Cost-Matching Model Predictive Control for Efficient Reinforcement Learning in Humanoid Locomotion

In humanoid motion control, model predictive control (MPC) offers physically grounded prediction and constraint handling, while reinforcement learning (RL) enables robust whole-body skills through large-scale simulation. However, using MPC inside RL often requires time-consuming problem construction or excessive training overhead, making such frameworks difficult to justify in practice. This work studies efficient training-time MPC guidance for humanoid locomotion and manipulation, termed MPC-RL. We introduce a centroidal-dynamics MPC reward formulation that leverages guidance from MPC trajectories in training time. To make this practical in massively parallel RL, we develop $π^n$MPC, a parallel-in-horizon and construction-free batched GPU MPC solver that operates directly on time-varying dynamics to avoid high memory usage and pre-compilation. Through a variety of comparative studies and hardware validations, we have found that MPC-RL achieves superior performance in locomotion and manipulation skills. The code base is available at https://github.com/junhengl/mpc-rl.

We propose a contact-explicit hierarchical architecture coupling Reinforcement Learning (RL) and Model Predictive Control (MPC), where a high-level RL agent provides gait and navigation commands to a low-level locomotion MPC. This offloads the combinatorial burden of contact timing from the MPC by learning acyclic gaits through trial and error in simulation. We show that only a minimal set of rewards and limited tuning are required to obtain effective policies. We validate the architecture in simulation across robotic platforms spanning 50 kg to 120 kg and different MPC implementations, observing the emergence of acyclic gaits and timing adaptations in flat-terrain legged and hybrid locomotion, and further demonstrating extensibility to non-flat terrains. Across all platforms, we achieve zero-shot sim-to-sim transfer without domain randomization, and we further demonstrate zero-shot sim-to-real transfer without domain randomization on Centauro, our 120 kg wheeled-legged humanoid robot. We make our software framework and evaluation results publicly available at https://github.com/AndrePatri/AugMPC.

Model Predictive Control (MPC) provides a structured and constraint-aware mechanism for decision-making, but its reliance on optimization-friendly analytical dynamics models limits its use in tasks with contacts and other hard-to-model state dependencies. Model-free reinforcement learning avoids explicit modeling assumptions but typically requires large amounts of interaction data. We present a learning-based MPC framework that combines the data efficiency and structure of local model-based planning with learned components that compensate for incomplete dynamics and finite-horizon myopia. The method augments a nominal analytical model with a residual dynamics network that learns missing state-dependent effects from data and combines the resulting planner with a learned action-value critic that injects long-horizon MDP structure into the local iLQR optimization. To make this practical at reinforcement-learning scale, we develop a GPU-accelerated batched iLQR solver that evaluates learned dynamics and critic networks inside the optimal-control loop and solves thousands of trajectory-optimization problems in parallel. The complete system is integrated into a robotics simulator, enabling scalable model-based reinforcement learning under incomplete dynamics. Experiments on biased and incompletely modeled control tasks show that the approach improves closed-loop control performance while preserving the model-based structure needed for efficient constrained trajectory optimization.