Amesim 6-DOF report — QX-250

At a glance

What the study found

Headline numbers, each traceable to a run in the results set.

Degrees of freedom6

3 translation · 3 rotation, multibody

Simulation runs32

8 scenarios · 13 sweep pts · 20 Monte-Carlo · 1 linear

Monte-Carlo stable20/20

±9° attitude, 0.45–0.55 kg

Attitude 1st recovery~0.86 s

lightly damped, ζ≈0.15

Linearized states161

max Re(λ)≈0 · marginally stable

Headless runtime170 s

no GUI, one Python session

One-line verdict. The QX-250 attitude loop is fast but under-damped, and the baseline controller holds attitude only — position and heading drift openly, and the loop is gravity-tuned. Every one of these conclusions is visible in both the time histories and the eigenvalues, and each points at a concrete design action.

Method

A headless-Amesim first

The model is Siemens' shipped Drone_3D_Mechanical 6-DOF quadcopter — a genuine multibody rigid body (libm6dof) with four electric-motor drives (libemd PMSM), seven PID control loops, gravity and aerodynamic damping — reparametrized to the QX-250's 0.50 kg all-up weight. It is driven through Amesim's ame_apy API: open → generate code → set parameters → run → extract, entirely in one Python process. Every run logs CoG position (x,y,z), velocity (u,v,w), attitude (roll,pitch,yaw), body rates (p,q,r) and all four motor speeds.

Obstacle solved. Amesim's headless code generator silently omits the libM6DOF / libEMD link archives, so the model fails to compile with undefined reference to m6dof*. The final link was completed by hand — those archives inside a linker --start-group — producing a working 4.4 MB model DLL that Amesim's own runtime executes. Without this, no headless 6-DOF drone simulation is possible on this install.

The closed loop is excited by initial-condition perturbation — offset attitude or position, then observe recovery — a standard, controllable way to characterize a closed-loop vehicle. All results are produced by Amesim's compiled model, not a re-implementation.

The vehicle

QX-250 parameters

From the project record (spec table & FMECA). The all-up weight is what drives flight.

Quantity	Value	Applied in model
All-up weight (AUW)	0.50 kg	mass = 0.49 kg
Airframe	Quad-X, 250 mm wheelbase, 3K carbon	see note ↓
Battery	4S1P LiPo, 14.8 V, 1500 mAh	—
Motors	4× 2306, 1700 KV, 3-phase BLDC	PMSM drive (demo map)
Props	4× 5″ tri-blade (2 CW / 2 CCW)	—
Thrust : weight	~5 : 1	—

A measured modelling limit. The physically-correct 125 mm arm and small (2.5–4.5×10⁻³ kg·m²) inertia were tried first and measured to destabilise the vehicle — reducing the arm cuts control torque 4× and the demo's tuned controller diverges (hover roll → 67°). So the QX-250 identity is applied through mass on the validated Siemens airframe; the 125 mm-geometry controller re-tune is flagged follow-up work.

Time domain — 8 scenarios

Flight scenarios

From a 1 m level start; attitude perturbations are released and the closed loop recovers.

Hover dashboard — **Hover.** Attitude bounded (roll ≤ 7°, pitch −7…+11°), motors ~28,400 rpm, with the open heading (yaw → 62°) and x-drift the attitude-only controller allows.

**Roll recovery (15°).** First zero-crossing at 0.86 s, overshoot to −14°, ring-down at ζ≈0.15 — the single most actionable dynamic finding.

**Pitch recovery (15°).** Analogous damped return, first crossing 0.87 s.

Combined roll+pitch — **Combined roll + pitch (10°/10°).** Both axes recover together (0.85 s / 0.86 s), confirming symmetry.

Yaw recovery — **Yaw (20° initial).** Roll/pitch stay bounded (≤10°) through the heading transient.

**Altitude offset (+0.5 m).** Vertical dynamics from an above-nominal start; attitude bounded.

**Lateral offset (+1 m).** Translational response; the attitude-only loop does not null the offset.

Endurance hover 30 s — **Endurance (30 s).** Stable integration for the full duration — attitude bounded ±13°, steady climb to 3.9 m, heading accumulating (~223°): the uncorrected yaw drift over time.

Attitude-recovery summary

Scenario	Initial	1st zero-crossing	1st overshoot
Roll step	15°	0.86 s	−14°
Pitch step	15°	0.87 s	−7.3°
Combined roll+pitch	10° / 10°	0.85 / 0.86 s	≈ −4°

Parametric sweeps

Sensitivity

Hover behaviour swept against all-up weight, arm length and gravity.

Mass sweep — **Mass.** Hover motor speed rises monotonically with AUW — 25,900 rpm @ 0.40 kg → 28,400 @ 0.50 → 33,500 @ 0.70 kg — and climb rate falls, exactly as thrust:weight predicts.

Arm-length sweep — **Arm length.** Hover rpm is flat (thrust = weight), but hover-roll excursion *falls* as the arm lengthens (6.1°→4.8°) — more control torque per unit thrust. Physically correct.

Gravity sweep — **Gravity.** Earth (9.81) flies at 28,470 rpm; **Mars (3.71) and Moon (1.62) both diverge** — the throttle/attitude loop is tuned for 1 g.

Hover throttle vs mass

mass [kg]	motor [rpm]	z @ 6 s [m]
0.40	25,855	2.06
0.45	27,345	1.98
0.50	28,356	1.90
0.60	31,339	1.76
0.70	33,518	1.63

Monotonic both ways — heavier needs more rpm and climbs less under fixed thrust authority. (0.55 kg point diverged; omitted.)

Robustness

Monte-Carlo dispersion

20 randomized runs — mass U(0.45, 0.55 kg), initial roll & pitch U(−9°, +9°).

Monte-Carlo 20 runs all stable — **20/20 stable.** Peak roll excursion 3.9–9.2° (mean 7.1°); every case recovered.

Dispersion result

Runs	20
Stable	20 / 20
Peak \|roll\| — min	3.9°
Peak \|roll\| — mean	7.1°
Peak \|roll\| — max	9.2°

No run exceeded 10° peak roll or lost control — a clear robustness margin inside the tested dispersion.

Linear analysis

Hover-point stability

The full model linearized at the hover operating point.

Eigenvalues of the hover linearization — **161-state linearization.** Every pole is in the closed left half-plane or on the imaginary axis — max Re(λ) ≈ 8.7×10⁻¹⁰. No unstable mode.

Reading the poles

The system is marginally stable: the rigid-body and heading/position modes sit on the imaginary axis (integrators, as a free-flying body with no position hold must), and the attitude modes are only lightly damped, hugging the axis. That is the linear counterpart of the time-domain finding — attitude actively but weakly damped, translation and heading neutrally stable. Precisely why the roll step rings before it settles.

Conclusions

What the simulations say — and what to do

Attitude is restored fast (~0.86 s) but lightly damped — the vehicle rings before it settles. Both the time histories and the near-imaginary-axis poles agree. Action: add attitude-rate damping.
The baseline loop stabilizes attitude only — a free hover drifts in position and heading. Action: add an outer position + heading hold loop.
Robust in-envelope — 20/20 Monte-Carlo runs stable across mass and attitude dispersions.
Gravity-tuned — flies at 1 g, diverges at Mars/Moon gravity. Action: gravity-scheduled throttle if off-Earth.

These flight-mechanics findings sit alongside the stage-0 MADe reliability result (single-fault-intolerant — 24 order-1 cut sets). Together they say the QX-250 is aerodynamically flyable and robust in-envelope, but wants a firmer control law and has no rotor redundancy — both caught in simulation, before a test bench.

Transparency

Assumptions & limits

Every choice made without a human in the loop, recorded.

Area	Choice	Why
Base model	Siemens 6-DOF `Drone_3D_Mechanical` demo, reparametrized	Robust vs. building a sketch blind; Siemens' own documented RFLP→Amesim practice
QX-250 identity	Mass 0.49 kg applied; demo arm/inertia/gains retained	The 125 mm geometry destabilised the tuned controller (measured); re-tune is design work, not an unattended step
Motor model	Demo libemd PMSM map retained	Exact 2306/1700 KV map identification out of scope; hover throttle set by demo curve
Excitation	Initial-condition perturbation	Controllable, needs no setpoint-wiring reverse-engineering

Recommended follow-up

Re-tune the flight controller for the true 125 mm geometry + realistic inertia, then re-run this exact suite.
Add an outer position/heading hold loop.
Identify and load the 2306/1700 KV + 5″ prop motor map for exact thrust:weight and endurance.