Koopman-Based Model Predictive Control of Quadrotors

A novel formulation of model predictive control (MPC) coupled with Koopman operator theory is presented and tested for the trajectory tracking problem of a quadrotor UAV. The analytical derivation of Koopman observables allows for the quadrotor model to be written as a fully-actuated quasi-linear system which enables the control problem to be posed as a linear control problem. In fact, the adopted approach embeds the quadrotor nonlinear dynamics into a quasi-linear form through the evolution of the Koopman op-erator generalized eigenfunctions, a special kind of Koopman observables. Hence, the linear MPC formulation in Koopman coordinates is equivalent to a nonlinear implementation in the original state space. Moreover, in an enhancement from the standard feedback linearization, the Koopman based quadro-tor model does not present underactuation, which drastically simplifies the computational requirement for the solution of the MPC optimization problem. The presented methodology is tested through detailed numerical simulations and results are compared to single-loop nonlinear MPC (NMPC). The satisfactory tracking performance are additionally enhanced by the obtained computational speedup which is crucial for real time implementation of flight controllers.