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Dynamical systems provide a mathematical framework for understanding complexphysical phenomena. The mathematical formulation of these systems plays acrucial role in numerous applications; however, it often proves to be quiteintricate. Fortunately, data can be readily available through sensormeasurements or numerical simulations. In this study, we employ the SparseIdentification of Nonlinear Dynamics (SINDy) algorithm to extract amathematical model solely from data. The influence of the hyperparameter$\lambda$ on the sparsity of the identified dynamics is discussed.Additionally, we investigate the impact of data size and the time step betweensnapshots on the discovered model. To serve as a data source, a ground truthmathematical model was derived from the first principals, we focus on modelingthe dynamics of a generic 6 Degrees of Freedom (DOF) quadrotor. For the scopeof this initial manuscript and for simplicity and algorithm validationpurposes, we specifically consider a sub-case of the 6 DOF system forsimulation, restricting the quadrotor's motion to a 2-dimensional plane (i.e. 3DOF). To evaluate the efficacy of the SINDy algorithm, we simulate three casesemploying a Proportional-Derivative (PD) controller for the 3 DOF caseincluding different trajectories. The performance of SINDy model is assessedthrough the evaluation of absolute error metrics and root mean squared error(RMSE). Interestingly, the predicted states exhibit at most a RMSE of order ofmagnitude approximately $10^{-4}$, manifestation of the algorithm'seffectiveness. This research highlights the application of the SINDy algorithmin extracting the quadrotor mathematical models from data.

Data-driven Discovery of The Quadrotor Equations of Motion Via Sparse Identification of Nonlinear Dynamics