  Exploring the limits of quadruped robot agility, particularly in the context
of rapid and real-time planning and execution of omnidirectional jump
trajectories, presents significant challenges due to the complex dynamics
involved, especially when considering significant impulse contacts. This paper
introduces a new framework to enable fast, omnidirectional jumping capabilities
for quadruped robots. Utilizing minimum jerk technology, the proposed framework
efficiently generates jump trajectories that exploit its analytical solutions,
ensuring numerical stability and dynamic compatibility with minimal
computational resources. The virtual model control is employed to formulate a
Quadratic Programming (QP) optimization problem to accurately track the Center
of Mass (CoM) trajectories during the jump phase. The whole-body control
strategies facilitate precise and compliant landing motion. Moreover, the
different jumping phase is triggered by time-schedule. The framework's efficacy
is demonstrated through its implementation on an enhanced version of the
open-source Mini Cheetah robot. Omnidirectional jumps-including forward,
backward, and other directional-were successfully executed, showcasing the
robot's capability to perform rapid and consecutive jumps with an average
trajectory generation and tracking solution time of merely 50 microseconds.
