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

Abstract

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 highlevel RMPC are then mapped to the full-order model using a lowlevel 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.

Beyond Inverted Pendulums: Task-optimal Simple Models of Legged Locomotion

“…Additionally, we optimize both the reduced-order dynamics and the embedding function (a projection operation from the full model to the reduced-order model). This is different from Pandala et al [31] which only optimized for the dynamics, and also different from our prioir work [32] which only optimized for the embedding function. Lastly, we embed the reduced-order model exactly along the full model trajectories during optimization, while Pandala et al [31] approximated the embedding where the embedding error depended on the feedback controller.…”

“…Pandala et al [31] attempted to close the gap between the full model and the reduced-order model, where they modeled the difference between the two models as a disturbance to the reduced dynamics. Our prior work [32] optimized for the Angular Center of Mass model by minimizing the angular momentum error between the reduced-order model and full model.…”

“…First, it allows us to embed the reduced-order model into the full model exactly via constraints. Second, it is more sample efficient than the approaches in reinforcement learning (such as [31]). However, using trajectory optimization leaves a potential performance gap between the offline training and online deployment, because trajectory optimization is an openloop optimal control method which does not consider any controller heuristics by default.…”

Modeling and Trajectory Optimization for Standing Long Jumping of a Quadruped with A Preloaded Elastic Prismatic Spine

“…Owing to developments in actuators, embedded singleboard computers and perception units, quadrupedal robots have become more versatile in various agile locomotion tasks [1]- [3] including rapid running [4], aggressive jumping [5], [6], fast stepping [7], and other acrobatic maneuvers [7]- [10]. A range of existing quadrupedal platforms [1], [8], [11]- [22] adopt a single rigid body (SRB) design and extend the overall morphological degree-of-freedoms (DoFs) by employing 3-DoF legs.…”