A joint burns power standing still

Start with the strangest fact about electric humanoids. Mechanical power is torque times speed, so a knee that holds a crouch without moving does zero mechanical work. The battery doesn’t care. To make torque, the motor needs current, and current through copper windings dissipates I²R as heat, moving or not.

Motor makers boil this down to one figure: the motor constant, Km, in N·m per square-root watt. It’s the torque you get for a given amount of heat in the windings, Km = τ / √P. Flip it around and the copper loss is P = (τ / Km)². Double the torque and you quadruple the heat. That square is the whole story of why a humanoid standing with bent knees costs real power, and why designers obsess over posture, gear ratio and motor size long before they look at anything else.

Two practical consequences follow. A bigger motor with a higher Km runs cooler at the same torque but adds mass the legs have to carry. And a higher gear ratio cuts the motor torque needed for a given joint torque, which cuts copper loss sharply – but it adds gear friction and makes the joint harder to back-drive. Every humanoid actuator sits somewhere on that trade.

Where the watts go

Follow a joule from the pack to the floor and it gets taxed four times. The servo drive loses some in switching and conduction. The motor loses copper and iron losses. The reducer loses mesh and bearing friction. What’s left moves the limb – and when the limb brakes, some of that energy can run backwards into the bus. Off to the side, compute and sensors draw power whether the robot moves or not; Hard Tech Deep Dives puts that at roughly 100–300 W for compute and perception, plus tens of watts for sensors.

The gearbox tax

Reducer efficiency isn’t one number. Harmonic Drive’s CSG-2A engineering data plots it against input speed, ratio and temperature, and the curves span a wide range – from around 40% at the cold, high-ratio end to the mid-90s under the best conditions. Below rated torque it gets worse: the catalog has you multiply by a correction factor K that falls from 1.0 at rated load to about 0.6 near zero load. A humanoid joint spends most of its life well below rated torque, so the headline curve flatters it.

Measured side by side, the gap between gearbox types can be startling. A 2026 journal study built matched harmonic-drive and planetary actuation units for an exoskeleton. The harmonic unit needed 58.9 mN·m to break away versus 8.5 for the planetary, and in transparency mode – where the motor works to cancel the gearbox’s resistance as a person moves the joint – it drew 444.57 W against 93.21 W. That’s a test rig, not a humanoid. Still, it shows how much power can disappear just fighting friction.

Braking is free energy – if the drive can take it

Walking is full of negative work. Every footfall has to be decelerated; every time the robot sits, lowers a box or bends a knee under load, the joint absorbs energy instead of supplying it. A hydraulic system throws that away through valves. An electric motor can run as a generator.

MIT’s Cheetah team built their robot around this. Their efficiency work named three culprits – heat in the motors, friction in the transmission and wasteful control – and designed against each: high-torque motors to cut Joule heating, a low-loss transmission, and electrically controlled damping so that, in the team’s words, the majority of impact energy goes back to the battery. The catch for humanoids is that regeneration only helps if the drive electronics and battery management can accept reverse current, and if the reducer is efficient enough in the back-driving direction to let energy through at all. High-ratio, high-friction gearboxes eat most of it before it gets to the motor.

Cost of transport: the scoreboard

Legged-locomotion researchers compare robots with cost of transport (CoT): power divided by weight times speed. It’s dimensionless, so a 10 kg walker and an 80 kg humanoid sit on the same scale. Lower is better.

Cornell’s Ranger is the outlier worth studying. It walked 40.5 miles in 2011 on a single charge, drawing 16 W in total – 11.3 W for its motors and 4.7 W for electronics. It got there by not controlling every joint angle: it let its legs swing and essentially fell forward from step to step. The Duke Humanoid team took the same idea into reinforcement learning, rewarding a policy for using the leg’s natural dynamics, and measured a 31% lower CoT on hardware at 0.3 m/s, with simulation showing up to 50% at low speeds.

Commercial humanoids sit much further up the scale, because they carry hands, arms, cameras and a GPU-class computer. Figure rates the 2.3 kWh pack in Figure 03 for 5 hours at peak performance, which works out to an average of about 460 W. Unitree’s H1 carries an 864 Wh swappable pack. Neither company publishes a cost of transport, so that’s the number to ask for.

What to check on a spec sheet

• Motor constant Km or torque constant plus winding resistance, so you can work out copper loss at the torque your joint actually holds.
• Reducer efficiency at partial load and low temperature, not just the peak value at rated torque and 40 °C.
• Whether the drive supports regenerative braking, and what happens to reverse current when the battery is full.
• Run time under a defined duty cycle. “Up to 5 hours” with no task description says little about a shift spent crouching at a shelf.

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