Koopman Analytical Modeling of Position and Attitude Dynamics: a Case Study for Quadrotor Control

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This research presents a novel, analytical, Koopman Operator based formulation for position and attitude dynamics which can be used to derive control strategies for underactuated systems.

• Compared to data driven Koopman based techniques, the analytical approach presented in this work is model based and allows for an exact linear representation of the original nonlinear position and attitude dynamics.
• In fact, the resulting infinite dimensional model, defined in the lifted state space, is linear in the autonomous component and state dependent in the control.
• A boundary study is carried on to define the range of validity of the finite truncation of the Koopman based model followed by a controllability and stabilizability analysis to show the feasibility of employing the derived model for control system design.