Towards Dynamic Quadrupedal Gaits: A Symmetry-Guided RL Hierarchy Enables Free Gait Transitions at Varying Speeds

TL;DR

This paper tackles the challenge of dynamic gait generation for quadrupeds by enabling a single policy to switch among multiple gaits without predefined sequences. It introduces a symmetry-guided reinforcement learning framework that encodes temporal, morphological, and time-reversal symmetries into gait parameterization and rewards, trained with PPO on the Unitree Go2. The results show accurate velocity tracking, coordinated footfall across trotting, bounding, half-bounding, and galloping, and successful sim-to-real transfer with robustness to perturbations. The work demonstrates that symmetry can dramatically simplify reward design and expand gait repertoires for real-world dynamic locomotion.

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.

Figures (7)

• Figure 1: Concept overview of the symmetry-guided reinforcement learning framework. User commands and gait parameters feed an MLP policy with temporal and morphological symmetries, enabling a single policy to generate trotting, bounding, half-bounding, and galloping on the Unitree Go2 without predefined trajectories.
• Figure 2: Overview of the proposed framework. Left: User commands ($v_x^{\text{cmd}}, v_y^{\text{cmd}}, \omega_{\text{yaw}}^{\text{cmd}}$) and selected gait sequences (trotting, bounding, half-bounding, galloping) are mapped into gait parameters $\mathbf{\boldsymbol{\Gamma}} = [\theta_{\text{LH}}, \theta_{\text{LF}}, \theta_{\text{RF}}, \theta_{\text{RH}}, v_x^{\text{cmd}}]$. Middle: Training framework design integrates reward function design (command tracking, smoothness, temporal and morphological symmetry), along with time-reversal mapping, domain randomization, and velocity/gait resampling. Right: The framework drives training of our MLP policy network, which outputs joint targets tracked by a PD controller on the Unitree Go2 robot, with a user interface providing real-time command input.
• Figure 3: Footfall patterns of four quadrupedal gaits. Colored bars denote stance and blanks denote swing. LH, LF, RF, RH indicate left hind, left front, right front, and right hind legs. These examples span the symmetry classes analyzed.
• Figure 4: Velocity tracking across four gaits under varying commanded forward speeds. (A) Sequential transitions with $v_{x}^{\text{cmd}} \in \{-2,\,-1,\,0.2,\,2\}$ [m/s]. (B) Tracking of $v_{y}^{\text{cmd}}=0$ during the same test.
• Figure 5: Gait tracking at $v_{x}^{\text{cmd}}=0.5~[\text{m/s}]$. (A) Representative frames of trotting, bounding, half-bounding, and galloping, including transition phases. (B) Desired footfall sequences (hollow bars) compared with realized touchdown sequences in simulation (solid bars).