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

Abstract

This letter aims to develop a hierarchical nonlinear control algorithm, based on model predictive control (MPC), quadratic programming (QP), and virtual constraints, to generate and stabilize locomotion patterns in a real-time manner for dynamical models of quadrupedal robots. The higher level of the proposed control scheme is developed based on an event-based MPC that computes the optimal center of mass (COM) trajectories for a reduced-order linear inverted pendulum (LIP) model subject to the feasibility of the net ground reaction force (GRF). The asymptotic stability of a desired target point for the reduced-order model under the event-based MPC approach is investigated. It is shown that the event-based nature of the proposed MPC approach can significantly reduce the computational burden associated with the real-time implementation of MPC techniques. To bridge the gap between reduced- and full-order models, QP-based virtual constraint controllers are developed at the lower level of the proposed control scheme to impose the full-order dynamics to track the optimal trajectories while having all individual GRFs in the friction cone. The analytical results of the letter are numerically verified to demonstrate stable and robust locomotion of a 22 degree of freedom quadrupedal robot, in the presence of payloads, external disturbances, ground height variations, and uncertainty in contact models.