“…1) Model-based optimal control for legged jumping: Prior model-based methods for legged jumping control usually build up a layered optimization scheme, which includes offline trajectory optimization with detailed models of the robot's dynamics and ground contacts [10,12,46,63], and online controllers that leverage simplified models of the robot's dynamics [45,55,65,72]. In order to optimize trajectories for jumping, which needs to switch among modes with different underlying dynamics, there are two commonly employed solutions: (i) relying on human-specified contact sequences [9,19,29,47,71], which is not scalable to different jump distances and/or directions, or (ii) leveraging contactimplicit optimization [8,14,33,52,77] which plans through contacts to avoid breaking the trajectory or using computationally expensive mixed-integer programming [1,11,12].…”