Enhancing Fractional-Order Control of Inchworm Robots via KAN-Based Koopman Operator Learning

Previous work on inchworm robot control employed a Convolutional Neural Network (CNN)-based Koopman operator framework integrated with a Fractional-Order PID (FOPID) controller to handle nonlinear locomotion dynamics. While effective, the CNN based model exhibited limitations in generalization, convergence consistency, and inter pretability due to its dependence on data-driven feature extraction. Building on this foundation, the present study introduces a Kolmogorov–Arnold Network (KAN)-based Koopman learning framework that replaces the CNN with spline-based functional map pings to achieve smoother and more structured representations of the system's dynamics. The Koopman operator, optimized online through the KAN model, linearizes the under lying nonlinear motion, enabling robust FOPID-based trajectory regulation. Through simulation and experimental validation, the KAN-based Koopman control demonstrates significant improvements in tracking precision, dynamic adaptability, and robustness to external perturbations compared to the CNN-based approach. The results highlight the ef fectiveness of integrating KAN-enhanced Koopman operator theory with fractional-order control as a promising pathway for achieving interpretable, data-efficient, and high performance control of nonlinear robotic systems.