Learning Legged MPC with Smooth Neural Surrogates

2026-01-17

AI Summary

This work addresses the challenges faced by learning-based model predictive control (MPC) for legged robots, which are often hindered by contact-induced discontinuities, non-physical nonsmoothness, and non-Gaussian errors. To overcome these issues, the authors propose a “smooth neural surrogate”—a neural network with tunable smoothness that preserves the true contact dynamics while eliminating unphysical nonsmooth behaviors. Furthermore, they enhance robustness by modeling prediction errors with a heavy-tailed likelihood function. Evaluated on zero-shot legged locomotion tasks, the proposed approach substantially outperforms standard neural dynamics models: it reduces cumulative cost by 10–50% on simple behaviors and achieves a dramatic improvement in challenging scenarios, raising success rates from 0% to 100% and decreasing costs by factors of 2 to 50.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Natural Language Processing: Safety and Robustness
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

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.

Problem

• legged robotics
• model predictive control
• neural dynamics
• non-smoothness
• contact transitions

Innovation

• smooth neural surrogate
• model predictive control
• legged robotics
• heavy-tailed likelihood
• trajectory optimization