Modeling and Dynamics Formulation

The goal of this section is to provide an overview and intuitive introduction on the basic concepts of modeling of aerial robotics. The ultimate goal of modeling is to derive the equations of motion - the dynamics of the vehicle. These equations are typically nonlinear and often very complicated. Therefore, modeling can also be considered an art: we typically aim to find the proper simplification that will allow us to capture all the dominant -and considered to be important- characteristics of the dynamic response of the system, while keeping the mathematical formulation of the model sufficiently simple. 

As typically in systems theory, a model is represented as an input-output relationship, as a set of differential equations (of some kind) that relate how the states (e.g. position, velocity, orientation, rate of change of orientation) change and evolve given that the inputs are excited or non-rest initial conditions are present. 

To develop a mathematical model of the dynamic response of an aerial vehicle, one needs to understand the fundamental concepts of coordinate system transformations, modeling of rigid bodies as well as the nature and formulations of the aerodynamic forces acting on it. This section contains the following subsections: 

1. Frame Rotations and Representations
2. Dynamics of a Multirotor Micro Aerial Vehicle
3. Dynamics of a Fixed-Wing Unmanned Aerial Vehicle