How robots walk and balance

Walking has largely been solved, by reinforcement learning in simulation. A humanoid won the Beijing half marathon in April 2026 in 50 minutes 26 seconds, faster than the human world record, and a Unitree R1 Air that walks costs US$4,900 verified Sep 2026. The recipe is published and the simulators are open source. What's left to win is walking while doing useful work, for years, without falling on anything expensive.

Balance: the centre of mass and the support polygon

Everything about balance comes down to two shapes on the floor. The first is the point directly under the robot's centre of mass, the average position of all its weight. The second is the support polygon, the outline you get by stretching a rubber band around every part of the robot touching the ground. Stand on two feet and the polygon covers both feet and the gap between them. Lift one foot and it shrinks to a single sole.

Walking has a rhythm called the gait cycle. Each leg alternates between stance phase, foot on the ground carrying weight, and swing phase, foot in the air moving forward. In walking, the stance phases overlap for a moment called double support, when both feet are down and the polygon is at its largest. In running, they don't overlap: there's a flight phase with no support at all, and balance is entirely a matter of where the next foot lands.

The capture point: where to step to stop

The single most useful idea in bipedal walking models the whole robot as an inverted pendulum: all its mass in one point on top of a massless leg, like a broom balanced on your palm. From that model you get the capture point, the spot on the floor where the robot must put its foot to come to a complete stop.

Classical walking: preview control and bent knees

Before reinforcement learning took over, most humanoids walked with a pipeline an engineer could draw on a whiteboard. Plan footsteps. Plan a ZMP path that runs heel to toe down each foot and hops across during double support. Use the inverted pendulum model to compute a centre-of-mass path that produces that ZMP path, looking a second or two ahead, which engineers call ZMP preview control. Track the result with whole-body control and joint loops. Later stacks replaced the preview step with model predictive control, re-planning forces at 25 to 100 Hz over a 0.5 s horizon verified, which is how quadrupeds learned to trot and bound.

The linear pendulum assumes the centre of mass stays at one height, which is why classical humanoids walk with bent knees, like someone sneaking across a room. A few Chinese makers now sell straight-knee gaits as a feature: Dobot claims its straight-leg walk uses 42% less energy than bent-knee walking unverified, and Kepler's K2 uses one too. The energy a gait burns per kilogram per metre is its cost of transport, the number that decides runtime per battery charge.

Speeds as of Sep 2026. Everyone walks at about human pace, so speed no longer separates the leaders.

The reinforcement learning revolution

The pipeline above takes a team of PhDs years to tune for one robot. Reinforcement learning replaced it with trial and error at enormous scale. You build a simulation of the robot, write a reward function that scores each moment, and let a neural network, the policy, practise until the score stops improving. Thousands of simulated copies practise at once on GPUs, so a robot gets years of falling over in a day.

The catch is the sim-to-real gap. Simulators get rigid bodies right and get friction, motor heat, cable drag, backlash and sensor delay wrong. The fix is domain randomization: every episode, the simulator changes masses, friction, motor strength, delay and terrain at random, so the real world is one more variation the policy has already seen. It works for walking because walking is cyclic and forgives centimetre errors. It works much less well for hands, where tiny contact errors flip a grip from holding to slipping verified. A rough industry rule says 8 simulated samples are worth about 1 real teleoperated sample estimate.

The second trick is teacher-student distillation. In simulation you know everything: the exact height of every patch of ground, the friction, every contact force. A teacher policy trained with that privileged information learns fast. A real robot has none of it, so you then train a student policy to copy the teacher's actions using only what the robot's own sensors provide, plus a short memory of recent motion that lets it infer the terrain.

Look at the right side of that figure again. The learned part only replaces the top of the control stack. Underneath, the same PID-family joint loops and current loops run as they always did. When a learned policy misbehaves, the joints still do exactly what they're told, which is how an overconfident policy cooks a motor.

Motion imitation: why robots dance and do kung fu

Reward functions for walking are easy to write. Reward functions for a cartwheel are not. So engineers skip them: record a person with motion capture, map the human skeleton onto the robot's different limb lengths and joint limits, which is called motion retargeting, and reward the policy for matching the recording while staying upright. The same training loop then produces dance routines, boxing and kung fu in days.

That's why Unitree H1 humanoids danced on CCTV's Spring Festival Gala in 2025 and set off a rental boom verified, and why so many launch videos feature flips. Figure used the same idea for work: its Helix 02 balance network trained on more than 1,000 hours of retargeted human motion verified.

Falling, fall damage and recovery

Every legged robot falls. What separates products is what the fall costs. Fall protection covers everything from detecting the fall early (the IMU sees an unrecoverable tilt), to cutting or softening joint torque, to twisting so the fall lands on padded, replaceable parts, to a get-up routine afterwards.

• Falls are public. At the first Beijing humanoid half marathon on 19 Apr 2025 many robots fell verified. At the 2026 World Humanoid Robot Games, 2,056 robots from 666 teams competed and some tripped, broke apart or caught fire verified.
• Falls aren't covered. Makers' warranties typically exclude falls, collisions, water and debris, the most common causes of damage verified. A base G1 carries 8 months of warranty verified Sep 2026.
• Policies cause falls. One lab's RL policies drove a G1 into violent motion in states they had never trained on; the collisions broke a wrist gear and overheated the other arm, and the lab couldn't send it back because of a deadline owner report, May 2025.
• Mass decides damage. A 30 kg NEO falling on a person hurts less than a 90 kg Atlas or a 129 kg Digit 5 verified, which is part of why 1X built NEO light and soft for homes and why Agility's newest Digit is designed to sit down when a person comes close.

Legs, wheels and wheel-legs

Legs are expensive, power-hungry and fall over. Buy them only when the floor demands them. Many of the robots in the Chinese atlas quietly offer a wheeled version for exactly this reason.

Apptronik's reasoning for offering Apollo 2 on wheels is the clearest statement of the trade: on a flat factory floor, wheels remove balance risk and fit existing mobile-robot safety standards, a faster route to certification than legs verified. LimX's TRON 2 reconfigures between a biped, a wheel-legged robot and a fixed two-arm station, and sells for about US$6,800 to US$10,000 contested. Quadrupeds beat humanoids on rough ground, stairs and rubble, and they're cheaper: a Go2 Air costs US$1,600 against US$13,500 for a base G1 verified Sep 2026. Humanoids win only where the job needs two arms at human height in spaces built for people.

Stairs and perceptive locomotion

A blind policy feels the ground through its joints and IMU and handles bumps, slopes and small steps by reacting after contact. Stairs, gaps and stepping stones need the robot to see ahead. Perceptive locomotion feeds the policy a height map of the ground in front of the feet, built from a LiDAR or depth cameras. The Go2's 4D LiDAR sits under its chin and scans a 360 by 96 degree field verified. The teacher-student trick earns its keep here: the teacher trains on perfect terrain heights, the student learns to use a noisy, partial height scan.

Why locomotion is close to commoditised

Walking has largely fallen to reinforcement learning in simulation: it's contact-rich, and also cyclic, self-stabilising and forgiving of centimetre errors verified. The recipe is published, the simulators are free, and GPUs are rentable. More than 150 firms in China make humanoids verified Nov 2025, and the cheapest walking one costs US$4,900. The Honor humanoid that won the 2026 half marathon came from a smartphone company verified.

What isn't commoditised sits next to locomotion. Walking while carrying 20 kg and turning in a crowded aisle is loco-manipulation, and it's where Figure's whole-body network earns its keep. Walking for years is reliability: Figure's F.02 fleet logged about 1.2 million steps, roughly 200 miles, at BMW before retirement verified Nov 2025, and that's a small number next to what a factory needs. And walking without cooking the ankles is a thermal budget, set by the controller, as the control chapter shows.

Terms in this chapter