Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications

Reinforcement learning (RL) for legged robots is advancing locomotion, demonstrating its ability to adapt to new and challenging terrain. Traditionally, these RL locomotion frameworks are position-based, making the policy less adaptable to terrain types and requiring state estimation techniques in the observation space, i.e., linear velocity. Moreover, these RL frameworks often use small, lightweight quadrupeds that are limited in their viability for high-complexity tasks due to hardware constraints. This work explores an RL torque control framework for heavyweight high-torque quadrupeds. The RL framework in this paper can traverse rough terrain and effectively track a desired linear velocity without requiring knowledge of the agent's current velocity. Using Nvidia's Isaac Sim and Isaac Lab, simulation results of the RL torque control policy are shown on the Unitree B1 quadruped, achieving speeds of 3.5 m/s and 1.5 rad/s. In addition, the quadruped can walk up and down stairs without the aid of an exteroceptive sensor.

Learning-based quadrupedal locomotion typically relies on complex reward formulations that entangle task specification, operational limits, gait preference, and terrain adaptation within a single optimization objective. We instead treat these functions through distinct mechanisms: rewards for task specification, constraints for operational limits, energy minimization for gait preference, and exteroceptive perception for adapting energy use to terrain difficulty. We show that these components jointly enable efficient, terrain-adaptive locomotion, and that removing each component exposes a distinct failure mode. Our formulation removes explicit gait priors (including air-time, contact-count, and foot-clearance targets) in favor of emergent behavior. Compared to a conventional complex-reward baseline, our formulation achieves comparable terrain traversal while reducing cost of transport by 56% and operational-limit violations by 96%. The resulting policies transfer zero-shot to a physical Unitree Go2 using LiDAR-based elevation mapping. Project website with videos: https://tinyurl.com/locomposition.

Existing robot locomotion learning techniques rely heavily on the offline selection of proper reward weighting gains and cannot guarantee constraint satisfaction (i.e., constraint violation) during training. Thus, this work aims to address both issues by proposing Reward-Oriented Gains via Embodied Regulation (ROGER), which adapts reward-weighting gains online based on penalties received throughout the embodied interaction process. The ratio between the positive reward (primary reward) and negative reward (penalty) gains is automatically reduced as the learning approaches the constraint thresholds to avoid violation. Conversely, the ratio is increased when learning is in safe states to prioritize performance. With a 60-kg quadruped robot, ROGER achieved near-zero constraint violation throughout multiple learning trials. It also achieved up to 50% more primary reward than the equivalent state-of-the-art techniques. In MuJoCo continuous locomotion benchmarks, including a single-leg hopper, ROGER exhibited comparable or up to 100% higher performance and 60% less torque usage and orientation deviation compared to those trained with the default reward function. Finally, real-world locomotion learning of a physical quadruped robot was achieved from scratch within one hour without any falls. Therefore, this work contributes to constraint-satisfying real-world continual robot locomotion learning and simplifies reward weighting gain tuning, potentially facilitating the development of physical robots and those that learn in the real world.