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 Pr...