Robust Predictive Control for Quadrupedal Locomotion: Learning to Close the Gap Between Reduced- and Full-Order Models

Template-based reduced-order models have provided a popular methodology for real-time trajectory planning of dynamic quadrupedal locomotion. However, the abstraction and unmodeled dynamics in template models significantly increase the gap between reduced- and full-order models. This letter presents a computationally tractable robust model predictive control (RMPC) formulation, based on convex quadratic programs (QP), to bridge this gap. The RMPC framework considers the single rigid body model subject to a set of unmodeled dynamics and plans for the optimal reduced-order trajectory and ground reaction forces (GRFs). The generated optimal GRFs of the high-level RMPC are then mapped to the full-order model using a low-level nonlinear controller based on virtual constraints and QP. The proposed hierarchical control framework is employed for locomotion over rough terrains. We leverage deep reinforcement learning to train a neural network to compute the set of unmodeled dynamics for the RMPC framework. The proposed controller is finally validated via extensive numerical simulations and experiments for robust and blind locomotion of the A1 quadrupedal robot on different terrains.