Learning Symmetric Legged Locomotion via State Distribution Symmetrization

Abstract

Morphological symmetry is a fundamental characteristic of legged animals and robots. Most existing Deep Reinforcement Learning approaches for legged locomotion neglect to exploit this inherent symmetry, often producing unnatural and suboptimal behaviors such as dominant legs or non-periodic gaits. To address this limitation, we propose a novel learning-based framework to systematically optimize symmetry by state distribution symmetrization. First, we introduce the degree of asymmetry (DoA), a quantitative metric that measures the discrepancy between original and mirrored state distributions. Second, we develop an efficient computation method for DoA using gradient ascent with a trained discriminator network. This metric is then incorporated into a reinforcement learning framework by introducing it to the reward function, explicitly encouraging symmetry during policy training. We validate our framework with extensive experiments on quadrupedal and humanoid robots in simulated and real-world environments. Results demonstrate the efficacy of our approach for improving policy symmetry and overall locomotion performance.