## 4 Design of the Origami Crawling Robot
### 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 \(\times\) 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 \(\sim\)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. 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. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  
Figure 20: Origami crawling robot with electromagnetic sliding feet on an iron plane: (**a**) side view of forward motion; (**b**) control signals of motors and electromagnets of forward motion. Figure 21: Top view of the forward motion of the origami crawling robot with electromagnetic sliding feet on an iron plane. Figure 22: Schematic view of the friction force and moving status of electromagnetic sliding feet with forward motion in one cycle. Figure 23: Origami crawling robot with electromagnetic sliding feet on an iron plane: (**a**) side view of backward motion; (**b**) control signals of motors and electromagnetics of backward motion. 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\({}^{\circ}\) to the left.