A Physics‐Informed Koopman Operator Framework for Decentralized Discrete‐Time Sequential Control of a Modular Aerial Parcel Delivery Robot

ABSTRACT

This paper presents a Physics‐Informed Koopman Operator (PIKO) framework integrated with a discrete‐time Sequential Action Control (SAC) for real‐time, decentralized control of a modular aerial parcel delivery robot composed of multiple independently actuated propeller modules. The proposed framework addresses the challenge of controlling modular multiagent aerial systems whose nonlinear dynamics are only partially known and subject to unmodeled aerodynamic effects. By employing a Strang‐splitting‐based hybrid Koopman formulation, the system dynamics are decomposed into known physics‐based and unknown data‐driven components. The continuous‐time Koopman matrix is identified from simulated first‐principles trajectories, while the discrete‐time Koopman matrix is learned from real flight data, yielding a globally linear and computationally efficient representation of the modular system. This split Koopman construction constitutes the central modeling contribution of the proposed framework, since it preserves the known first‐principles dynamics through the continuous‐time operator while restricting data‐driven learning to the residual dynamics through the discrete‐time operator. The resulting lifted linear model enables the closed‐form computation of SAC control actions without iterative optimization. The framework is experimentally validated on a modular aerial platform with decentralized Pixhawk 6X controllers communicating over uncomplicated application‐level vehicular computing and networking, where the SAC–PIKO controller demonstrates superior stability, precision, and robustness compared with adaptive and tube‐based Model Predictive Controllers. Across fixed‐point hover, L‐shaped, and square trajectory tracking tasks, the SAC–PIKO achieves up to 52% lower normalized root‐mean‐square error and over 40% reduction in dynamic time warping distance relative to baseline controllers, while maintaining subsecond computational latency and minimal memory footprint. The results highlight the effectiveness of embedding physics priors within Koopman operator learning to achieve scalable, data‐efficient, and real‐time control of modular aerial systems.