Compound Koopman data-driven control for an inchworm robot: Validation through virtual experiments

Locomotion control of inchworm robots presents significant challenges due to their highly nonlinear dynamics and complex interactions with the environment. Traditional control methods often struggle with achieving precise tracking and adaptive performance in dynamic conditions. To address these limitations, this article proposes a novel data-driven compound control system that integrates fractional proportional-integral derivative (FPID) control with Koopman operator theory. Unlike conventional approaches, which rely on direct nonlinear control or simplified linear approximations, our method leverages data-driven modeling to transform the nonlinear dynamics into a linear representation, making control design more systematic and scalable. A deep neural network is trained to identify the Koopman operator, enabling an FPID controller to operate within this transformed space for improved tracking accuracy and robustness. The proposed framework is validated using NVIDIA Isaac SIM simulation software, demonstrating superior locomotion efficiency and tracking performance compared to existing control strategies. This study advances the control of bio-inspired robots by bridging fractional-order control with data-driven Koopman-based modeling, addressing the fundamental challenge of achieving high-precision locomotion in complex environments.