Quadrotor Dynamics

Problem Statement

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

Model and Formulation

Translational dynamics:

$$m\ddot{p}=mg+R(\varphi ,\theta ,\psi )\left[\begin{array}{c}0\\ 0\\ T\end{array}\right]$$

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