sputtered onto the copper layer in the shape of a circuit using a solid-ink printer. The remaining intact copper material is then etched by being soaked in ferric chloride for about 15 min, and is scrubbed away. Slits are added using a cutter, and bent manually to fit into the inner skeleton that was previously cut by a laser cutting machine and folded. The fabricated layer is resistant to heat, but is also lightweight at 0.442 g. We list the components used in the robot in Table 1.

The controller consists of a micro control unit (MCU), two vibration motors with respective motor drivers, electricity-regulating components, a battery, and other accessories, such as connectors. We selected the Atmel ATtiny2313A for its low operation voltage and for its serial communication capability for future use. Since the circuit becomes part of the robot, the weight distribution of components was considered and designed.

Figure 10 shows the weight distribution plotted in a pie chart. The body (outer skeleton) contributes only 18.27% of the weight, which is remarkably little, and shows the merits of forming a body through foldings.

Figure 11 shows the demonstrated locomotions. Control of the velocity is managed by an open-loop control, whose driving current is managed by pulse width modulation (duty ratio = 50%). It is seen that both translational (Figure 11a) and rotational (Figure 11b) motions are achieved by altering the directions of rotation of the vibration motors. When moving forward, we turn both motors in the same direction, and measure the translational locomotion speed as 2.95 cm/s. When turning, the motors turn in opposite directions, and the measured robot's turning angular speed is 0.74 rad/s (42.4°/s). However, especially for the translational motion, the motion is sensitive to the friction of the ground, and does not necessarily happen at the same speed on changing the motor speeds. We also assume that the asymmetric pleat patterns will have an influence on the stability of motion.

This article presents a scheme for self-folding for the autonomous fabrication of an origami robot using global heating. We first develop a method that enables autonomous and simultaneous folds of mountain and valley creases in a sheet structure. We then focus on the characteristics of the V-fold spans, where one of the angles can be precisely controlled by kinematically coupling it to another angle. The X-form span mechanism is then incorporated as an extension of V-fold. Using uniform heat on the designed sheet in this fashion, a cylindrical robot body is attained. We developed an easy, fast, and reliable fabrication technique for constructing the self-folding sheet. The self-folding of 62 folds are simultaneously managed at 65°C. We further develop a mobile robot using this self-folded body. The robot has two vibration motors for locomotion, caged by the self-folded outer skeleton for stabilization. The robot's locomotion proves the functionality of a self-folded origami structure.

This research was conducted in the Distributed Robotics Laboratory at CSAIL, MIT. Support for this work has been partly provided by NSF grants 1240383 and 1138967, and the Swiss National Science Foundation Fellowship Grant PA00P2_142208.