Design of an Origami Crawling Robot with Reconfigurable Sliding Feet

Abstract

This paper presents a novel reconfigurable crawling robot based on an origami twisted tower structure. Compared with other origami structures, the twisted tower can achieve extension, contraction, and bending motions as the flexible body parts in robotic designs. The kinematics of a one-layer twisted tower were analyzed with rotation and bending angles. The mechanical properties of the one-layer, two-layer, and four-layer twisted towers were compared with compression experiments. A rope-motor-driven crawling robot was designed to realize forward, backward, left-turning, and right-turning motions. Two types of crawling robot with specific sliding feet were developed to adapt to different ground conditions: one made of rubber, and the other embedded with an electromagnet. The experimental results show that the proposed robots can move at an average forward speed of 0.48 cm/s on a wooden desk, and at 0.52 cm/s forward speed or 0.65 cm/s backward speed on an iron platform.

1. Introduction

Origami refers to a process of forming a three-dimensional (3D) structure by folding alone, without damaging the integrity of the two-dimensional (2D) paper [1]. The origami technique can be used to build various 2D material-based structures, opening up new ideas for the design, manufacturing, and assembly processes in the engineering fields [2,3,4]. Since the beginning of the 21st century, the concept of origami has been widely used in many fields, from DNA origami at the micro scale to deployable aerospace structures at the macro scale [5,6,7]. The potential advantages of an origami structure include its compact size, reconfigurability, and reduced manufacturing complexity. The origami structure can change between different shapes, fold as much as possible during storage to minimize the space it takes up, and expand into a specific structure when in use. The origami technique offers an innovative approach to reducing the number of parts required in the manufacturing and assembly processes.

The concept of origami has also been integrated into robot designs and applications [8,9,10,11,12]. Origami robots can be made of foldable materials, such as paper, plastic sheets, and metal foils, reducing both the robot weight and the manufacturing cost. In the future, degradable materials will appear as a popular raw material for origami robots due to their environmental friendliness. These advantages make origami robots enjoy a wide range of applications in pipeline detection, medical treatment, and space exploration. Origami robots use folding and unfolding mechanisms to perform functions such as self-assembly, shape change, movement, and manipulation. The existing driving methods today for origami robots include motor-driven, pneumatic-driven, and smart-material-driven. Smart materials used for this purpose include thermally activated materials, chemically activated materials, electro-activated materials, magnetically activated materials, and light-activated materials. Jun-Young Lee et al. proposed a multifunctional motor-driven soft robot based on transformable origami wheels [13]. Suk-Jun Kim et al. developed an origami self-locking foldable robotic arm using a tendon-driven system [14]. Lee et al. presented a cable-driven robotic gripper with a twisted tower structure [15]. The rope-motor-driven method is suitable for large origami structures due to its fast response, high accuracy, and large driving force; this method requires extra power supply and control units, which add to the complexity of the origami robot system. The pneumatic-driven method works by sealing an origami structure into an inflatable bag and using inflation and deflation mechanisms to control the contraction and expansion of the structure. Shuguang Li et al. presented a type of fluid-driven origami-inspired artificial muscles [16]. Schmitt et al. developed a flexible origami-based pneumatic actuator [17]. Sun et al. introduced a self-folding and self-actuating planar pneumatic system [18]. Robertson et al. presented a soft pneumatic modular robotic platform [19]. Kim et al. proposed a pneumatic quadruped robot with an origami pump actuator [20]. Yu et al. designed a crawling robot driven by pneumatic foldable actuators [21]. Since shape memory alloys (SMAs) have high energy density and two-phase (martensite/austenite) properties, they can also be considered as actuators for origami structures; because of the small intrinsic actuation strain for SMAs, they are suitable for soft and small-scale structures in order to amplify the overall deformation. Wood et al. presented an SMA-actuated lifting structure based on an origami water bomb structure [22]. Onal et al. designed an origami worm robot driven by embedded SMA coil actuators [23]. Tolley et al. presented a self-folding origami structure with shape-memory composites, which can be activated with uniform heating [24]. Kwan et al. reported a light-induced folding–unfolding actuator that can be used for origami structures [25].

Inchworm-inspired crawling robots have been widely investigated in recent years. Fang et al. demonstrated an origami-based DC-motor-actuated earthworm-like locomotion robot [26]. Koh et al. proposed an omega-shaped inchworm crawling robot using an SMA coil spring actuator [27]. Khan designed a 5 degree of freedom (DOF) crawling robot with two electromagnetic feet [28]. Ning et al. developed a 3D-printed pneumatic soft robot driven by air pressure [29]. Pagano et al. designed a crawling robot based on the Kresling origami pattern [30]. Most inchworm-inspired robots stride by bending or shrinking the body sections in a certain sequence; the anisotropic friction can enable the robot move forward or backward, and the researchers have to develop various links and joints to assemble different pieces together, which requires a lot of time and expense.

Compared with other origami structures, the origami structure known as the twisted tower shows good motion abilities, similar to the inchworm, and the configuration of its octagonal structure can provide enough strength during locomotion. In this paper, the basic structure of the twisted tower is firstly described; the rigid body kinematics method is used to analyze the extension, contraction, and bending motions of the twisted tower. Next, a reconfigurable crawling robot with a rope-motor-driven system and reconfigurable sliding feet is assembled with locomotion ability based on anisotropic friction, and two types of crawling mechanisms are compared based on the different types of ground on which the robot moves. Finally, forward motion, backward motion, left-turning, and right-turning experiments are conducted to demonstrate the performance of the proposed robot.

2. Description of the Origami Twisted Tower

2.1. Assembly of the Twisted Tower

First proposed by Mihoko Tachibana, the twisted tower structure can be used to assemble multilayer functionalized structures. This unique structure can realize extension, contraction, and bending motions as shown in Figure 1.

The one-layer twisted tower can be assembled from 16 basic segments, as shown in Figure 2. The paper used for forming the basic segments has a size of 6 cm × 3 cm and a thickness of 0.2 mm. The basic segment determines the length of the link plate and the initial height of the one-layer tower. Several types of paper with different thickness, from 0.08 mm to 1.0 mm, are tested and compared during the assembly process. Thick paper is not suitable for folding, while thin paper is easy to break; the 0.2 mm thickness paper can provide both good foldability and sufficient stiffness.

2.2. Kinematics of the Twisted Tower

The one-layer twisted tower can be considered to be a kind of deformable octagonal structure, as shown in Figure 3, and several such twisted towers can be superimposed to form a multilayer structure to achieve complicate functions. A unique feature of this origami structure is that the distance between the top and bottom plates can be changed by twisting the structure. If the center of the top plate and that of the bottom plate remain in the same vertical line, the process is defined as an “axial extension” or “axial contraction” motion. If the top plate tilts during the process and is no longer parallel to the bottom plate, the process is defined as a “bending” motion. Both clockwise and counterclockwise twisting operations can result in extension/contraction or bending motions.

2.2.1. Axial Extension/Contraction Motions

Firstly, the axial motion of the one-layer octagonal origami structure is analyzed. In Figure 3, h is the distance between the top and bottom plates, θ is the rotation angle around the z-axis, and s is the length of the link plate [31].

When the width of the unfolded segment paper is set to L, and the length of the unfolded segment paper is set to 2 L, the length s of the link plate can be represented as follows:

$$s=L-L\mathit{sin}\left(\pi /8\right)$$

(1)

The original distance between the top and bottom plates h₀ can be represented as follows:

$$h_0=s=L-L\mathit{sin}\left(\pi /8\right)$$

(2)

The rotation angle θ around the z-axis ranges from −4π to 4π. When a rotation force is applied on the top plate, the distance h between the top and bottom plates can be represented as follows:

$$h=s\sqrt{1-si{n}^2\left(\theta /2\right)/si{n}^2\left(\pi /8\right)}$$

(3)

The geometric model of a two-layer twisted tower is demonstrated in Figure 4. The coordinate system is set up in the center of the bottom plate of the first one-layer structure. The vertical line segment represents the link plate of the structure. The motion trajectory of the top plate can be considered as an arc on the circumscribed circle of the octagon.

There is an offset angle $\alpha$ between the link and bottom plates. The definition of offset angle $\alpha$ for clockwise and counterclockwise twisting is as shown in Figure 5. The relationship between offset angle $\alpha$ and rotation angle $\theta$ can be represented as follows:

$$h=s·\mathit{sin}\alpha$$

(4)

$$\alpha ={\mathit{sin}}^{-1}\left(\sqrt{1-si{n}^2\left(\theta /2\right)/si{n}^2\left(\pi /8\right)}\right)$$

(5)

Therefore, the motion of a multilayer twisted tower is the superposed motions of several one-layer twisted towers. The change in the overall structure can be calculated by measuring the offset angle $\alpha$ of each layer.

2.2.2. Bending Motion

For the convenience of analyzing the bending motion of the one-layer twisted tower, the bending motion can be considered as two synchronized parts: one is the inclination between the top and bottom plates, and the other is the rotation angle around the central axis. Figure 6a shows the side view of the bending motion for the i-th layer. Specifically, ${\varphi }_i$ is the inclination angle, $d_i$ is the distance between the center points of the top and bottom plates, and $h_i$ is the distance between the highest point of the top plate and the corresponding point of the bottom plate [32]. Figure 6b is the side view with the maximum bending angle. The maximum bending angle ${\varphi }_i^{max}$ can be represented as follows [33]:

$${\varphi }_i^{max}=2{\mathit{sin}}^{-1}(\left(h_i-{\epsilon }_d)/4R\right)$$

(6)

where ${\epsilon }_d$ is the thickness of the plate and R is the radius of the circumscribed circle. The radius R can be represented as follows:

$$R=\left(L+\sqrt{2}L/\mathit{sin}\left(\pi /8\right)\right)/2$$

(7)

The distance $d_i$ between the two center points can be represented as follows:

$$d_i=h_i-2Rsin\left({\varphi }_i/2\right)$$

(8)

As discussed earlier, the axial extension/contraction motion of the twisted tower can be uniquely determined by the offset angle $\alpha$. The bending angle $\varphi$ can also be uniquely determined by the offset angles ${\alpha }_1$ and ${\alpha }_2$ of a pair of link plates, as shown in Figure 7. The projection of the bottom octagon surface is represented by the line $A^{\prime }{B}^{\prime }$. The upper octagon shows the position of each point after the bending motion, and the dashed line represents the direction in which the bending motion occurs. It can be considered that the height of point A is the same as that of point C, while the height of point B is the same as that of point D. $A^{\prime }A$ and $B^{\prime }B$ are the two sides corresponding to the two link plates. The angle between $A^{\prime }A$ and the bottom plane is ${\alpha }_1$, while that between $B^{\prime }B$ and the bottom plane is ${\alpha }_2$. The height difference between points A and B can be obtained as $\Delta \mathrm{h}$, and the radius of the inscribed circle of the octagon is r. Thus, the bending angle $\varphi$ can be calculated as follows:

$$\varphi ={\mathit{sin}}^{-1}\left(\Delta h/2r\right)$$

(9)

3. Mechanical Properties of the Origami Twisted Tower

When a twisted tower is used as the skeletal structure for robots, compression will occur under the action of an external force. When the external force is removed, the twisted tower will return to its original state due to its restorability. The axial deformation produced by a twisted tower under a uniform axial compression force was explored in the following experiments. The experimental setup was as shown in Figure 8. The relationship between the axial deformation and compression force of the twisted tower can be measured with a dynamometer and a digital Vernier caliper. A balance plate was installed on the dynamometer to ensure that the twisted tower was compressed evenly. Three types of twisted towers with different numbers of layers (one-layer, two-layer, and four-layer) were measured four times to reduce the random error.

For the one-layer twisted tower, its initial height was 40 mm, and its fully compressed height was ~10 mm. The deformation was generated uniformly when the compression force increased from 5 N to 15 N, as shown in Figure 9a. For the two-layer twisted tower, its initial height was 80 mm, and its fully compressed height was ~18 mm, as shown in Figure 9b. For the four-layer twisted tower, its initial height was ~120 mm due to its own weight, and its fully compressed height was ~35 mm, as shown in Figure 9c.

As discussed, the mechanical properties of origami structure are largely determined by the material and thickness of the paper. Here, identical pieces of paper (6 cm × 3 cm, 0.02 mm thickness) and the same process were used to assemble these structures; one sample each of one-layer, two-layer, and four-layer structures were tested to demonstrate their deformation ability. Compared with the one-layer structure, the multilayer structure can be regarded as the series connection of multiple one-layer structures, and it can be seen that the stiffness of the whole tower structure decreases with the increasing number of layers; multi-layer structures are more sensitive to the change in driving force, and can provide more deformation in the same driving force range. Therefore, selecting the appropriate number of layers can better improve the control accuracy of the crawling robot.

The paper-based origami structure undergoes irreversible deformation after hundreds of contraction/extension operations. Figure 10a shows a one-layer structure having been used for several months, with more than 500 working cycles. There are several reasons that may cause the irreversible deformation; for example, the paper becomes soft after many times of folding and unfolding, the intersection parts become loose, and the support plates between the top and bottom layers are not stiff enough. The restoration experiment results in Figure 10b were achieved to compare with the results in Figure 9a. It can be seen that the body stiffness of this type of tower structure decreases after a long period of contraction/extension, making the whole structure loose and leading to a degradation of the body’s restoration ability. Although the stiffness of the origami structure degrades after 500 working cycles, it can still return to its starting status when the compression force is released, meaning that slight irreversible deformation may not affect the basic function (support and restoration) of the origami structure. However, it is highly recommended to replace the excessive deformed section in order to maintain the performance of the origami robot after a long period of use.

4. Design of the Origami Crawling Robot

As discussed earlier, the origami twisted tower can generate extension and bending motions; therefore, it can be used as a skeletal structure for different types of robots. In this section, a reconfigurable crawling robot is proposed and discussed. Crawling robots are widely proposed to perform exploration tasks in narrow environments, such as pipelines or air conditioning ventilation channels. In these scenarios, some paths are made of non-ferromagnetic materials (plastic, glass, aluminum, etc.), while others are made of ferromagnetic materials. For the purpose of improving mobility and reliability, our inchworm-inspired crawling robot has two types of replaceable “sliding feet” to fit with the local ground and environment. This robot is composed of a head, tail, body, and driving system by imitating the inchworm’s crawling gait. Here, the origami structure is employed to assemble the inchworm robot, which can greatly reduce the cost and complexity of the robot design.

4.1. Rope-Motor-Driven Mechanism of the Origami Robot

Typical driving methods for origami robots include rope-motor-driven, pneumatic-driven, and smart-materials-driven. To suit the size and weight of the proposed origami structure, the rope-motor-driven method was chosen for our origami crawling robot. The working mechanism of the rope-motor-driven system is as shown in Figure 11. The extension/contraction and bending motions of the origami twisted tower can be controlled by applying a tension force on four ropes. Axial motions can be achieved by tightening two or four ropes in the same direction. Bending motions can be achieved by tightening one of the ropes in the bending direction. Friction is the main obstacle when using this rope-motor-driven method. The shape and relative position of each layer changes during the operation, causing additional friction between the rope and the paper structure. Therefore, a powerful DC motor with enough driving capability is required in order to overcome the friction problem. More than 28 N of drag force would be required for full compression, and about a further ~12 N of drag force for full bending, with the bellowing four-layer structure.

Since the rope tightening operation requires a large force and the gear needs to run continuously around 360°, a DS04-NFC DC motor (WEGASUN, Shenzhen, China) is used to drive the origami twisted tower, as shown in Figure 12. The specific parameters of this motor are as shown in

Table 1. Parameters of the DS04-NFC DC motor.

Type of DC Motor	DS04-NFC
Voltage	4.8 V–6 V
Torque	5.5 kg/cm
Speed	60°/0.22 s
Weight	38 g
Size	40.8 mm × 20 mm × 39.5 mm

.

4.2. System Design of the Origami Crawling Robot

An eight-layer twisted tower is used as the skeleton of the crawling robot. The forward and bending motions of the crawling robot are achieved by operating on the four ropes interspersed in the origami structure. DC motors are installed on the head or tail of the crawling robot. Four sliding feet are used to support the body and increase the friction with the ground. In each contraction and extension cycle, a net forward motion is achieved due to the anisotropic friction between the sliding feet and the ground.

The conceptual design of the origami crawling robot is as shown in Figure 13. A 5 V battery is used to supply power for the DC motor array, microcontroller, and camera. The optional camera can be used to capture pictures in narrow environments, such as pipelines or ventilation ducts.

In the proposed crawling robot system, the anisotropic friction in different directions is used to generate a motion in the target direction. The side view of the crawling robot and the two types of sliding feet are as shown in Figure 14. The front contact part of the rubber sliding foot is arc-shaped and made of a material with a low friction coefficient. The end contact part is made of a patterned rubber pad to provide greater friction, as shown in Figure 14a. When the ground is made of ferromagnetic materials, a sliding foot with an embedded electromagnet can be used to generate an adhesion force and achieve reliable crawling motions, as shown in Figure 14c. The adhesion force is controlled by the current in the coil of the electromagnet. When the origami robot is crawling on the iron ground with electromagnetic sliding feet, the MCU can make the electromagnets switch between the “on” and “off” states in order to adjust the friction force of the four sliding feet periodically. The electromagnet with a size of Φ20 mm × 15 mm can generate a 2.5 kg force, as shown in Figure 14d. Further details of the electromagnet KB-20/15(KBAOELE, Leqin, China) are as shown in

Table 2. Parameters of the KB-20/15 electromagnet.

Type of Electromagnet	KB-20/15
Maximum adhesion force	2.5 kg
Size	Φ20 mm × 15 mm
Working voltage	24 V
Working current	0.1 A
Weight	25 g

.

Friction between the sliding feet and the surface plays an important role in the proposed origami crawling robots. Here, the sliding test with an inclined plane was used to estimate the maximum coefficient of static friction. The sliding feet were placed on the wooden or steel platform, and the angle between platform was increased until the object just began to slide on the plane. The angle φ can be measured with the angle meter, and the tangent of this angle tgφ is the maximum coefficient of static friction [34]. The experimental setup was as shown in Figure 15, and the coefficient of friction between the sliding feet and different surfaces can be found in

Table 3. Coefficients of friction between different sliding feet and surfaces.

Surface	Sliding Object	Coefficient of Friction
		Forward Friction	Backward Friction
Wooden desk	Rubber-type front foot	0.392	0.456
Wooden desk	Rubber-type back foot	0.248	0.313
Iron platform	Electromagnetic-type foot	0.496	0.532
Wooden desk	Rubber block	0.577
Wooden desk	Resin block	0.216
Iron platform	Resin block	0.424

. Since there are some difference in design between the rubber front foot and rubber back foot, both types were tested with forward sliding and backward sliding. The experimental results show that the friction coefficient of backward motion is commonly larger than that of forward motion for both rubber feet and electromagnetic feet; this design could help the robot move forward more easily.

The working principle of the control circuit of the electromagnetic sliding feet in Figure 16 is as follows: the four-way FET MOS power switch control board has four independent paths; each path is composed of an EL357 photocoupler and N-channel MOS tube; the input end of the photo coupler is a light-emitting diode; when the input is at high voltage level, the light-emitting diode is turned on, and there is a light-receiving device at the output end to convert the optical signal into an electrical signal. When the MOS tube is turned on, there is a voltage difference between the output terminal and VCC; the electromagnet is energized, and the electromagnet produces magnetism. On the other hand, when the input terminal is low, the MOS tube is in the cutoff state; there is no voltage difference between the two ends of the electromagnet, and the electromagnet is in the power-off state, so the magnetism disappears.

4.3. Experiments on Crawling Motions with Rubber Sliding Feet

The directional motions of the origami crawling robot can be achieved using the anisotropic friction between the sliding feet and the ground. One motor is on the tail and the other three are on the head. The forward moving process of the crawling robot on a wooden desk is as shown in Figure 17. It takes ~6 s to complete a motion cycle. During the forward moving process, the motors on the tail start to rotate, which tightens the rope to shrink the body, and the whole body of the crawling robot is slightly arched, causing a small contact angle. The contact part of the sliding feet on the head has a larger friction than that of the sliding feet on the tail; therefore, the sliding feet on the head provide a larger friction force than those on the tail, driving the tail to move forward. Similarly, the restorative origami structure generates an elastic force to drive the head forward to complete a motion cycle.

The average speed of the robot’s forward motion can be estimated by recording the change in position throughout the entire process. The position marks are as shown in Figure 18. In this experiment, a 100 g counterweight was attached to the body of the robot in order to verify the payload ability. The initial position was at 8.5 cm and the final position was at 20.5 cm after 25 s. The average forward speed was ~0.48 cm/s.

Moreover, the whole working cycle can be separated into four steps for more detail, as shown in Figure 19. The changes in the friction force and moving status of the rubber sliding feet can be found in

Table 4. Parameters of rubber sliding feet with forward motion in one working cycle.

Working Cycle	Foot Type	Force Analysis (fe, fr, fd)	Contact Angle (θa, θb)	Moving Status of Foot (Yes, No)	Motor Rotating Mode (Forward, Backward, Off)
Step 1	Front foot	fd = 0, fe = 0, fr = 0	θa = 0	No	Off
	Back foot	fd = 0, fe = 0, fr = 0	θb = 0	No
Step 2	Front foot	fd = fe + fr	θa = 0	No	Forward
	Back foot	fd > fe + fr	θb > 0	Yes
Step 3	Front foot	fe > fr, fd =0	θa > 0	Yes	Backward
	Back foot	fe = fr, fd =0	θb = 0	No
Step 4	Front foot	fd = 0, fe = 0, fr = 0	θa = 0	No	Off
	Back foot	fd = 0, fe = 0, fr = 0	θb = 0	No

. The rope drag force $f_d$, elastic force $f_e$, and friction force $f_r$ decide the motion direction and moving speed. There is a net forward force on the back foot in step 2, which causes the forward movement of the back foot; the net forward force on the front foot in step 3 has the same effect on the front foot. The contact angles ${\theta }_a$ and ${\theta }_b$ are generated by the imbalance of the above forces, which can greatly reduce the friction of the moving parts.

4.4. Experiments on Crawling Motions with Electromagnetic Sliding Feet

Crawling motions can also be achieved via the cooperation between the electromagnetic slider and motors on an iron plane. The area of the iron experiment platform was approximately 60 cm × 60 cm. The proposed motions include moving forward, moving backward, turning left, and turning right on the horizontal plane. All four motors were installed on the head of the crawling robot to provide a larger driving force. The motor installed on the bottom was labeled as No. 1, those on the left and right sides along the forward direction as No. 2 and No. 3, and that on the top as No. 4.

The forward motion on the horizontal iron plane is as shown in Figure 20a. It takes 7 s to complete a motion cycle. First, the electromagnets embedded in the front sliding feet are powered on to generate an adhesion force. At this point, the DC motors rotate and the four ropes are tightened to drive the body to shrink. Then, the electromagnets on the head sliding feet are powered off, while those on the tail sliding feet are powered on. At this point, the motors reverse to loosen the rope, and the origami structure is restored to its original length. The time sequences of the electromagnet and motor control signals are as shown in Figure 20b. The electromagnets are controlled by adjusting the level of the control voltage signal.

The speed of the robot’s forward motion on an iron plane can be measured with marked pictures, as shown in Figure 21. In our experiment, the robot could move 14 cm in 27 s, and its average speed was ~0.52 cm/s.

The whole working cycle can also be separated into four steps for more detail, as shown in Figure 22. The changes in the friction force and moving status of the electromagnetic sliding feet can also be found in

Table 5. Parameters of electromagnetic sliding feet with forward motion in one working cycle.

Working Cycle	Foot Type	Force Analysis (fe, fr, fd)	Electromagnet Status (On, Off)	Moving Status of Foot (Yes, No)	Motor Rotating Mode (Forward, Backward, Off)
Step 1	Front foot	fd = 0, fe = 0, fr = 0	Off	No	Off
	Back foot	fd = 0, fe = 0, fr = 0	Off	No
Step 2	Front foot	fd = fe + fr	On	No	Forward
	Back foot	fd > fe + fr	Off	Yes
Step 3	Front foot	fe > fr, fd = 0	Off	Yes	Backward
	Back foot	fe = fr, fd = 0	On	No
Step 4	Front foot	fd = 0, fe = 0, fr = 0	Off	No	Off
	Back foot	fd = 0, fe = 0, fr = 0	Off	No

. Similar to the rubber sliding feet, the rope drag force $f_d$, elastic force $f_e$, and friction force $f_r$ decide the motion direction and moving speed. There is a net forward force on the back foot in step 2, which causes the forward movement of the back foot; the net forward force on the front foot in step 3 has the same effect on the front foot. There is no contact angle generated due to the larger weight of the electromagnet itself. The electromagnet can be programed with a microcontroller to control the friction force on the front and back feet, which can help to generate backwards and turning motions.

By changing the working sequence of the electromagnets embedded in the sliding feet, backward motion can also be achieved. The backward moving process is as shown in Figure 23a. The backward motion cycle proceeds in the same way as the forward motion cycle discussed earlier. The time sequences of the control signals are as shown in Figure 23b.

The speed of the robot’s backward motion on an iron platform can be measured with marked pictures, as shown in Figure 24. In the backward experiment, the robot could move 11 cm in 17 s, and its average speed was ~0.65 cm/s.

The robot can turn left or right with the bending motion of the twisted tower structure. The left-turning process is as shown in Figure 25a. Motors and electromagnets work alternately to turn the robot to the left. It takes nearly 90 s for the robot to turn 90° to the left. The time sequences of the control signals are as shown in Figure 25b.

The right-turning motion takes place in a similar way to the left-turning motion. The right-turning process is as shown in Figure 26a. It takes nearly 97 s for the robot to turn 90° to the right. The time sequences of the control signals are as shown in Figure 26b.

Several existing origami crawling robots are compared in

Table 6. Comparison of motion capability of different origami crawling robot systems.

Publications	Type of Crawling Robot	Driving Methods	Motion Capability
Pagano et al. [30].	Paper-based Kresling pattern	DC motors	2.1–1.8 mm/s at forward
Vander Hoff et al. [31].	Paper-based twisted tower pattern	DC motors	6.3 mm/s at forward
Onal et al. [23].	Polymer-based water bomb pattern	SMA coil actuator	0.45 mm/s at forward
Fang et al. [26].	PETE- and PEEK-film-based water bomb pattern	DC motors, SMA actuator, and Balloon pneumatic	3.6–12.3 mm/s at forward
Yu et al. [21].	Silicone-based Miura-ori pattern	Pneumatic	5 mm/s at forward 15°/s at turning
Proposed prototype	Paper-based twisted tower pattern	DC motors and electromagnet	5.2 mm/s at forward 6.5 mm/s at backward 1°/s at turning

; most of the listed crawling robots can only provide the forward motion ability. The moving speed of these crawling robots ranges from 0.45 mm/s to 12.3 mm/s. The DC motor driving types have more advantages in terms of motion speed than the SMA and pneumatic types. Our crawling robot can perform forward, backward, and turning motions with a moderate movement speed.

5. Discussion and Conclusions

Paper has been widely used for origami structures due to its foldability and low cost. Some researchers have developed similar 3D-printed tower structures as a substitute [35]; 3D-printed structures have better durability in harsh environments, and the assembly process of 3D-printed structures is more suitable for large-scale manufacturing. However, paper-based structures are thinner, easier to degrade, and have less impact to the environment. The payload capability could be another concern with this kind of origami robot. Our prototype in this paper can carry ~80 g of extra load. A camera module (~30 g weight) was installed on the head of the robot. The future application of these crawling robots will involve some MEMS-based temperature or humidity sensors. These sensors could be integrated on the head or tail of the robot, and would not affect the locomotion ability due to their small size.

This paper presents a novel crawling robot based on the origami twisted tower structure, and discusses the transformation and modeling of the robot’s extension/contraction and bending motions via axial rotation and bending angles. A prototype was designed for the robot based on a rope-motor-driven system. A series of motion experiments including forward motion, backward motion, left-turning, right-turning, and upward climbing were conducted to evaluate the performance of the robot. The robot can move at an average speed of 0.48 cm/s on a wooden desk and 0.52 cm/s on an iron plane. The experimental results demonstrate the feasibility of using such an origami structure to make low-cost robots with various functions. However, there remains some insufficiency with such rope-motor-driven crawling robots; the relatively slow moving speed will greatly decrease their applicability, and while the feet design can be adapted different local ground, this does not help much with turning motions. The rope-motor-driven method can provide sufficient drag force, and seems more effective for origami structures with fewer layers. For those structures with more layers and a longer body, the pneumatic-driven method would be a better solution, and the driving force can be exerted to each layer synchronous with an air pump.

Future work should focus on the improvement of the mobility and driving mechanism of this type of crawling robot, and some other origami patterns and materials should be tested and compared with the current prototype. The structural durability, restoration ability, and motion precision of origami designs are still the key issues to be solved.