Koopman Operator Based Modeling and Control of Quadrotors

Abstract

A novel set of Koopman observables is introduced to transform the nonlinear quadrotor dynamics into a linear representation. The proposed approach is a combination of feedback linearization and Koopman observables, and it offers the advantage of overcoming the quadrotor underactuation problem. Compared to previous approaches that use dynamic inversion for both position and attitude dynamics, in this work, only the attitude dynamics are feedback linearized. The formulation is shown to be considerably more compact and capable of achieving lower model mismatch error when compared to already published similar work. The advantage of this formulation is that it allows for designing control architectures exploiting well-known linear control theory. As such, a Koopman based linear quadratic (LQ) controller is tested via numerical simulations to show applicability and implementability of the approach.