Where is the best rotor cant angle for a quadrotor co-designed with its controller?

What it found

Follow-up to codesign-aero-cant, whose joint optimum sat on its 35° cap. Here the cant bound is raised to 50°, 65° and 80° and a tilt efficiency loss (hover power divided by 1 − k sin²α, k assumed and swept at 0 and 0.2) is added. Joint CMA-ES over arm length, propeller size, cant and six PID gains (1920 evaluations, 5 seeds, 64 held-out episodes) reaches 12.32°, 12.30°, 12.30° and 12.30° at bounds 35°, 50°, 65° and 80°, against 15.18° with no cant (better in 5 of 5 paired seeds, about −2.9°). The chosen cant is 34–40° in all 20 runs, so the earlier result was a plateau just under the cap, not a bound-limited optimum. With k = 0.2 the error is 12.44–12.46° and the chosen cant 29–36°. Limits: the tilt-loss coefficient, reaction-torque ratio, cost model and plant ranges are assumed (k swept, the rest inherited from earlier projects), not measured; attitude steps only, no position hold, no hardware.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

More in Agentic co-design of low-cost robots

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

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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.