Whip-Torsion · Confidential preview for invited evaluator
Locomotion Efficiency Explorer
Bipedal locomotion is the single largest energy constraint on humanoid robots — today's
platforms run at a cost of transport roughly an order of magnitude worse than a human. Whip-Torsion is a
patented method that narrows that gap by exploiting elastic energy storage and return — the way tendons
do — instead of braking and re-driving the body every step.
What this is and isn't: this tool lets you size the opportunity on your own numbers, using only public, textbook physics. The method itself — the "how" — is the protected IP, disclosed only under a paid evaluation and validated on your own hardware.
Notes, method & sources
A two-minute orientation. This is an auditable model, not a sales sheet: every number
comes from textbook spring-mass physics and inputs you control. The point is to let you (and your team)
stress it until you trust it — or find where it breaks.
What this is — and what it isn't
It sizes the energy opportunity in bipedal
locomotion from public physics and your own platform's numbers. It does not contain, reveal, or
prove the Whip-Torsion method — the "how" is disclosed only under a paid evaluation and validated on your
own hardware. Nothing here is anything you couldn't reproduce from a first-principles spring-mass model.
The three numbers (read this once)
The textbook ceiling scales down to a
real-world figure in three steps:
90% textbook ceiling — isolated leg energy, elastic vs. stiff (not the claim)
→ L locomotion-energy reduction (intermediate)
→ W whole-robot cost-of-transport reduction — the figure we cite (≈15–50%).
So a large leg-energy number (say 70%) next to a
smaller whole-robot number (say 30%) isn't a contradiction — it's the scaling-down at work. Only W is the claim.
How to use each tab
1 · Size the opportunity — two sliders you set yourself: the recoverable elastic
fraction (how much of the 90% ceiling your hardware actually captures) and locomotion's share of total
power. The gauge shows W. Presets jump to typical existing-actuator vs. compliant-co-design setups.
2 · Your fleet economics — enter your platform's real
numbers. Runtime uplift is hard physics; annual energy savings are your inputs × W; the actuator line is illustrative.
3 · Where robots stand today — published cost-of-transport
values; pick a platform and watch W move it toward human efficiency (≈0.2).
4 · Break it yourself — the full surface of W across both
knobs. Find the corner where the claim weakens; it's exposed, not hidden.
Sources
Cost of transport (definition & figures), Wikipedia;
Collins, Ruina, Tedrake & Wisse, "Efficient Bipedal Robots Based on Passive-Dynamic Walkers," Science
307 (2005); published ASIMO / Atlas efficiency comparisons.
Size the opportunity — from a textbook maximum to your real number
A stiff actuator wastes energy on every step: it brakes the leg as the foot lands, then burns power to drive it forward again. Storing and returning that energy elastically — like a spring — recovers almost all of it; in a simplified model, about 90% of leg energy. But 90% is a ceiling, not a promise. Two things shrink it on a real robot: how much of that energy your hardware can actually recapture, and how much of the robot's total power goes into moving at all. Account for both and you get a realistic whole-robot number — shown throughout this tool as W, the reduction in whole-robot cost of transport.
↓ Whole-robot reduction (W) — the figure we cite27.2%
Conservative 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 opportunity 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 opportunity 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 opportunity disappear?
Don't take the headline on faith. This is the full map of whole-robot reduction W for every possible setting of the same two sliders from Page 1 — and the marker sits wherever you left them, moving automatically as you adjust. Find the corner where your assumptions live. If the gain 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 conservative 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.
Whip-Torsion · Confidential preview for invited evaluator