# Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications

arXiv: https://arxiv.org/abs/2607.00442 · HTML: https://mlsanity.com/paper/2607.00442/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 44 of its 79 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 30 of 44)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [Learning Robust Rewards with Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1710.11248/) (2017)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [Sim-to-Real: Learning Agile Locomotion For Quadruped Robots](https://mlsanity.com/paper/1804.10332/) (2018)
- [A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress](https://mlsanity.com/paper/1806.06877/) (2018)
- [Learning Agile Robotic Locomotion Skills by Imitating Animals](https://mlsanity.com/paper/2004.00784/) (2020)
- [Reward Machines: Exploiting Reward Function Structure in Reinforcement Learning](https://mlsanity.com/paper/2010.03950/) (2020)
- [Text2Reward: Reward Shaping with Language Models for Reinforcement Learning](https://mlsanity.com/paper/2309.11489/) (2023)
- [Legged Locomotion in Challenging Terrains using Egocentric Vision](https://mlsanity.com/paper/2211.07638/) (2022)
- [Reinforcement Learning With Temporal Logic Rewards](https://mlsanity.com/paper/1612.03471/) (2016)
- [MuJoCo Playground](https://mlsanity.com/paper/2502.08844/) (2025)
- [Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots](https://mlsanity.com/paper/2111.01674/) (2021)
- [Q-Learning for Robust Satisfaction of Signal Temporal Logic Specifications](https://mlsanity.com/paper/1609.07409/) (2016)
- [Dynamics Randomization Revisited:A Case Study for Quadrupedal Locomotion](https://mlsanity.com/paper/2011.02404/) (2020)
- [Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control](https://mlsanity.com/paper/1909.06586/) (2019)
- [Fast and Efficient Locomotion via Learned Gait Transitions](https://mlsanity.com/paper/2104.04644/) (2021)
- [DeepGait: Planning and Control of Quadrupedal Gaits using Deep Reinforcement Learning](https://mlsanity.com/paper/1909.08399/) (2019)
- [Dealing with Sparse Rewards in Reinforcement Learning](https://mlsanity.com/paper/1910.09281/) (2019)
- [Barkour: Benchmarking Animal-level Agility with Quadruped Robots](https://mlsanity.com/paper/2305.14654/) (2023)
- [Robust Online Monitoring of Signal Temporal Logic](https://mlsanity.com/paper/1506.08234/) (2015)
- [Learning Free Gait Transition for Quadruped Robots via Phase-Guided Controller](https://mlsanity.com/paper/2201.00206/) (2022)
- [Temporal-Logic-Based Reward Shaping for Continuing Reinforcement Learning Tasks](https://mlsanity.com/paper/2007.01498/) (2020)
- [Modular Deep Reinforcement Learning with Temporal Logic Specifications](https://mlsanity.com/paper/1909.11591/) (2019)
- [ManyQuadrupeds: Learning a Single Locomotion Policy for Diverse Quadruped Robots](https://mlsanity.com/paper/2310.10486/) (2023)

## Built on by (most cited first, 2 of 2)

- [From LLM-Generated Specifications to Learned Quadruped Locomotion](https://mlsanity.com/paper/2609.07111/) (2026)
- [Video2STL: Grounding VLM-Generated Temporal Specifications for Robot Learning](https://mlsanity.com/paper/2609.37519/) (2026)

## Abstract (arXiv)

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/.