Learning-Based Kinematic Residual Compensation with Latent Regime Mixture-of-Experts for Quadruped Odometry

Reliable state estimation on low-cost quadruped robots is hindered by sensor noise, mechanical backlash, and structural compliance. Current methods face distinct limitations: the reliance on precise contact sensors in pure kinematics, training-coverage dependence in end-to-end networks, and sub-optimal mode averaging in conventional hybrid models. To address this, we propose a physics-informed Latent Regime Mixture-of-Experts (MoE) framework. First, we establish a robust kinematic baseline using a heuristic contact estimator to bypass unreliable force sensing and provide a stable physical prior. Second, we introduce a lightweight MoE network to predict nonlinear velocity residuals. By inferring latent motion regimes from a temporal window of proprioceptive history, the network performs regime-aware routing and fuses specialized experts for context-aware residual compensation. Consequently, the framework provides both accurate velocity corrections and adaptive covariance estimation for downstream fusion. Furthermore, due to the limited availability of dense velocity ground truth in self-collected outdoor data, we adopt a two-stage training strategy combining indoor velocity and sparse outdoor positional supervision. Experiments demonstrate a 14.2% velocity RMSE reduction on the ANYmal benchmark and a 28.2% drift reduction on Unitree Go1 across diverse scenarios. The system operates at over 240 Hz on an embedded Jetson platform.