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

TL;DR

This paper introduces a physics-informed Koopman operator method that enhances soft robotic simulation accuracy with limited data, leveraging splitting techniques to combine continuous and discrete models.

Contribution

The paper presents a novel physics-informed Koopman operator identification approach using Strang splitting, improving data efficiency and accuracy for soft robot modeling.

Findings

Significant reduction in shape error compared to standard methods.

Orders of magnitude improvement in simulation accuracy.

Effective use of small datasets for complex soft robotic systems.

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.