Whip-Torsion — Locomotion Efficiency Prize Explorer

Size the prize — honest dilution of a textbook mechanism

In an isolated reduced-order model, elastic storage-and-return cuts leg energy by roughly 90% versus a stiff actuator that brakes and re-drives every step. That is the ceiling, not the claim. Dilute it honestly for how much energy is actually recoverable on your hardware, and for locomotion's share of total power, and you bracket the whole-robot prize — expressed throughout this tool as W, the whole-robot cost-of-transport reduction.

Start from: Existing actuators Partial compliant retrofit Full compliant co-design

Recoverable elastic fraction0.55

↔ drag to explore

Of the mechanism's ~90% leg-energy ceiling, how much your actuators/structure actually capture and return.

Locomotion's share of total power0.55

Fraction of the robot's electrical budget spent moving the body (vs. compute, sensing, manipulation).

Per-step leg energy: stiff actuator vs. elastic storage-and-return, after your recoverable-fraction dilution.

Whole-robot cost-of-transport reduction

Mechanism ceiling (isolated leg energy)90%

Locomotion-energy reduction (L)49.5%

Whole-robot reduction (W)27.2%

Honest framing brackets 15–50% whole-robot: low end on existing actuators, high end with compliant co-design. W carries into tabs 2 and 4.

Your fleet economics — make the prize concrete

Enter your own platform's numbers. This applies the whole-robot reduction W = 27% (from tab 1 — adjust there) to runtime, energy spend, and lower-limb actuator wear across your fleet. Everything is editable; nothing here assumes our method, only its size.

Fleet size (units)
Usable battery (kWh)
Avg. total power draw in operation (W)
Operating hours / day
Operating days / year
Energy cost ($/kWh)
Lower-limb actuator set ($/unit)
Baseline actuator life (years)

Defaults are illustrative (≈ a 2.3 kWh class humanoid). Replace with yours.

Runtime per charge — uplift

+37%

Baseline runtime per charge5.1 h

With W7.0 h

Hard physics: a whole-robot energy reduction W lifts runtime per charge by W/(1−W). Operationally that is more work per charge, or fewer units and chargers for the same coverage.

Annual fleet energy savings

$—

Energy saved (kWh / year)—

Actuator wear avoided / yr (illustrative)$—

Energy savings are hard — your inputs × W. The actuator line is a directional illustration only: lower-limb wear scales with locomotion load (≈ L = 49%). Treat it as an upside signal, not a quote.

Where robots stand today — the gap, in published numbers

Dimensionless cost of transport (energy ÷ weight ÷ distance; lower is better). Humans and passive-dynamic walkers sit near 0.2; today's powered humanoids run an order of magnitude higher. That spread is the room the prize lives in. Pick a starting platform and watch W move it.

Apply W to: ASIMO (3.23)

Selected platform CoT3.23

After W reduction2.35

Still vs. human walking (0.2)11.8×

The point isn't to reach human efficiency in one step — it's that even a fraction of this gap is large, recurring energy cost across a deployed fleet. Tab 2 turns this into dollars.

Break it yourself — where does the prize disappear?

Don't take the headline on faith. This is the full surface of whole-robot reduction W across both honest dilution knobs. Find the corner where your assumptions live. If the prize is only real in the optimistic corner, you should know that before any conversation — so here it is, exposed.

Your current point (tab 1)0.55 / 0.55

W here27%

X axis: recoverable elastic fraction (0.40 → 0.80).
Y axis: locomotion's share of power (0.40 → 0.70).
Contours: 15%, 25%, 35%, 45% whole-robot reduction.
Marker: your current assumptions.

The honest read: W stays at or above ~15% across essentially the entire plausible region, and only reaches the high-40s in the compliant-co-design corner. That is the claim, stated as a surface instead of a slogan.