MPC-Injection: Biasing Off-Policy Locomotion RL Toward Controller-Induced Behavior Basins

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.

Reinforcement learning for legged locomotion has matured into a stack of multi-component reward functions and physics-engine benchmarks whose morphologies are uniformly derived from real commercial hardware. Game NPCs, however, are bound by stylistic constraints absent from sim-to-real robotics and routinely take the form of creatures with no real-robot counterpart. We introduce ARC-RL, a suite of four MuJoCo continuous-control environments featuring robotic morphologies inspired by the bestiary of ARC Raiders: the 18-DoF tall hexapod Queen, the 12-DoF armoured hexapod Bastion, the 18-DoF compact hexapod Tick, and the 12-DoF quadruped Leaper. All four robots share a unified observation template, action convention, simulation cadence, and a single closed-form multi-component reward function whose only per-morphology variation lives in a small set of weights and parameters. The reward fuses a velocity-tracking tent, a healthy survive bonus, a phase-locked gait-compliance bonus/cost pair, action regularisers, three safety penalties, and a posture anchor; no motion-capture data enters the reward at any point. We additionally provide hand-crafted Central Pattern Generator demonstrators per morphology, which serve both as fixed expert references and as sources of prior data for offline-to-online training. On this playground, we conduct a controlled empirical study comparing standard online algorithms (SAC, SPEQ, SOPE-EO) and methods augmented with prior data (SACfD, SPEQ-O2O, SOPE), and characterise how each paradigm copes with the playground's morphological diversity and animation-style stylistic constraints. Source code is available at https://github.com/CarloRomeo427/ARC_RL.git.

Reinforcement learning (RL) for quadruped locomotion commonly depends on fixed, hand-crafted, and Markovian reward functions that limit both interpretability of learned policies and lack explicit control over gait behaviors. We introduce a framework where distinct gaits are specified using parameterized constraints expressed in Signal Temporal Logic (STL). These include safety bounds, gait synchronization constraints, command tracking, and actuation bounds. From these specifications, we develop a reward shaping mechanism that provides learning agents a dense, continuous reward landscape that encodes desired behavior. We define parametric STL templates for three speed regimes (walking-trot, trot, bound), calibrate their parameters from reference rollouts, and compute rewards from using smooth approximations of STL robustness over the rollouts. The generated rewards can be used to provide shaped gradients compatible with Proximal Policy Optimization (PPO). We instantiate the approach on Google's Barkour quadruped robot in MuJoCo XLA (MJX). We use parallelization within the simulator to improve training speeds and use domain randomization to robustify learned policies. We show that compared to a baseline of hand-crafted rewards, the STL-shaped rewards yield tighter velocity tracking and more stable training. Videos can be found on our project website: https://stl-locomotion.github.io/.