From Spring Mass Damper Dynamics to Drone Control Models

Abstract

Complex dynamical systems can be modeled clearly by building them from simpler systems with similar mathematical structure. We begin with a one-dimensional spring-mass-damper system to establish a basic state-space framework, then extend this framework to three-dimensional translational motion and quaternion-based rotational motion. The 3D model is finally combined with rotor dynamics into a unified first-order nonlinear drone model. Numerical simulations are used to compare the behavior of the intermediate models and the final drone model. Our results show that simpler models provide a useful foundation for constructing and interpreting more complex systems, while also showing where that foundation must be extended to account for nonlinear orientation dynamics and input-driven control.