Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications

arXiv:2607.00442v2 Announce Type: replace-cross Abstract: Reinforcement learning (RL) for quadruped locomotion commonly depends on fixed, hand-crafted, and Markovian reward functions that may limit interpretability of learned policies and may 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. Compared with hand-crafted rewards, an expert-switching oracle, and Text2Reward, Human-STL maintains high command-tracking success across the evaluated speed range while exhibiting substantially higher consistency with the intended speed-dependent gait structures. Videos can be found on our project website: https://stl-locomotion.github.io/.