# Conceptual Design of the Combinable Legged Robot Bio-Inspired by Ants' Structure
## 5 Results
### Walking Motion for Connected Robots  
To assess the walking motion of the connected robots (in Section 4.2), the walking trajectories for Robot 1 and Robot 2 are presented in Figure 9, and the rotational angle of the leg joints for the two robots is shown in Figure 10. Table 1 is the summary of the variation of the rotational angle. During the first 10 s of motion, Legs 1 and 2 of Robot 1 are turned to the side to prepare for the combination with Robot 2, as indicated by the foot trajectories along the robot's y-axis shown in Figure 9b, which gradually increased from \(-257.7\) mm to \(-158.0\) mm and from \(-257.4\) mm to \(-149.0\) mm for Legs 1 and 2, respectively. As seen in Figure 9e, both Legs 1 and 2 of Robot 2 show the same pattern from 10 to 20 s during the combining process. Corresponding to these observations, Figure 10a,d also shows evidence of a change in the rotational angle at Joint 1 of Leg 1 and Leg 2 of both Robot 1 (\(1.4^{\circ}\) and \(-1.4^{\circ}\), respectively) and Robot 2 (\(-1.2^{\circ}\) and \(-0.5^{\circ}\), respectively), which reaches its maximum angle after the first 5 s and remains constant thereafter. Next, Leg 3 and Leg 4 of Robot 2 walk toward Robot 1 during the period \(t\) = 20-30 s. As seen in Figure 9d, the trajectory of the foot of Leg 3 changes from \(-270.5\) mm to \(-179.4\) mm along the \(x\)-axis of Robot 2's base frame and then decreases to \(-291.2\) mm, while the trajectory of Leg 4 moves from 268.1 mm to 186.8 mm and then to 283.1 mm. In Figure 9e, the trajectory of the foot of Leg 3 along the \(y\)-axis of Robot 2's base frame experiences a gradual increase, then a decrease (from \(-252.2\) mm to \(-157.2\) mm and then to \(-251.5\) mm), and Leg 4 moves from \(-258.7\) mm to \(-155.6\) mm and then to \(-253.4\) mm. In Figure 9f, the trajectory of the foot along the \(z\)-axis of Robot 2's base frame for Leg 3 and Leg 4 changes from \(-257.0\) mm to \(-220.3\) mm and then to \(-258.0\) mm and from \(-260.6\) mm to \(-180.8\) mm and then to \(-256.4\) mm, respectively. During the same period, Figure 10d-f also shows that the rotational angles for the leg joints of Robot 2 change for Leg 4 and then Leg 3. As observed in Figures 9 and 10, both robots remain still from \(t\) = 30 s to \(t\) = 48 s, indicating that they have connected. Because the coupling mechanism holds Robots 1 and 2 together face-to-face, Leg 1 of Robot 1 and Leg 2 of Robot 2 are close together and treated as the left-middle leg of the combined robot, while Leg 2 of Robot 1 and Leg 1 of Robot 2 are treated as the right-middle leg. Therefore, when combined, the robots walk according to the robot locomotion principle, in which four legs are always on the ground (with the left and right middle portions of the combined robot assumed to be one leg) to form a polygon base support, as shown in Figures 9 and 10. As a result, the walking motion of the combined robot can be described as stable [21]. Figure 8: IMU results for a single robot. Figure 9: Feet trajectory for two connected robots walking together. Displacement of the feet trajectory of Robot 1 along with the (**a**) \(x\)-axis, (**b**) \(y\)-axis, and (**c**) \(z\)-axis. Displacement of the feet trajectory of Robot 2 along the (**d**) \(x\)-axis, (**e**) \(y\)-axis, and (**f**) \(z\)-axis. As with the single robot walking test, the IMU results for Robots 1 and 2 are used to check whether the combined robot overturns while walking or not. Figure 11a shows the IMU output for Robot 1, with the \(z\)-axis, the opposite y-axis, and the opposite \(x\)-axis representing the yaw (y), pitch (p), and rolls (r), respectively, for the rotational angle of the center of Robot 1's body while walking. The results here support the information provided in Figures 9 and 10. For instance, for \(t\) = 5-10 s, the angles along the yaw axis (from \(0^{\circ}\) to \(-1.5^{\circ}\) then to \(6.1^{\circ}\)) and the pitch axis (from \(0^{\circ}\) to \(-6.3^{\circ}\) then to \(-4.6^{\circ}\)) both increase then decrease.