This paper aims to develop a hierarchical nonlinear control algorithm, based\non model predictive control (MPC), quadratic programming (QP), and virtual\nconstraints, to generate and stabilize locomotion patterns in a real-time\nmanner for dynamical models of quadrupedal robots. The higher level of the\nproposed control scheme is developed based on an event-based MPC that computes\nthe optimal center of mass (COM) trajectories for a reduced-order linear\ninverted pendulum (LIP) model subject to the feasibility of the net ground\nreaction force (GRF). The asymptotic stability of the desired target point for\nthe reduced-order model under the event-based MPC approach is investigated. It\nis shown that the event-based nature of the proposed MPC approach can\nsignificantly reduce the computational burden associated with the real-time\nimplementation of MPC techniques. To bridge the gap between reduced- and\nfull-order models, QP-based virtual constraint controllers are developed at the\nlower level of the proposed control scheme to impose the full-order dynamics to\ntrack the optimal trajectories while having all individual GRFs in the friction\ncone. The analytical results of the paper are numerically confirmed on\nfull-order simulation models of a 22 degree of freedom quadrupedal robot,\nVision 60, that is augmented by a robotic manipulator. The paper numerically\ninvestigates the robustness of the proposed control algorithm against different\ncontact models.\n