  This work presents a two part framework for online planning and execution of
dynamic aerial motions on a quadruped robot. Motions are planned via a
centroidal momentum-based nonlinear optimization that is general enough to
produce rich sets of novel dynamic motions based solely on the user-specified
contact schedule and desired launch velocity of the robot. Since this nonlinear
optimization is not tractable for real-time receding horizon control, motions
are planned once via nonlinear optimization in preparation of an aerial motion
and then tracked continuously using a variational-based optimal controller that
offers robustness to the uncertainties that exist in the real hardware such as
modeling error or disturbances. Motion planning typically takes between
0.05-0.15 seconds, while the optimal controller finds stabilizing feedback
inputs at 500 Hz. Experimental results on the MIT Mini Cheetah demonstrate that
the framework can reliably produce successful aerial motions such as jumps onto
and off of platforms, spins, flips, barrel rolls, and running jumps over
obstacles.
