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This paper aims to develop a hierarchical nonlinear control algorithm, basedon model predictive control (MPC), quadratic programming (QP), and virtualconstraints, to generate and stabilize locomotion patterns in a real-timemanner for dynamical models of quadrupedal robots. The higher level of theproposed control scheme is developed based on an event-based MPC that computesthe optimal center of mass (COM) trajectories for a reduced-order linearinverted pendulum (LIP) model subject to the feasibility of the net groundreaction force (GRF). The asymptotic stability of the desired target point forthe reduced-order model under the event-based MPC approach is investigated. Itis shown that the event-based nature of the proposed MPC approach cansignificantly reduce the computational burden associated with the real-timeimplementation of MPC techniques. To bridge the gap between reduced- andfull-order models, QP-based virtual constraint controllers are developed at thelower level of the proposed control scheme to impose the full-order dynamics totrack the optimal trajectories while having all individual GRFs in the frictioncone. The analytical results of the paper are numerically confirmed onfull-order simulation models of a 22 degree of freedom quadrupedal robot,Vision 60, that is augmented by a robotic manipulator. The paper numericallyinvestigates the robustness of the proposed control algorithm against differentcontact models.

Quadrupedal Locomotion via Event-Based Predictive Control and QP-Based Virtual Constraints