# Stability Criterion for Dynamic Gaits of Quadruped Robot
## 5 Results and Discussion
### Simulation 2  
A second set of comparative simulations was designed to verify the following: (1) it is difficult to correctly evaluate the stability by only considering the distance between _ZMP_ and the current support line; (2) the accuracy and effectivity of LAR are worse than the stability-evaluation method proposed in this paper; and (3) the stability-evaluation method proposed in this paper can satisfy the first two requirements of a good-stability criterion and evaluation method presented in Section 1. In addition to the motion trajectory of the CoG used in Simulation 1 (denoted as Test 1), two other CoG trajectories were used for off-line planning of the quadruped robot's movement (the actual trajectories of CoG did not necessarily coincide with the planned trajectory); refer to the animation (Video S2). * Test 2: [PERSON] moves around the current support line (the velocity parallel to \(z_{i}\) is 0.2 m/s, and the velocity and acceleration parallel to \(y_{i}\) at the two ends of this direction are zero), as shown in Figure 17.
* Test 3: [PERSON] starts to move from the midpoint of the current support line to that of the next support line at a constant speed when the previous support line has just disappeared, as shown in Figure 16.  
The posture angles, positions, and velocities of the body for the three tests are shown in Figure 18a-c, respectively. The driving moments of the three joints of the left hind leg are shown in Figure 18d. Figure 16: Trajectory of the CoG in Test 3. Figure 15: Attitude angles of the body. The wave heights of the data curves referring to the difference between adjacent peaks and troughs show the severity of data fluctuations if the fluctuation period is similar. The wave-height-variation range of each dataset and the driving-torque-variation ranges of the three joints of the left hind leg are shown in Figure 19.  
Figure 17: Trajectory of the CoG in Test 2. Figure 18: Sensor data of the motion in Simulation 2: (**a**) posture angles; (**b**) positions; (**c**) velocities of the body; and (**d**) driving moments of the left hind leg. As shown in Figure 19, the motion of Test 3 was the steadiest and required the minimum joint-driving torque, and the stabilities of the other two tests were about the same. In fact, stability cannot be evaluated accurately using individual-sensor data, which is one of the reasons the stability criterion and measurement must be proposed. The generally accepted stability-evaluation method (denoted as Method 1), i.e., the one that measures the distance between the traditional _ZMP_ and the current support line; LAR (denoted as Method 2); and the proposed stability measurement for the trot gait of a quadruped robot (denoted as Method 3) were used to evaluate the stability of the three tests (Figure 20a-c). Figure 19: Variation ranges of: (**a**) wave heights of posture angles; (**b**) wave heights of positions; (**c**) wave heights of velocities; and (**d**) joint torques. The average values (over 15 s) of the stability evaluations obtained using these three methods are shown in Table 4.  
Test 2 had the lowest stability, followed by Test 3 and then Test 1 according to Method 1. However, this result was not consistent with the actual movement of the robot. Method 2 indicated that the stability of the robot in Test 3 was better than Test 2, followed by Test 1. Using the second method, the stability of Test 1 was found to be slightly better than that of Test 2, with Test 3 being the most stable case. The last two methods could both indicate that the stability of Test 3 was best, but one more simulation should be designed to compare the stability of Test 1 and Test 2. Two impact forces parallel to \(y_{c}\) in the opposite direction were both applied to the CoM of the body during the trotting in Test 1 and Test 2. The magnitudes, timings, and durations of these forces are shown in Table 5.  
The robot is supported by the same set of diagonal legs during the first half of each gait cycle of the trotting gait.