Quadrotor Dynamics

Problem Statement

Quadrotor dynamics modeling provides the foundational equations used by estimators, planners, and controllers.

Model and Formulation

Translational dynamics:

$$ m\ddot{p}=mg + R(\phi,\theta,\psi)\begin{bmatrix}0\0\T\end{bmatrix} $$

Rotational dynamics:

$$ I\dot{\omega} + \omega \times I\omega = \tau $$

with thrust T and body torque vector \tau.

Practical Notes

• Model fidelity depends on aerodynamic drag and propeller assumptions.
• Hover linearization is valid only near small angles and low rates.
• Actuator limits and delays must be represented for realistic control studies.

Evidence

References

• Bouabdallah, Design and Control of Quadrotors (EPFL Thesis)
• Beard and McLain, Small Unmanned Aircraft

Related Algorithms

• PID Hover
• LQR Hover