Several insights gained from observing quadruped robots in omnidirectional static walking experiments at high speed on a slope are presented here. In order to allow a robot to move as fast as possible, the height of center of gravity (COG) and three rotating axes, i.e., roll, pitch, and yaw, were used to discuss the COG with the corresponding optimal body posture (COBP). The COBP is the posture in which the motion velocity is maximized according to the height of COG, stability, degree of slope, and direction. Successive gait transition with a minimum number of steps is achievable with the use of a common foot position before and after a gait transition. The time required to change gaits may be reduced by designing the foot positions during crawling and rotating while limiting reachable region of the foot on a slope. The robot, thus, walks in any direction fast and statically with COBP by dynamically changing the height of COG and body posture during gait transitions.