A Novel Real-Time Data-Driven Fractional-Order Proportional–Integral–Derivative Control of a Worm Robot Using Koopman Theory

Abstract Conventional control approaches for inchworm robots often exhibit limitations in achieving high-precision trajectory tracking and robust adaptability due to dynamic and uncertain interaction conditions inherent to their locomotion. To address this, we present the effectiveness of integrating fundamental control strategies such as proportional–integral–derivative (PID), model predictive control (MPC), and fractional-order PID (FOPID) controllers, with Koopman operator theory, which is demonstrated in managing the nonlinear dynamics of worm robot locomotion. We leverage data-driven modeling using the Koopman operator, transforming nonlinear dynamics into infinite-dimensional linear operators, and enabling the application of linear control strategies. The Koopman operator is calculated using a deep neural network to optimize it at each time-step, ensuring the highest possible accuracy. Through rigorous simulations and experimental validation, their capability to regulate movement, maintain stability, and achieve precise trajectory tracking in worm robots is highlighted. The study underscores how conventional controllers provide a practical and computationally efficient solution for nonlinear robotic control, making them viable options for real-world applications where adaptability and reliability are crucial.