Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2305.16500

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

Zeyad M. Manaa·Mohammed R. Elbalshy·Ayman M. Abdallah
View original source ↗Read source document ↗Export metadata ↓

Abstract

Dynamical systems provide a mathematical framework for understanding complex physical phenomena. The mathematical formulation of these systems plays a crucial role in numerous applications; however, it often proves to be quite intricate. Fortunately, data can be readily available through sensor measurements or numerical simulations. In this study, we employ the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm to extract a mathematical model solely from data. The influence of the hyperparameter $λ$ on the sparsity of the identified dynamics is discussed. Additionally, we investigate the impact of data size and the time step between snapshots on the discovered model. To serve as a data source, a ground truth mathematical model was derived from the first principals, we focus on modeling the dynamics of a generic 6 Degrees of Freedom (DOF) quadrotor. For the scope of this initial manuscript and for simplicity and algorithm validation purposes, we specifically consider a sub-case of the 6 DOF system for simulation, restricting the quadrotor's motion to a 2-dimensional plane (i.e. 3 DOF). To evaluate the efficacy of the SINDy algorithm, we simulate three cases employing a Proportional-Derivative (PD) controller for the 3 DOF case including different trajectories. The performance of SINDy model is assessed through the evaluation of absolute error metrics and root mean squared error (RMSE). Interestingly, the predicted states exhibit at most a RMSE of order of magnitude approximately $10^{-4}$, manifestation of the algorithm's effectiveness. This research highlights the application of the SINDy algorithm in extracting the quadrotor mathematical models from data.

Explore related subjects

math.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zeyad M. Manaa, Mohammed R. Elbalshy, Ayman M. Abdallah. 2023-11-05. Data-driven Discovery of The Quadrotor Equations of Motion Via Sparse Identification of Nonlinear Dynamics. https://arxiv.org/abs/2305.16500

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Pivoting technique for the circle homeomorphism group

We adapt Gou{ë}zel's pivoting technique to the circle homeomorphism group. As an application, we give different proofs of Gilabert Vio's probabilistic Tits alternative and Malicet's exponential synchronization.

math.DS↗
arXiv2026

Optimal rates of uniform convergence for weighted Birkhoff averages via almost all rotations

In this paper, we investigate weighted Birkhoff averages for toral translations associated with compactly supported weighting functions. By introducing several new analytical techniques, we establish optimal uniform convergence rates for almost all rotations and specific (or even all) initial points. Unlike the $\mathcal{O}(N^{-1})$ rate best achieved in classical ergodic theory, we show that these weighted averages exhibit polynomial or even exponential convergence. We establish the optimality of these convergence rates in multiple aspects, particularly concerning regularity indices across four distinct cases: finite differentiability, the $C^\infty$ class, logarithmic $C^\infty$ classes, and Gevrey classes. Our results demonstrate that the regularity of the observable essentially dictates the convergence rate; furthermore, we prove that no admissible choice of weighting function can, in general, overcome the lower bounds imposed by this regularity. In contrast to the generically slow convergence of standard time averages, this work provides an optimal and nearly complete characterization of rapid convergence for weighted Birkhoff averages.

math.DS↗
arXiv2026

Spectral theory of frame flows on closed hyperbolic manifolds

We prove a resolvent estimate for the generator of the frame flow on hyperbolic manifolds away from vertical lines of resonances. A byproduct of the proof is an optimal essential spectral gap property for the generator, hence giving another proof of exponential mixing of frame flows with respect to the volume measure of the frame bundle. This extends the result of [https://arxiv.org/abs/2005.08387v2] in dimension 3 to any dimension. We make extensive use of the Borel-Weil calculus developed in [https://arxiv.org/abs/2405.14846] to overcome difficulties of this higher-dimensional case.

math.DS↗