Agentic co-design of low-cost robots

A parametric 3D-printable gripper finger (length, thickness, pad width, V angle) scored in MuJoCo on eight objects with a per-design grip force. At 40 evaluations the median best objective is 0.991 for Bayesian optimisation, 0.979 for CMA-ES, 0.965 for random search and 0.963 for a session agent’s hand-written proposals (one run; Bayesian optimisation matched or beat it in 10 of 10 seeds). The best designs are tiny flat fingers (0.5 g), but re-scored with object offsets tripled they hold 5 of 8 objects against 6 of 8 for the agent’s wide V. Rigid, stylised, no learned policy, nothing printed.

Five design variables (wheel radius, wheelbase, flipper length, drive torque, battery) are scored on twelve held-out random-rubble terrains with Gamma-patchy friction, each design with its own evolution-strategies speed-and-flipper policy (not PPO). Wheel radius at its 90 mm bound with torque of about 0.5 N m reaches the ceiling J = 0.783 (16 of 20 m) at 69 USD. Median best J at 40 evaluations: Bayesian optimisation 0.782, CMA-ES 0.782, session agent 0.783, random search 0.716; the gaps at the top are within policy-search noise. Falls were zero throughout, so the tip-over and recovery path is untested. Stylised statics, assumed unsourced prices, one agent run with a calibration-time prior.

Five design variables (pad width, pad length, pad modulus, grip force, finger count) are scored on 600 simulated fruit with ripeness-dependent bruise thresholds, wet and dry friction and placement error, using closed-form line-contact pressure, friction hold and a capture-and-clutter law. At 40 evaluations the median best objective is 0.635 for Bayesian optimisation, 0.618 for a session agent’s hand-written proposals (one run, by the model’s own author), 0.611 for CMA-ES and 0.574 for random search; all 20 Bayesian-optimisation seeds matched or beat the agent. The best design (25 mm pads, 0.19 MPa, 8 N, three fingers) picks 74% clean; about 20% of fruit are lost to clutter collisions that no pad setting can change. Stylised, with assumed constants and no learned policy.

Five design variables (cup diameter, cups in a row, pump vacuum, pump flow, cup compliance) are scored on 600 simulated items (boxes, leaky polybags, bottles) with a cup-fit law on each item’s flat patch, vacuum lost to leaks, holding force against 1.5× a 1 g-accelerated load, and a pick-time penalty. At 40 evaluations the median best objective is 0.478 for Bayesian optimisation, 0.361 for CMA-ES and 0.328 for random search; a session agent’s hand-written proposals (one run, by the model’s own author) reached 0.519, and 1 of 20 Bayesian-optimisation seeds matched it. The best design (two 18.5 mm cups, 80 kPa, 60 L/min) holds 77% of items quickly; a catalogue-default single 30 mm cup holds none quickly (J 0.075). Stylised, with assumed constants, no learned policy and no general-purpose arm modelled.

A 15-minute inspection quadrotor with two airframe variables (arm length, prop diameter) and a three-gain roll policy found by CMA-ES, scored on held-out gusty step-tracking episodes. At 320 evaluations, joint CMA-ES reaches 5.25° RMS (the brute-force grid optimum is 5.25°), against 5.63° for joint random search, 5.52° for a frozen controller, 5.88° for bilevel search and 7.06° for design-first (lightest airframe, then tune). A controller tuned on one airframe and reused on others is 1° or more worse on 41% of cells. Gust level did not move the optimum. Stylised roll-axis model with assumed constants; the policy is linear, not deep RL; no flight software-in-the-loop.

Robustness follow-up to codesign-aero: 50 feasible airframes, each with roll gains tuned on the nominal, a narrow or a wide randomised plant (torque 0.7–1.0×, inertia 0.9–1.3×, motor lag 1–2×, assumed). With nominal-tuned gains the nominal and wide rankings have Spearman 0.75 and the same top five; the nominal optimum is 2nd of 50 on the wide plant, 0.17° behind the best. Tuning gains on the wide plant helps the median airframe by 0.91°. One tuning run per cell, so neighbouring ranks are within noise. Stylised, roll axis only, simulation only.

Follow-up to codesign-aero-robust: joint CMA-ES over arm length, prop diameter and three roll gains, trained on the wide randomised plant, against uniform random search at equal budget and against grid-then-tune. On held-out episodes the median CMA-ES winner reaches 5.75° at 960 evaluations (8 seeds, 5.70–5.87°) and 5.74° at 4800, random search 6.17° and 5.96°, and the grid’s best cell (4800 evaluations, picked on the held-out set) 6.00°. Stylised: assumed constants and ranges, roll axis only, five parameters, coarse grid reference.

Seed-repeat follow-up to codesign-aero-robust: the 50-airframe grid is re-tuned and re-scored six times with independent CMA-ES, training and held-out seeds. With gains tuned on the wide randomised plant the ranking is highly reproducible (Spearman 0.99 between replicates, same top five every time); with nominal-tuned gains it is noisier (0.84, winner varies in arm length), so the earlier “rank 2, 0.17° regret” was inside the noise. Retuning for the wide plant helps the median airframe by 0.88° on average. Stylised (assumed constants, roll axis only, six replicates).

Takes the codesign-agri contact model unchanged and widens what it holds fixed: per world the fruit size, placement error, wetness, bruise threshold and stem pull are drawn, and the printed gripper differs from the design (pad modulus, force and width tolerance). Over 600 random feasible designs and 30 held-out worlds the Spearman rank correlation with the nominal world is 0.993, so a nominal winner is a good candidate. The level still falls: the nominal CMA-ES optimum loses 13% of its objective (0.653 to 0.567), and a robust optimum trained on 10 other worlds gains only 0.015 on average and 0.034 in the worst world, from single runs. Sim-to-sim in a stylised model with assumed ranges; no gripper was printed.

Why every method in codesign-diagnose plateaued near 0.85. A MuJoCo sweep of 150 feasible gripper designs over 140 grasp scenes (cylinders, spheres, boxes of 150–1500 g) finds that 10 scenes (7%) are held by no design at any force, and all 10 are spheres where the simulated hand sits more than about 2 mm above the sphere’s centre height. Lowering only the hand height holds all 10 (hand at table level) or 8 of 10 (hand at sphere-centre height), so the ceiling comes from the scene geometry, not from friction, mass, force or finger strength; relaxing the finger strength limit lifts the best single design from 0.77 to 0.89 on fresh scenes. Stylised simulator; the 10-scene pattern was found after the fact and confirmed by one intervention.

Three scripted readers of a MuJoCo gripper co-design loop differ only in what they may read about each design: the score, a failure summary, or full rollout logs. At 40 designs and 8 seeds all end at 0.84–0.86 median best held-out grasp success, the same as random search, CMA-ES and Bayesian optimisation (standard error about 0.05), and the richest reader proposes the worst designs on average. Negative and stylised: the readers are author-written rules, not an LLM.

Companion to codesign-gripper with a different objective and a searched grasp force. Five parameters of a 3D-printable two-finger gripper (width, thickness, length, V-groove depth, TPU pad) are searched under a print-time cap; for each design a grasp force is tuned in MuJoCo and the design is scored on 40 held-out scenes (cylinders, spheres, boxes of 100–900 g). With 40 designs each, the best seeds of all three baselines reach 0.93–0.95 test success (medians 0.875, 0.887, 0.900 over 8 seeds) and one session-agent trajectory (n = 1, hand-written proposals) reaches 0.95 after 20 designs. On 100 fresh scenes every method’s best design drops 0.06–0.07 on average and the agent’s falls to 0.81, level with the baseline median: the task is nearly saturated and the ranking is within noise (standard error about 0.05). Stylised: assumed costs and strengths, rigid fingers, grid-plus-refine policy search rather than deep RL, nothing printed.

Follow-up to codesign-aero-coupled, which found yaw (reaction-torque limited) dominates quadrotor attitude error and that no control law changed that. Here the rotor cant angle α is a design variable: tilting rotors about their arms, alternating with spin direction, raises yaw authority to 2ΔT(κ cosα + r sinα) but costs thrust (every rotor is sized for T/cosα: more mass, more cost). With the PID retuned at each angle (6 airframes × 5 seeds, 64 held-out episodes), error falls from 17.77° at α = 0 to 15.38° at 35° (paired: better in 20 of 20 feasible pairs, mean −2.85°); the gain survives a 0.5× and 3× reaction-torque ratio. Joint CMA-ES co-design of arm length, propeller size, cant and gains (1920 evaluations, 5 seeds) reaches 12.32° against 15.22° with cant fixed at 0, and picks 34–35°, the edge of the allowed range, every time, so the optimum is not located. Higher cant also makes some airframes infeasible under the cost cap (20 of 30 grid cells feasible at 30–35°). Limits: the reaction-torque ratio, plant ranges and cost model are assumed and swept, not measured; tilt-induced efficiency loss, internal force fighting and roll/pitch cross-coupling from the tilted thrust vectors are not modelled; attitude only, step references.

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.

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.

Five earlier codesign-aero-cant* projects deferred position hold. Here the quadrotor gets translation, an outer position loop and the body-lateral force of a canted rotor, F = τ tan α / r per unit commanded roll or pitch torque (closed form checked against an explicit four-rotor allocation). Joint CMA-ES over arm length, propeller size, cant and nine gains (3200 evaluations, 5 seeds, 64 held-out episodes). Cant still cuts yaw error by 5.8° (bound 35°) and 6.0° (bound 80°), better in 5 of 5 paired seeds, while position error is unchanged within noise (0.25 m against 0.22 m with no cant). Designs tuned with the lateral force switched off and then scored with it on reach 1.1–1.2 m position error, worse in 5 of 5 seeds; the force acts as a disturbance (switching it off improves force-aware designs), with an unhelpful sign on the roll axis for this layout. Limits: 2 s episodes, objective weights (0.1 m against 10°) chosen, several seeds stop in local optima, one arm layout, perfect altitude hold; cost model, noise, offset and plant ranges are assumed or inherited, not measured; no hardware.

Closes the open limitation of codesign-aero-cant-kappa, where κ = Q/T = c D used a swept c. Here c = C_P/(2π C_T) is computed from the UIUC Propeller Data Site static tests (160 propellers; 77 of 3.15–9.85 in): median 0.081, 10th–90th percentile 0.065–0.13, maximum 0.193, no diameter trend (r = −0.11); the parent's upper sweep value 0.25 is above every propeller. Joint CMA-ES over arm length, propeller size, cant and six PID gains (1920 evaluations, 5 seeds, 64 held-out episodes), bound 0, 35° or 80°, at those four c values. At 80° the held-out error is 12.50°, 12.46°, 12.22°, 12.00° against 17.22°, 17.06°, 16.12°, 14.91° with no cant: better in 5 of 5 paired seeds each, by 4.7°, 4.6°, 3.9°, 2.9°; chosen cant 36–41°. Limits: static coefficients only (hover), c is a median over test RPMs, cost, mass and plant ranges are inherited assumed fits, attitude steps only, no hardware.

Follow-up to codesign-aero-cant-propdata (next step: compare at equal cost with a motor upgrade). Thrust-to-weight (motor headroom, 1.5–4.0) becomes an optional design variable beside arm length, propeller size, cant and six PID gains; κ = c D with c at the 10th, 50th and 90th percentile of measured UIUC static propeller data (0.065, 0.081, 0.13). Four arms, 1920 CMA-ES evaluations, 5 seeds, 64 held-out episodes, $300 cost cap. Without cant, free headroom cuts the held-out error from 17.2/17.1/16.1° to 14.7/14.0/12.6° (5 of 5 seeds at every c) but the optimiser sits on the 4.0 ceiling, so these are lower bounds on what headroom buys. With headroom free, cant to 35° still improves it to 11.3/11.2/11.0° (better in 5 of 5, by 3.4, 2.8 and 1.6°); the chosen cant falls from 35° to 23–29° and TWR is 3.7–3.8. At the largest c, cant with TWR 2 is only 0.3° better than no cant with free TWR. Limits: the TWR range, the motor mass/cost fits and plant ranges are assumed, TWR ceiling binds for no cant, attitude steps only, no position hold, no hardware.

Follow-up to codesign-aero-cant-twr, whose no-cant design sat on its assumed TWR ceiling of 4. Same joint CMA-ES co-design (1920 evaluations, 5 seeds, 64 held-out episodes, $300 cap, c at the 10th, 50th and 90th percentile of measured UIUC propeller data) with the ceiling at 4, 6 and 8. Raising it from 4 to 6 improves the no-cant design by 0.2–0.35° and the optimiser then picks TWR 4.9–5.1; from 6 to 8 nothing changes (within ±0.1°). Cant to 35° still beats no cant in 5 of 5 seeds at every c and ceiling, by 1.5–3.0° at ceiling 8, so the earlier gap was overstated by 0.1–0.4°. Limits: the interior optimum comes from inherited, assumed motor mass and cost fits (not a catalogue), attitude steps only, no position hold, no hardware.

Follow-up to codesign-aero-skip: roll, pitch and yaw with Euler gyroscopic coupling and a weak yaw axis. On six airframes × five CMA-ES seeds, held-out combined RMS attitude error is 17.76° for a 576-evaluation per-axis PID, 18.08° for PID plus an 83-parameter zero-initialised residual network (PID better in 26 of 30 pairs), and 18.20° for the 96-evaluation PID with or without analytic gyroscopic compensation (difference −0.001°). A 12-condition sweep over Iz/Ix (1.0–3.0), manoeuvre size and yaw authority finds the PID ahead of the residual in all 12 and compensation worth at most 0.016°, even where the gyroscopic term peaks at 71% of the torque limit. Yaw (about 29° RMS on 30° steps) is authority-limited and dominates the error; tripling yaw authority helps by 1.8°, the control-law class does not. Limits: the yaw reaction-torque ratio, inertia ratio and plant ranges are assumed and swept, not measured; attitude only with step references; the residual overfits 16 training episodes and a different learner might differ.

Follow-up to codesign-aero-robust: a 6-unit tanh network (31 parameters) trained by CMA-ES replaces the three-gain PID roll law on six airframes spanning the wide-plant ranking, three seeds each, scored on 64 held-out wide-plant episodes. At the same 96 evaluations the network is worse on 5 of 6 airframes (mean 8.96° against 7.72°); at 960 evaluations it matches the PID (7.59°, gains of 0.00 to 0.09° on five airframes and 0.53° on one). The best airframe and the ranking (Spearman 1.00) do not change, so the three-gain law did not distort the earlier sizing result. Limits: evolution strategies rather than PPO, no skip path, six airframes, roll only; the plant and randomisation ranges are assumed round numbers carried over from codesign-aero, not measurements.

Follow-up to codesign-aero-mlp: the controller is the tuned PID plus a 31-parameter residual network that is exactly zero at the start, so CMA-ES begins at the PID. On six airframes spanning the wide-plant ranking, three seeds each, scored on 64 held-out episodes, PID (96 evaluations) plus residual (480) reaches 7.68° mean, against 7.58° for a PID given all 576 evaluations; the residual is better in 7 of 18 airframe-seed pairs and worse in 11, with most of the gap on one airframe. Against the 96-evaluation PID it started from it is better in 14 of 18 but by 0.04° on average, within seed scatter. The airframe ranking is unchanged (Spearman 1.00). A negative result: the error floor is set by gust, sensor noise and motor lag rather than the control-law class in this roll-only model. Limits: evolution strategies rather than PPO, one small network, roll only, six airframes; plant ranges are assumed round numbers carried over from codesign-aero, not measurements.

codesign-agri drew stem pull-off force from a lognormal with an assumed median of 3.5 N, and codesign-agri-sweep varied it only from 1.75 to 7 N. Here the median is set to measured values reported by Rajendran et al. (2022) from Dimeas et al.: 3.17 N (a 1.78 mm peduncle detached by bending and pulling) and 13.94 N (2.17 mm, pulling alone), plus 6 and 10 N between them, with the grip-force bound at the parent’s 8 N or the published 10 N gripping limit. Random search, CMA-ES and Bayesian optimisation get 40 evaluations and 20 seeds on the same 600 fruit; a 400-evaluation Bayesian run (5 seeds) gives a reference optimum. At 3.5 N and 8 N the parent’s numbers are reproduced (0.574, 0.611, 0.635). Bayesian optimisation leads CMA-ES, which leads random search, in 8 of 10 cells. The reference optimum falls from 0.665 (3.17 N) to 0.502 (6 N), 0.249 (10 N) and 0.075 (13.94 N) at the 8 N bound; raising the bound to 10 N adds 0.03 to 0.04 at low pull-off and 0.04 at 10 N, and the best design moves from two fingers (low pull-off) to four (6 to 13.94 N). Limits: the bruise threshold, friction, ripeness law and prices are still assumed, the pull-off spread and ripeness factor are the parent’s, and only two measurements are available for the pull-off median.

Re-runs the codesign-agri soft-fruit gripper model in 100 Latin-hypercube worlds that move its 12 assumed constants (fruit size, bruise threshold, stem force, placement error, wetness, friction, collision length, prices, bruised-fruit value) by factors of about two, with the original optimisers at 40 evaluations and 8 seeds. Median regret to a per-world reference optimum is 0.013 for Bayesian optimisation, 0.060 for CMA-ES and 0.093 for random search; the original order holds in 82 worlds and Bayesian optimisation loses to random search in 4, where a flat landscape leaves some seeds on designs that pick nothing. The reference optimum has 2, 3 or 4 fingers in 42, 21 and 37 worlds (Spearman +0.74 with stem strength), and the nominal winner is over the cost cap in 37 worlds and, in the other 63, 0.056 J short at the median. The sweep ranges are my choices, not sourced; no gripper was printed.

Re-runs the codesign-diagnose ablation after fixing the scene generator that codesign-ceiling blamed for the 0.85 plateau (hand height capped at the object’s centre). Three rule-based readers (score only, failure summary, full rollout logs) and random search, CMA-ES and Bayesian optimisation, 8 seeds × 40 designs in MuJoCo. Every method gains only 0.00–0.05 (median best test success 0.85–0.90) and the ranking is not resolved at 40 test scenes (standard error about 0.05); feedback still does not beat blind search, and the best designs still lose 0.05–0.06 on fresh scenes. Stylised; readers are rules, not an LLM.

Re-scores the final designs of every codesign-headroom run (6 methods × 8 seeds × 3 checkpoints, 77 distinct designs) on 600 new scenes, with no re-optimisation. After 40 designs the mean true success is 0.846 for random search and CMA-ES, 0.845 for Bayesian optimisation and the score-only reader, 0.836 for the failure-summary reader and 0.817 for the rollout-log reader; no difference to random search has a 95% bootstrap interval excluding 0 (rollout logs: −0.029, [−0.073, +0.010]). The 40-scene test score overstates the chosen designs by 0.04–0.05 and ranks designs only moderately (Spearman 0.63). Eight runs per method, not the scene count, now limit resolution. Stylised; readers are rules, not an LLM.

Adds 16 new runs per method (24 in all) to the codesign-headroom comparison and scores every run’s final design on 600 scenes. Mean true success after 40 designs: CMA-ES 0.858, Bayesian optimisation 0.842, score-only reader 0.837, random search 0.833, failure-summary reader 0.832, rollout-log reader 0.811. No difference to random search is significant (CMA-ES +0.025, interval −0.007 to +0.056, p = 0.15); CMA-ES tied random search on the original 8 runs but led by 0.037 on the new 16, showing how far 8 runs can mislead. Richer feedback does not help. Run-to-run SD is about 0.06, so a 0.02 gap needs about 140 runs per method. Stylised; readers are rules, not an LLM.