Quadrotor

Full 6DOF Newton-Euler rigid-body dynamics with per-motor first-order response.

R. Mahony, V. Kumar, P. Corke, "Multirotor Aerial Vehicles: Modelling, Estimation and Control of Quadrotor", IEEE RAM, 2012. doi:10.1109/MRA.2012.2206474

Source: flybots/vehicles/multirotor/

Quick start

import numpy as np
from flybots.vehicles.multirotor import Quadrotor

quad = Quadrotor()
quad.reset(position=np.array([0.0, 0.0, 2.0]))

hover = quad.hover_wrench()
for motor in quad.motors:               # motors start stopped
    motor.reset(motor.thrust_to_omega(hover[0] / 4.0))

for _ in range(500):
    quad.step(hover, 0.005)

State and control

state  = [x, y, z, φ, θ, ψ, vx, vy, vz, p, q, r]
wrench = [T, τx, τy, τz]

Position and velocity are world ENU; rates are body-frame. The control input is a body wrench — total thrust along body +z plus three moments.

Actuation chain

The wrench is not applied directly. It goes through the mixer and the motors, so the aircraft feels the thrust the motors can actually produce:

wrench -> mixer -> per-motor thrust -> ω command
                                        │
                              first-order motor lag (τ)
                                        │
                        actual ω -> actual thrust -> actual wrench

quad.get_motor_speeds()     # rad/s, per motor
quad.params.motor_tau       # motor time constant [s]
quad.params.omega_max       # saturation

This is why an instantaneous step in commanded thrust does not produce an instantaneous change in acceleration, and why aggressive controllers can excite the motor dynamics.

Mixer

Mixer maps between wrench and per-motor thrust for x and + frames, using the arm length and the thrust/torque coefficients. Yaw torque comes from the reaction torque of the counter-rotating pairs.

Both matrices are derived from the rotor positions and spin directions rather than written out by hand, which is what lets the same code mix a hexacopter or a coaxial X8 — see Multirotor. The X-frame column order is rear-left, rear-right, front-right, front-left, spinning CCW, CW, CCW, CW.

Presets

from flybots.vehicles import VehiclePreset, create_quadrotor

quad = create_quadrotor(VehiclePreset.CRAZYFLIE)      # 27 g nano
quad = create_quadrotor(VehiclePreset.DJI_MINI)       # 249 g
quad = create_quadrotor(VehiclePreset.RACING_250)     # 1.5 kg (default)
quad = create_quadrotor(VehiclePreset.DJI_MATRICE)    # 3.6 kg
quad = create_quadrotor(VehiclePreset.RACING_250, mass=2.0)   # override

Preset	Mass	Arm	ω max
CRAZYFLIE	0.027 kg	46 mm	2500 rad/s
DJI_MINI	0.249 kg	110 mm	1800 rad/s
RACING_250	1.5 kg	175 mm	1100 rad/s
DJI_MATRICE	3.6 kg	320 mm	800 rad/s

The three-order-of-magnitude mass span is a useful stress test for any controller you write.

Numerical guards

step() clamps body rates to ±50 rad/s, wraps Euler angles to [-π, π], replaces any NaN that appears, and stops the aircraft sinking below z = 0. These exist so a diverging controller produces a visibly bad trajectory rather than a wall of NaN.

Control stack

The cascaded controllers in flybots.control layer over this model:

PositionController -> VelocityController -> AttitudeController -> RateController

with FlightController composing them and StateManager running the ARM → TAKEOFF → HOVER → TRACKING → LAND mode sequence.

Quadrotor is a preset over the general Multirotor model, so everything here applies to a hexacopter or an octocopter too.

See also

• Multirotor — any rotor count
• Quadrotor dynamics simulation
• PID hover
• LQR hover