Whip-Torsion · Confidential preview for invited evaluator
Locomotion Efficiency Explorer
Whip-Torsion resolves a problem the field has openly conceded for decades: it can measure
human running economy but has never specified what produces it -after a century of biomechanics finding its
nuts and bolts in isolation but never assembling them. The gap current humanoid platforms face in reaching
that economy is not the hardware; the springs already exist. What is missing is the specification itself: a
control-architecture method.
We are not describing it here; instead, the tool below lets you prove the
size of the opportunity on your own numbers, on public physics alone, with none of the method exposed.
Patent-pending, disclosed only under a paid evaluation.
What this is and isn't: this tool sizes the opportunity on your own numbers, using only public, textbook physics, and is fully auditable. It contains none of the method; the protected "how" is validated on your own hardware under the paid evaluation.
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: the elastic energy available per step, isolated leg, elastic vs. stiff (not the claim)
→ L locomotion-energy reduction (intermediate)
→ W whole-robot cost-of-transport reduction, the figure we cite (≈15–50%).
The ceiling is the energy physically available each step; today's spring-equipped robots capture little of it, because capturing it is a control problem, and W is what the control method realizes. 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 the system actually captures, which is a control problem, not a hardware spec) 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 ceiling to your real number
A stiff actuator wastes energy every step: it brakes the leg on landing, then spends power to drive it forward again. In a simplified model, elastic storage and return can recover about 90% of that leg energy. But 90% is a physical ceiling, not a promise: springs make the energy available, yet capturing it is a control problem, which is why adding springs or actuators alone does not close the gap. Your real number then depends on two things: how much of that available energy the system actually captures, and how much of the robot's total power goes into moving at all. Account for both and you get a realistic whole-robot figure, 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 the size of the opportunity.
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