Learning Legged MPC with Smooth Neural Surrogates

TL;DR

This paper introduces smooth neural surrogates for learned dynamics in legged MPC, significantly enhancing robustness, reliability, and performance in complex locomotion tasks by addressing non-smoothness and model error issues.

Contribution

The authors propose a novel neural network with tunable smoothness and a heavy-tailed training likelihood to improve learned dynamics for legged MPC, enabling better contact handling and robustness.

Findings

Substantial reduction in cumulative cost (10-50%) on simple behaviors.

Large performance gains and improved reliability in challenging regimes.

Order-of-magnitude improvements in robustness and execution success.

Abstract

Deep learning and model predictive control (MPC) can play complementary roles in legged robotics. However, integrating learned models with online planning remains challenging. When dynamics are learned with neural networks, three key difficulties arise: (1) stiff transitions from contact events may be inherited from the data; (2) additional non-physical local nonsmoothness can occur; and (3) training datasets can induce non-Gaussian model errors due to rapid state changes. We address (1) and (2) by introducing the smooth neural surrogate, a neural network with tunable smoothness designed to provide informative predictions and derivatives for trajectory optimization through contact. To address (3), we train these models using a heavy-tailed likelihood that better matches the empirical error distributions observed in legged-robot dynamics. Together, these design choices substantially improve the reliability, scalability, and generalizability of learned legged MPC. Across zero-shot locomotion tasks of increasing difficulty, smooth neural surrogates with robust learning yield consistent reductions in cumulative cost on simple, well-conditioned behaviors (typically 10-50%), while providing substantially larger gains in regimes where standard neural dynamics often fail outright. In these regimes, smoothing enables reliable execution (from 0/5 to 5/5 success) and produces about 2-50x lower cumulative cost, reflecting orders-of-magnitude absolute improvements in robustness rather than incremental performance gains.