Does the best rotor cant angle change when yaw reaction torque scales with propeller size?

research/codesign-aero-cant-kappa

Does the interior cant optimum survive a reaction torque that grows with propeller diameter (κ = c·D) instead of a fixed 0.016 m? In simulation yes: for c = 0.06, 0.126 and 0.25 the joint co-design reaches 12.5°, 12.3° and 11.8° held-out attitude error with the bound at 80°, picks 33–41° each time, and cant still beats no cant in 5 of 5 seeds; the gain is largest (−4.8°) for the weakest reaction torque.

15 tests

What it found

Follow-up to codesign-aero-cant-bound, where the yaw reaction torque per newton of thrust κ was a fixed 0.016 m whatever the propeller. For a propeller Q/T = (C_P/C_T) D/(2π), so here κ = c D with c swept over 0.06, 0.126 and 0.25 (C_P/C_T about 0.38, 0.79, 1.6; 0.126 reproduces 0.016 m at 127 mm). Joint CMA-ES over arm length, propeller size, cant and six PID gains (1920 evaluations, 5 seeds, 64 held-out episodes), cant bound 0, 35° or 80°. At bound 80° the held-out error is 12.54°, 12.28° and 11.84° for c = 0.06, 0.126, 0.25 (fixed κ: 12.30°); with no cant it is 17.30°, 16.26°, 14.13° (fixed: 15.18°), so cant helps by 4.8°, 4.0° and 2.3°, better in 5 of 5 paired seeds each. The chosen cant is 33–41° at bound 80°, and the 35° bound loses at most 0.03° against it. Limits: c is swept, not taken from propeller data (the UIUC propeller database host was unreachable from the run sandbox); cost, mass and plant ranges are inherited assumed fits; attitude steps only, no hardware.

A figure from its own output

Figure produced by research/codesign-aero-cant-kappa: kappa — codesign-aero-cant-kappa/experiments/kappa.png, written by the project's own experiment code.

Paper, code and results

More in Agentic co-design of low-cost robots

Does rotor cant still pay once a co-designed quadrotor must hold position?Once the vehicle must hold position, does a canted-rotor quadrotor still win? In simulation cant still buys yaw (−6° RMS, 5 of 5 seeds) but not position, and the sideways force a tilted rotor makes under roll/pitch torque breaks designs tuned without it (1.1 m against 0.25 m position error).
What reaction-torque-to-thrust ratio do real small propellers have, and does the best rotor cant angle survive it?What is the reaction-torque-to-thrust ratio of real small propellers, and does the best cant angle survive it? Measured static data for 77 propellers of 3.15–9.85 in give c = CP/(2π·CT) = 0.065–0.13 (median 0.081); in simulation cant still beats no cant in 5 of 5 seeds at every c, by 2.9–4.7°, and the joint design picks 36–41°.
Is rotor cant just a cheap way to buy yaw authority that bigger motors would buy as well?Does rotor cant still help once motor headroom is a design variable? With thrust-to-weight free in 1.5–4 (no cant picks the 4.0 ceiling), cant to 35° still beats no cant in 5 of 5 seeds at each of three measured propeller c values, by 1.6–3.4°; headroom alone recovers 2.5–3.5° of the 3.8–4.7° the parent credited to cant.
Was the thrust-to-weight ceiling of 4 what made rotor cant look good?Does raising the TWR ceiling from 4 to 6 and 8 erase the cant advantage? No: cant to 35° still beats no cant in 5 of 5 seeds at three measured propeller c values, by 1.5–3.0° at ceiling 8 (1.6–3.4° at 4); the optimiser stops near TWR 5 without cant.
Does a neural residual help a quadrotor attitude controller once roll, pitch and yaw are coupled?Does a residual network or analytic gyroscopic compensation beat per-axis PID on a coupled three-axis quadrotor? No: the residual is worse than PID in 26 of 30 pairs (+0.32° held out) and compensation changes the error by 0.001°; yaw authority sets the error.
Does a small neural roll controller beat the three-gain PID on a randomised quadrotor, and does it change which airframe is best?Does a 31-parameter neural roll controller beat the three-gain PID on a randomised quadrotor? Not at equal evaluations (7.7° PID against 9.0°); with 10× the evaluations it only matches it (7.6°), and the airframe ranking is unchanged (Spearman 1.00).

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.