MS-PPO: Morphological-Symmetry-Equivariant Policy for Legged Robot Locomotion
Submitted to ICRA 2026
Sizhe Wei*, Xulin Chen*, Fengze Xie, Garrett E. Katz, Zhenyu Gan, Lu Gan.
[PDF] | [DEMO]
Abstract: Reinforcement learning has recently enabled impressive locomotion performance on quadrupeds and other articulated robots, yet most policy architectures remain morphology- and symmetry-agnostic, leading to inefficient training and weak generalization. This work introduces MS-PPO, a morphology-symmetry-equivariant policy learning framework that encodes robot kinematic structure and morphological symmetries directly into the policy network. We construct a graph-based neural architecture that is provably equivariant to morphological group actions, ensuring consistent responses under sagittal-plane reflections while maintaining invariance in value estimation. This design eliminates the need for reward shaping or data augmentation, which are typically required to enforce symmetry. We evaluate MS-PPO in simulation on Unitree Go2 and Xiaomi Cyberdog2 robots across multiple locomotion tasks, including trotting, pronking, slope walking, and bipedal turning, and further deploy policies on hardware. Extensive experiments show that MS-PPO achieves superior training stability, command generalization ability, and sample efficiency in challenging tasks, compared to state-of-the-art baselines. These findings demonstrate that embedding both kinematic structure and morphological symmetry into policy learning provides a powerful inductive bias for legged robot locomotion control. ... See More

Towards Dynamic Quadrupedal Gaits: A Symmetry-Guided RL Hierarchy Enables Free Gait Transitions at Varying Speeds
Submitted to ICRA 2026
Jiayu Ding*, Xulin Chen*, Garrett E. Katz, and Zhenyu Gan.
[PDF] | [CODE]
Abstract: Quadrupedal robots exhibit a wide range of viable gaits, but generating specific footfall sequences often requires laborious expert tuning of numerous variables, such as touch-down and lift-off events and holonomic constraints for each leg. This paper presents a unified reinforcement learning framework for generating versatile quadrupedal gaits by leveraging the intrinsic symmetries and velocity-period relationship of dynamic legged systems. We propose a symmetry-guided reward function design that incorporates temporal, morphological, and time-reversal symmetries. By focusing on preserved symmetries and natural dynamics, our approach eliminates the need for predefined trajectories, enabling smooth transitions between diverse locomotion patterns such as trotting, bounding, half-bounding, and galloping. Implemented on the Unitree Go2 robot, our method demonstrates robust performance across a range of speeds in both simulations and hardware tests, significantly improving gait adaptability without extensive reward tuning or explicit foot placement control. This work provides insights into dynamic locomotion strategies and underscores the crucial role of symmetries in robotic gait design. ... See More

Lipschitz-Regularized Critic Leads to Policy Robustness against Transition Dynamics Uncertainty
Submitted to IEEE RA-L
Xulin Chen*, Ruipeng Liu, Zhenyu Gan, Garrett E. Katz.
[PDF] | [CODE]
Abstract: Uncertainties in transition dynamics pose a critical challenge in reinforcement learning (RL), often resulting in performance degradation of trained policies when deployed on hardware. Many robust reinforcement learning (robust RL) approaches follow two strategies: enforcing smoothness in actor or actor-critic modules with Lipschitz regularization, or learning robust Bellman operators. The former does not address the impact of critic-only Lipschitz regularization on policy robustness, while the latter lacks comprehensive validation in real-world scenarios. Motivated by prior work, we propose WCVE-PGDLC, an algorithm based on Proximal Policy Optimization that integrates Projected Gradient Descent to solve the robust Bellman operator and learns a Lipschitz-regularized critic. Experimental results on two classic control tasks and a real-world locomotion task indicate that WCVE-PGDLC improves policy robustness and smoothness compared to baselines. ... See More