  Specialized motions such as jumping are often achieved on quadruped robots by
solving a trajectory optimization problem once and executing the trajectory
using a tracking controller. This approach is in parallel with Model Predictive
Control (MPC) strategies that commonly control regular gaits via online
re-planning. In this work, we present a nonlinear MPC (NMPC) technique that
unlocks on-the-fly re-planning of specialized motion skills and regular
locomotion within a unified framework. The NMPC reasons about a hybrid
kinodynamic model, and is solved using a variant of a constrained Differential
Dynamic Programming (DDP) solver. The proposed NMPC enables the robot to
perform a variety of agile skills like jumping, bounding, and trotting, and the
rapid transition between these skills. We evaluated the proposed algorithm with
three challenging motion sequences that combine multiple agile skills, on two
quadruped platforms, Unitree A1, and MIT Mini Cheetah, showing its
effectiveness and generality.
