This paper develops an all-encompassing nonlinear dynamic model of a quadrotor drone using Newton-Euler dynamics and a PD controller to control altitude and attitude simultaneously. The 12-state system model (position, velocity, Euler angles, and body angular rates) is modeled in Python using SciPy’s solve_ivp integrator. The control design comprises an altitude PD controller coupled with an attitude stabilizer using proportional mixing of the rotors’ angular velocities in order to generate roll, pitch, and yaw torques. Numerical simulation starting from an offset position (z = 1 m, small roll/pitch errors) demonstrates successful convergence to the hover reference (z = 2 m) within approximately 1.5 s. Altitude errors and fast damping of transient effects is achieved. The results demonstrate the success of the simple PD controller in vertical attitude control but reveal the underactuation problem causing slow horizontal movements. The limitations of the system, tuning considerations, and future work on full position control systems will be addressed. Rapid prototyping and teaching is possible with the open source framework in Python.

Keywords— Quadrotor UAV; Nonlinear dynamics; PD control; Hover stabilization; Python simulation; Underactuated systems