Symbolic Learning of Interpretable Reduced-Order Models for Jumping Quadruped Robots

2025-08-04

AI Summary

Addressing the challenges of high-dimensional, nonlinear dynamics modeling and poor interpretability in quadrupedal jumping robots, this paper proposes a reduced-order modeling method that integrates physical priors with sparse symbolic regression. We design a neural latent-space architecture incorporating physics-based constraints and enhance the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm to automatically discover interpretable, physically meaningful, and predictive nonlinear dynamical equations in a low-dimensional latent space. Our approach overcomes structural and representational limitations of conventional actuated Spring-Loaded Inverted Pendulum (aSLIP) models, significantly improving modeling fidelity across diverse jumping behaviors—including stationary hopping and forward leaping. Simulation and real-robot experiments demonstrate that the proposed model outperforms existing baselines in fitting accuracy, generalization capability, and interpretability. This work establishes a reliable, transparent dynamical foundation for jumping control synthesis, stability analysis, and human–robot collaborative design.

Technology Category

• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Reduced-order models are essential for motion planning and control of quadruped robots, as they simplify complex dynamics while preserving critical behaviors. This paper introduces a novel methodology for deriving such interpretable dynamic models, specifically for jumping. We capture the high-dimensional, nonlinear jumping dynamics in a low-dimensional latent space by proposing a learning architecture combining Sparse Identification of Nonlinear Dynamics (SINDy) with physical structural priors on the jump dynamics. Our approach demonstrates superior accuracy to the traditional actuated Spring-loaded Inverted Pendulum (aSLIP) model and is validated through simulation and hardware experiments across different jumping strategies.

Problem

• Develop interpretable reduced-order models for jumping quadruped robots
• Simplify high-dimensional nonlinear dynamics into low-dimensional latent space
• Improve accuracy over traditional aSLIP model for jumping strategies

Innovation

• Combines SINDy with physical structural priors
• Learns low-dimensional latent space dynamics
• Outperforms traditional aSLIP model accuracy