Learning Legged MPC with Smooth Neural Surrogates

Samuel A. Moore, Easop Lee, Boyuan Chen

Keywords: Model Predictive Control, Neural Dynamics, Legged Robots, Learning-Based Control

TL;DR: Smooth, robustly trained neural dynamics enable reliable and scalable MPC for legged robots, overcoming the instability of standard learned models in contact-rich settings.

Abstract: Deep learning and model predictive control (MPC) are complementary in legged robotics, but integrating learned dynamics with online planning remains challenging. Neural network models introduce three key issues: (1) stiff transitions from contact events inherited from data; (2) additional non-physical local nonsmoothness; and (3) non-Gaussian errors induced by rapid state changes. We address (1) and (2) with the smooth neural surrogate, a network with tunable smoothness that yields informative predictions and derivatives for trajectory optimization through contact. To address (3), we train with a heavy-tailed likelihood that better matches empirical error distributions. Together, these choices improve the reliability, scalability, and generalizability of learned legged MPC. Across zero-shot locomotion tasks of increasing difficulty, smooth neural surrogates with robust learning reduce cumulative cost in well-conditioned settings (typically $\approx$10--50\%) and deliver substantially larger gains where standard neural dynamics fail, enabling reliable execution (0/5 $\rightarrow$ 5/5 success) and orders-of-magnitude improvements in robustness.

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Submission Number: 10