Physics-informed Split Koopman Operators for Data-efficient Soft Robotic Simulation

2025-01-31

AI Summary

High-fidelity simulation of soft robots typically demands extensive labeled data and incurs high modeling costs. To address this, this paper proposes a hybrid modeling framework that integrates physical priors with Koopman operator theory. We innovatively adopt the Strang splitting scheme to construct a continuous–discrete coupled Koopman operator framework and design a physics-informed split identification mechanism that jointly leverages sparse trajectory measurements and phase-space data. The method achieves significantly improved dynamical fidelity under small-sample conditions, eliminating reliance on large-scale simulation-generated labeled datasets. Experimental validation on a tendon-driven soft robotic arm demonstrates a one- to two-order-of-magnitude reduction in shape reconstruction error, confirming the approach’s dual advantages: high modeling accuracy and minimal data requirement.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Low Level & Physics-based Vision

Application Category

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

Abstract

Koopman operator theory provides a powerful data-driven technique for modeling nonlinear dynamical systems in a linear framework, in comparison to computationally expensive and highly nonlinear physics-based simulations. However, Koopman operator-based models for soft robots are very high dimensional and require considerable amounts of data to properly resolve. Inspired by physics-informed techniques from machine learning, we present a novel physics-informed Koopman operator identification method that improves simulation accuracy for small dataset sizes. Through Strang splitting, the method takes advantage of both continuous and discrete Koopman operator approximation to obtain information both from trajectory and phase space data. The method is validated on a tendon-driven soft robotic arm, showing orders of magnitude improvement over standard methods in terms of the shape error. We envision this method can significantly reduce the data requirement of Koopman operators for systems with partially known physical models, and thus reduce the cost of obtaining data.

Problem

• Soft Robot Simulation
• Data Efficiency
• Cost Reduction

Innovation

• Machine Learning
• Koopman Operator
• Soft Robot Simulation