Section 47.6: Quadrotor dynamics and flight control

"The outer loop dreams of waypoints; the inner loop keeps the aircraft from arguing with gravity."

A Field-Tested Control Loop

Quadrotor State And Forces

A quadrotor state can be written as position $p$, velocity $v$, attitude $R$, body angular velocity $\omega$, and rotor speeds $\Omega_i$. The translational and rotational dynamics are commonly summarized as:

$$m\dot v = mg e_3 - f R e_3 + d, \qquad J\dot\omega = \tau - \omega \times J\omega.$$

The total thrust $f$ and body torque $\tau$ come from rotor thrusts through an allocation matrix. For a plus or x quadrotor, the command vector $[f,\tau_x,\tau_y,\tau_z]^T$ is generated by squared rotor speeds, so the high-level planner is really choosing targets that must remain inside a polytope defined by rotor saturation, battery voltage, and motor dynamics. If the planner asks for a force or moment outside that envelope, the mission is already infeasible even if the waypoint list looks smooth.

Cascaded Flight Control

Most practical quadrotor stacks use cascaded control: position control produces velocity or acceleration targets, velocity control produces attitude and thrust targets, attitude control produces body-rate targets, and rate control produces motor commands. The outer loops can be slower. The inner loops must be fast, stable, and well tuned.

PX4 makes this hierarchy visible in its controller diagrams: multicopter position, attitude, and rate controllers are separate contracts with clear setpoints and saturation points. For a learning system, those boundaries are not implementation trivia. They decide whether the policy should command a waypoint, velocity, attitude, body rate, or direct actuator target.

Geometric Control And MPC

Geometric control treats attitude directly on $SO(3)$, avoiding Euler-angle singularities. Nonlinear MPC adds constraints for thrust, tilt, obstacle clearance, geofences, and energy. The practical question is not which controller sounds more advanced, but which one meets the update deadline while keeping enough safety margin.

# Drone control evidence record.
# Roll out one flight-test metric packet after a wind-perturbed run.
# The fields mirror what a PX4 or simulator experiment should save.
from dataclasses import dataclass, asdict

@dataclass
class DroneMissionMetric:
    controller: str
    wind_mps: float
    mean_tracking_error_m: float
    max_tilt_deg: float
    failsafe_events: int

    def as_row(self) -> dict[str, object]:
        return asdict(self)

metric = DroneMissionMetric("geometric_controller", 6.0, 0.21, 24.0, 0)
print(metric)

Expected output: the printed record should show a controller name, a perturbation level, and at least one safety-relevant consequence such as tilt excursion or failsafe count. If your experiment logs only average tracking error, it hides the distinction between graceful recovery and a controller that briefly leaves the safe flight envelope.