# Modeling of Walking-Gait Parameters and Walking Strategy for Quadruped Robots
## 3 Results and Discussion
### The Gait Planning of the Bionic-Robot Dog  
#### 3.3.1 Basic Concepts of Gait Planning  
Gait is the sequence of motion of the limbs of a walker (human, animal, robot) in time and space [22]. The movement of a footed robot must depend on gait. There are various gaits in the biological world. Depending on the number of limbs, bipedal, quadrupedal, and hexapodal walking styles are different. The same four-limbed animals, horses, dogs, cats, and other species, walk in different ways. Even the same dog will walk in different ways when facing different terrains. Irregular rough roads and regular flat roads will make bionic-robot dogs choose different ways of walking. From this, it can be seen that there are various ways of walking in the biological world. Scholars have defined the relevant concepts of the gait of a quadruped walker. When the limbs are in contact with the ground, the state of the limbs is the support phase; when the limbs are swinging in the air, the state is the swing phase; the time required for the same limb to reach the same state is the period (T); the gait of the biological dog when three or more limbs are in the landing phase at any time is the static gait; the gait when only two or fewer limbs are in the landing phase at any time is the dynamic gait; the ratio of landing-phase duration to cycle is the duty cycle (\(\beta\)); and the minimum convex polygon formed by the landing points is the support area [23]. The common gaits of quadruped robots are shown in Figure 7.  
The duty cycle \(\beta_{i}\) is the ratio of the duration \(t_{st}\) of the \(i\)-th limb on the ground to the period \(T\). The calculation equation is shown in Equation (20):  
\[\beta_{i}=\frac{t_{st}}{T} \tag{20}\]In the equation, \(t_{st}\) represents the duration of the ground phase, and \(T\) represents the period. In addition to the duty cycle \(\beta_{i}\), another important parameter describing gait is the phase difference \(\varphi_{i}\). The phase difference is defined as the ratio of the difference between the landing time \(t_{i}\) of the \(i\)-th limb and the landing time \(t_{0}\) of the reference limb and the movement period. The calculation method follows in Equation (21):  
\[\varphi_{i}=\frac{t_{i}-t_{0}}{T} \tag{21}\]  
The phase difference \(\varphi_{i}\) describes the phase relationship between the limbs, and the response in the gait is the sequence of movements of the limbs. Figure 8 lists the relative relationships between the phases of each limb in several common gaits. In the figure, \(LF\) represents the left-front limb. \(RF\) represents the right-front limb. \(LH\) represents the left-hand limb, and RH represents the right-hand limb, all with the left-front limb as the reference limb, i.e., \(\varphi_{LF}=0\). The duty cycle \(\beta_{i}\) and the phase difference \(\varphi_{i}\) together describe the gait. The former reflects the speed of the walker's movement, and the latter reflects the coordination relationship between the limbs. In order to clearly describe the movement speed of the walker, it is also necessary to know the trajectory curve of the foot end of the walker. When determining the stability of gait, the zero-moment point (ZMP) method is needed. Its definition is shown in Figure 9, where the \(X\)-direction is the forward direction of the robot. The ZMP is defined as the intersection point of the extension line of the combined force of gravity and inertial force on the ground, i.e., \(P\) in Figure 9. The combined moment of inertial force and gravity at the ZMP is zero, so this point is also known as the zero-moment point. If the ZMP falls within the polygonal support area formed by the foot and ground, the gait is stable. On the contrary, if the ZMP falls outside the support area, the gait is unstable. Figure 7: Common gaits of quadruped robots.