physicalai-bmi/punch-energetics

Punch Energetics

Everything needed to check, rerun, or disagree with TR-2026-41, Joules per Punch (Institute for Physical AI @ John Bailey Institute, The Charlot Lab).

Eleven single-file Rust benches, no dependencies, and the thirteen run receipts every published figure in TR-2026-41 and TR-2026-45 is taken from.

The question

A humanoid throws a cross. Roughly three-quarters of a human straight punch comes from leg drive and trunk rotation, and a Unitree G1 has one yaw joint where that power path lives. So: give it a spine? Priced against an identified electrical power model, the answer is not the expected one, and it has two halves that only make sense together.

• A segmented trunk costs more than the single waist joint at every demand both bodies can meet. Serial joints share motion, not torque: N rotary modules pay N torque-squared copper terms, worsened to roughly N^(8/3) under a fixed actuator-mass budget. This survives the motor scaling exponent swept to its most generous physical value.
• Above 18 kg·m/s of delivered momentum, the single-joint and eight-joint bodies stop delivering at all, and the seventeen-segment multiarticular trunk is the only architecture that still throws the strike. The spine is a feasibility technology before it is an efficiency one.

Run it

rustc -O bench/punch_energetics.rs -o /tmp/pe && /tmp/pe

Each bench's header names the receipt it writes and why that path is the only one it may use.

Bench	What it does
bench/punch_energetics.rs	The parent. Dynamics core, loss model, eight runtime gates, the architecture tables.
bench/punch_reward_learning.rs	Cross-entropy policy search over the same strike; thirteen reward forms by five seeds.
bench/punch_demand_frontier.rs	The demand sweep that located the feasibility frontier.
bench/punch_verify_c.rs	Equal-budget replication at a given P*, every draw printed.
bench/total_task_energy.rs	The sibling bench this work extends, per completed reach rather than per strike.

The first four share one dynamics core by verbatim copy, held byte-identical by a gate in the report's repository.

The anatomy benches — TR-2026-45

Five more benches ask which energy-saving mechanisms in human movement transfer to a machine. They share this bundle but not the dynamics core above, and each carries its own gates and its own predictions registered before its run. Four of those predictions were falsified; the falsifications are in the file headers rather than edited out.

Bench	Question	What it found
bench/standing_load.rs	Who should hold the body up?	A latch, not the motor: 78.9 J against 278.9 J over ten seconds. Holding body weight costs a drive 20 W while doing no work. On energy only — the thermal half of that claim was withdrawn when the thermal bench's constants were anchored to a datasheet.
bench/yielding_leg.rs	What is a spring for, and an actuator for?	Below the spring's capacity the actuator costs nothing; above it, 0.55 J of copper per joule absorbed.
bench/windlass_gearing.rs	Is variable stiffness worth joules?	0.3% against a free, zero-overhead oracle. The binding constraint is static sag, not the stiffness schedule.
bench/freefall_reorient.rs	Can a body turn in mid-air for free?	Mechanically free to numerical precision, and far too slow: 38 cycles for a quarter turn.
bench/preflex_latency.rs	What does control latency cost?	Past roughly a tenth of a limb's period, no gain recovers the lost rejection. Delay inverts an impedance rather than blunting it.

The thermal shadow

bench/thermal_shadow.rs asks what the rest of the bundle was assuming. Every joule of copper loss counted anywhere in this work is also a joule of heat, deposited in a winding with a small thermal mass and a poor path to still air. A battery is a total; a winding is a rate.

A trunk drive at its measured 184 W peak is rated for 106 W continuous and sustains 57 percent duty. The hottest winding in the same strike is an arm actuator at 617 W on a motor a third the mass, rated for 76 W, sustaining 11.4 percent: one 0.28 s strike every 2.5 seconds against the trunk's 0.5. Thermally rationed rather than thermally impossible, and the rationing is a duty cycle.

The 9.3-point gap between those two duties is itself a result. It is the standing load eating the burst budget: holding the body up costs 20 W of copper for no work, and that 20 W comes out of what is left for striking. It is the same quantity the latch bench measures in joules, arriving here as 40 percent fewer strikes per minute. That does not contradict the energy results, it reorders what they are for — every mechanism that removed a watt removed a watt of heat, and heat is where the short limit lives.

Four corrections are recorded in that file rather than edited out, and an earlier version of this README carried the first two. It reported the ceiling reached in "four seconds at the 2686 W peak of a strike". That number was wrong twice over. The 2,686 W figure is the WHOLE BODY summed over every actuator, and the bench models ONE winding — 0.2 kg of copper, one housing, one path to air — so the calculation asked how long one motor survives seventeen motors' heat. And a strike lasts 0.28 s, so "four seconds at peak" described fourteen strikes thrown back to back with no rest, pricing a peak as though it were sustained, which is the very axis the bench's own P4 section falsifies. The parent bench had already printed whole-body peak and trunk-group peak as separate columns and said which one a drive is sized by; this one read the wrong column. The aggregate rows are now refused outright, at the pricing path rather than in a table-drawing loop, and a gate asserts the refusal changes the answer by more than an order of magnitude so it cannot become decorative. Recovering them honestly needs the per-actuator peak — the hottest winding, not the mean — which no receipt here carries, so it is left open.

A third correction, and the sharpest. Having replaced time-to-ceiling with a sustainable duty, the bench computed that duty as p_cont / p and printed it as a result. That closed form silently assumes zero power between bursts, while the first row of the same table puts a 20 W standing load on the same drive. Fed its own printed values back into its own integrator, the claim was false: the mean is 58.7 W against a 43.3 W rating, and the winding reaches the ceiling. If a file owns an integrator, its headline goes through it — a closed form printed beside a simulator is a hypothesis about that simulator. Both duties are now found by bisection on the integrator.

A fourth, inside the first. The trunk-group row was written as "440 W over 17 actuators". Neither number was right: the receipt says 449.2 W, and that architecture is 17 joints driven by 3 actuators. Writing the joint count repeated the exact category error the parent report exists to correct, since the copper bill follows actuator count. Corrected, the row is also less alarming than it looked: 449.2 W over 3 actuators averages 150 W each, below the 183.6 W a single waist drive already carries. That is a bound rather than a measurement, because the constraint binds on the hottest winding — but it is worth stating, because distributing a load across actuators can be a thermal win at the same time as it is an energy loss, and this series has so far priced only the loss.

The binding winding is in the arm, and it took a new column to see it. (TR-2026-41 v1.4 §7 publishes the architecture-by-architecture form of this; what follows is the thermal bench's reading of the same two columns.) Every thermal figure above is the trunk drive, because a trunk figure was the only per-actuator number any receipt in this series carried. punch_energetics.rs now reports the hottest single actuator in the strike alongside the whole-body and trunk-group sums, and it is an arm winding at 617 W — 3.4x the trunk drive, on a motor a third of the mass and therefore rated for about 32.0 W rather than 66.6. It sustains roughly 4.2 percent duty: one strike every 6.6 seconds, against the 1.0 s the trunk drive suggested. The thermal rationing this series has been describing is 6.7x harsher than published, and it does not live in the spine at all.

The column also gives the segmentation penalty a thermal signature. Across every architecture that keeps full-size motors — rigid trunk, fixed-per-module spines up to seventeen segments, and the multiarticular arrangements — the hottest winding stays in the arm at 620 to 666 W. Only the family that splits a fixed actuator budget into ever-smaller modules migrates: the arm is still hottest at two segments, the trunk takes over at three, and from there it runs 666 W, 1,426, 3,512, 6,211, and 11,260 W at seventeen. Which actuator is hottest turns out to be the same finding as where the joules go, read off a different column.

⚠ The 617 W is measured. The 76 W rating behind it comes from a robot-joint catalogue row for a motor of almost exactly the arm's mass — and getting there took four sets of constants, three of which were wrong.

They began with no source at all: plausible numbers chosen by the author, with the continuous rating every conclusion rested on being (155 − 25)/(R_wh + R_ha) of two invented resistances.

The anchor is now Kollmorgen frameless motors, a line whose catalogue names robotic joints as its first application. Two catalogues together publish winding-to-ambient thermal resistance for 24 motors from 0.111 to 4.15 kg — TBM2G supplies 21, TBM(S) the three largest. Fitted across all of them, R ~ m^−0.299 (R² = 0.862).

⭐ There is no extrapolation left. Both classes sit inside the measured range: the 0.6 kg arm between catalogue rows at 0.596 and 0.644 kg, the 1.8 kg trunk between 1.430 and 3.250 kg. Every earlier version of these constants reached outside its data by 1.26×, 3× or 10.9× — or had no data at all.

Two maxon datasheets are kept as a pessimistic bracket, and they earned their place by refuting the scaling law they were first used with. Between them, winding-housing resistance goes as m^+0.74 where a mass law says m^−0.67 — the wrong sign. Thermal resistance is a property of housing topology, not mass. What survives is that the sum is regular even though neither term is, which is why Kollmorgen publishes only the sum and why the sum is what gets scaled. Ratings transfer across motor classes; times-to-ceiling do not.

⚠ Mounting is worth more than any other assumption here. maxon measures end-on to a plastic plate; Kollmorgen on an aluminium heatsink. That is a factor of 2.1 on every rating, and a robot joint sits in load-bearing metal — so the heatsunk figure is the right one and the plastic-plate figure is a floor. Both are printed.

⭐ What did not move is the ratio, and the finding is a ratio:

constants	trunk	arm	one strike every	arm-to-trunk
invented, no source	43.3 W	20.8 W	10.5 s	5.2×
one datasheet, 10.9× extrapolated	66.6 W	32.0 W	6.6 s	6.6×
two maxon, arm exact, plastic-mounted	42.2 W	22.2 W	10.0 s	4.8×
24 robot joints, heatsunk, no extrapolation	106 W	76 W	2.5 s	5.1×

The arm binds under all four, including the invented ones. The absolute seconds moved by four times; the ordering did not. A finding stated as an ordering survives constants that a finding stated as a duration does not — which is the argument for reporting the ordering.

⭐ What would actually replace all of this can now be named. Lin, Qian, Luo & Liang, "Temperature distribution prediction of the quadruped robot based on the lumped-parameter thermal networks", Robot 47(2):188–199, March 2025 (in Chinese), identify a whole-body thermal network for a Unitree A1 by least-squares fitting against measured motor temperatures — natural cooling, prescribed joint-torque commands, and locomotion trials — reporting MSE below 2.5 (°C)² including a 4 kg payload. arXiv 2605.27046 then drives that identified model into an RL pipeline. Theirs is in situ: a motor in a robot, not a motor on a test bench.

⛔ Their model form exposes two gaps here that are not about constants at all. Their network couples neighbouring nodes — twelve motors and the onboard computer — while this bundle models each winding in isolation; in a strike the hot actuators are adjacent, so coupling would push the hottest winding higher and the arm figure is optimistic on that account. And their convection depends on body velocity, while this bundle is still-air throughout, so its figures are pessimistic on that account. The two point opposite ways, neither is quantified here, and both act on every actuator — which is again why the ordering is the part to trust.

⚠ The honest remaining list: one manufacturer's catalogue and one measurement convention; frameless motors rather than joint modules with gearing; mounting worth 1.9× and bracketed rather than known; and no humanoid vendor publishes per-actuator thermal data for the machine these power figures are calibrated against.

None of the underlying thermal physics is new, and the file says so first. Legged-robot thermal limits are an active research area and a standing rule in actuator selection: arXiv 2605.27046 drives a whole-body motor thermal model into an RL policy for a quadruped; ICRA 2009 derives the same ceiling-limited operating point for a climbing robot; field data has a legged robot shutting down at 84 °C after 34 minutes with charge to spare. What this bench adds is only that the constraint is priced in the same units, and against the same measured power levels, as the rest of this bundle. A connection, not a discovery.

freefall_reorient.rs carries the cleanest control in the bundle: a system whose joint axes are parallel cannot reorient at zero angular momentum, because planar angular momentum is holonomic. It returns exactly zero there and a real turn for skew axes, which is the best gate a simulator can be given.

Read the receipts, not just the summary

The *.out.txt files are the actual runs. Each opens with its gate results, so a receipt whose gates failed is visibly different from one whose gates passed. DATASHEET.md says what each file carries.

Two things worth knowing before comparing numbers:

• A gap under about five percent between two architectures is search scatter, not a difference. The search is multi-start; the per-draw spread printed in the verify files is the measurement's uncertainty. A thirty-draw replication moved every optimum 2 to 3 percent without changing any ordering.
• Feasibility evidence pools one-sidedly. A found strike stands forever; an absence means only that the draws attempted found none.

What this is not

Modelled results, not hardware measurements. The loss model's form comes from arXiv 2606.15915 and its magnitudes are calibrated against the 71.5 J reach measured on a physical G1 in arXiv 2606.15918. This review did not locate a published joules-per-strike measurement for any humanoid to anchor against — metering one is the open work, and it is what would turn the report's first forcing-function row into a hardware claim.

Three figures in the published report were wrong before they were right, all three found by auditing the prose against these receipts. That history is in DATASHEET.md, and it is the reason this bundle exists.

Licence

CC0 1.0 — public domain. Cite TR-2026-41 if useful; you are not required to.