# Leg Trajectory Planning for Quadruped Robots with High-Speed Trot Gait
## 4 Discussion  
Our leg design concentrates all the motors on the shoulder joint. Hence the center of mass is near to the center of rotation, which makes the inertia of the swing leg change smaller so that the leg can achieve higher acceleration and a faster response. This leg configuration is also adopted by several quadrupeds, such as the MIT cheetah [25], Laikago robot [26], and SpotMini [7]. For the manufactured leg, it can be found that the swing inertia of the knee joint, which mainly provides the movement in the vertical direction, is very low and its movement is very flexible. Also, the force the quadruped robots bear most is also in the vertical direction. Hence such a leg structure is suitable to the high-speed movement and jumping for quadruped robots. Differing from the leg of MIT cheetahs, which was made with a bioinspired fabrication method [14], our leg structure is mainly connected by ribbed plates with only 4-mm-thin plates in the middle. The structure has a better performance of bearing pressure and bending moment and is simpler for manufacturing. In particular, wear washers and dry bushings were adopted in our joints design to reduce the friction of linkages' joint by the self-lubrication characteristics of the dry bushing. Moreover, two high torque density motors are used in the single leg, which can provide a strong power regardless of a low gear ratio. The coaxial motor configuration can achieve a coupled motion of two shoulder and knee joints, which has also been adopted by several quadrupeds, such as MIT cheetah [25] and Laikago robot [26]. The used single-stage gear can greatly decrease the size and mass of the reducer as well as reducing the energy loss in the process of mechanical transmission, making a significant contribution to energy efficiency. From the acceleration curves of the two schemes, it is obvious that the gait trajectory of spline curve in scheme 1 can ensure the continuity of acceleration, and the acceleration of the contact point between swing phase and stance phase is almost zero in scheme 1, which means no additional impact is generated from the ground. Because of the characteristics of the Bezier curve, the gait trajectory planned finds it difficult to achieve continuity of acceleration, and the acceleration of the legs once in contact with the ground is not zero. Therefore, there will be an impact on the legs, which will affect the walking stability of the quadruped robot. Besides, the shape of the curve in Figure 13c resembles human gait ground reaction forces [27]. According to [PERSON]'s virtual leg principle [28], a quadruped gait that uses four legs in two pairs, such as trot and pace, could be viewed as an equivalent biped, which means that human gait somewhat resembles quadruped gait. That may be the reason why the curves are similar, and it also proves that the gait trajectory is close to a biological gait. The characteristics of these two schemes were also evaluated with the simulation in Webots. During the simulation, the robot used the gait of scheme 1 and can walk more steadily with less body shaking; however, the quadruped robot, while using the gait of scheme 2, suffers from minor shaking, although it can walk normally. According to the change of the height of gravity center, the maximum difference of gravity center height in the scheme I is 22.62 mm, while that of scheme II is 23.79 mm. Overall, it can be seen that the gait stability of scheme I is better than that of scheme II especially for the change of pitch angle. Furthermore, the power consumption for the two schemes indicates that scheme 1 consumes less battery energy and has higher efficiency than that of scheme 2, as shown in Figure 20 and Table 3 in the results section, although scheme 1 consumes more mechanical energy. Besides, the RMS knee current, which corresponds to heating in scheme 1, is similar to that of scheme 2. While the RMS shoulder current in scheme 1 is much smaller than that in scheme 2. Hence, scheme 1 is superior to scheme 2 in energy consumption.