Contents I. Introduction
The quadrupedal animals possess extraordinary competence of navigating harsh terrains by executing agile yet well-coordinated movements. For example, mountain goats demonstrate their extraordinary mobility on traversing steep cliffs [2]. Domesticated canine animals could be trained to execute a variety of acrobatic Parkour maneuvers [3]. These remarkable abilities of quadrupedal animals motivated the development of many quadrupedal robots. Minitaur [4] realized various dynamic running gaits: ANYmal [5] and HyQ [6] could navigate challenging terrains autonomously; MIT Cheetah robots achieved galloping [7], high speed bounding [8], and dynamic yet robust locomotion [9]. As the capabilities of quadrupedal robot rapidly grow, related researches have geared toward motions beyond locomotion on flat terrains. For example, ANYmal demonstrated the stair climbing capability [10]; MIT Cheetah 2 overcame obstacles by planning jumping trajectories online [11]; MIT Cheetah 3 achieved leaping onto high platforms [12]; MIT Mini Cheetah could execute 360 backflips [13]. In general, the ability of quadrupedal robots is being developed toward applications that involve more dynamic maneuvers in increasingly complex scenarios.
