Every time a person lifts one foot and steps forward, they stand on a single foot for a brief moment. We do this without a second thought, but for a two-legged robot, walking means constantly catching a body that keeps trying to fall over. The concept long used as the yardstick for judging whether such a robot is about to fall is the Zero Moment Point.
Put simply, the Zero Moment Point is “the single point at which the force of the sole pressing on the ground and the force of the ground pushing back create no turning force that tips the body forward, backward, or sideways.” It is often shortened to ZMP. Miomir Vukobratović of the Mihajlo Pupin Institute in Belgrade, Serbia, first introduced it in his 1968 research on bipedal walking and gave it this name in the early 1970s.
In this piece we will look in turn at what the Zero Moment Point means and its partner concept, the support polygon; the difference between static and dynamic walking; examples from everyday life and real robots; and the limits of this criterion along with newer approaches.
How Two-Legged Robots Keep Their Balance
What Is the Zero Moment Point?
When a robot stands, the ground pushes up on every part of its sole. If you combine all those forces into one, the Zero Moment Point is where the ground-reaction moments about the two horizontal axes are zero. The vertical-axis moment need not be zero. When the sole is flat on the ground, it is treated as the same spot as the center of pressure, the center of the pressing force.
- Support Polygon: the area enclosing the soles in contact with the ground. Standing on one foot, it is that sole; standing on two, it is both feet and the space between them.
- Center of Mass: the point where the whole body’s weight can be thought of as gathered in one place. Its position shifts with every step.
The core rule is simple. As long as the Zero Moment Point stays inside the support polygon, the sole stays planted on the ground. If a tipping moment remains after the point reaches the toe or heel edge, the foot can rotate about that edge and the robot may tilt.
The Difference Between Static and Dynamic Walking
Why the Zero Moment Point matters becomes clear when you compare it with the way robots walked before it. The gait of two-legged robots can be broadly divided into two types.
(1) Static Walking
A way of walking in which the point directly below the center of mass always stays inside the support polygon. The robot will not fall even if it stops at any moment, but because it has to shift its body slowly with each step, it is very slow. WABOT-1, built in 1973 by Ichiro Kato’s laboratory at Waseda University in Japan, walked this way.
(2) Dynamic Walking
ZMP-based dynamic walking accounts for inertia, keeping the Zero Moment Point inside the support area even when the vertical projection of the center of mass briefly leaves it. Because it uses the forward-pitching force the way people do, it allows much faster and more natural walking. In 1984 WL-10RD, from the same laboratory, walked with dynamic balance on this principle, giving the first real-world demonstration of the Zero Moment Point.
Understanding the Zero Moment Point Through Easy Examples
[Example 1] Staying upright on a bus as it pulls away
If you are standing without holding a handle and the bus suddenly pulls away, your body is thrown backward and your weight shifts toward your heels. If a tipping moment remains after the center of pressure reaches the heel edge, the foot rotates about that edge and the body may tip backward. Bending your knees and leaning your upper body forward without thinking is, in effect, a movement that pulls the displaced Zero Moment Point back inside your soles.
[Example 2] The ankle sensors of humanoid robots
ASIMO, unveiled by Honda in 2000, and HUBO, unveiled in 2004 by Professor Jun-Ho Oh’s team at KAIST, both walked on the basis of the Zero Moment Point. HUBO used feedback from force-torque sensors in its ankles and acceleration sensors in its soles in real-time control, including ZMP control, to reduce landing impacts and vibration. The way these robots walk with their knees slightly bent is also one of the methods for fine-tuning balance.
The Limits of the Zero Moment Point and New Approaches
The Zero Moment Point was the criterion that first let two-legged robots walk stably, but it does not solve every situation.
(1) It assumes a flat, firm floor
The criterion assumes the sole touches the ground evenly without slipping. On gravel, ice, or a bumpy mountain trail, where the foot may slip or touch down on only one side, this point alone cannot guarantee safety.
(2) It stays with cautious steps
Because it is geared toward keeping balance with the sole planted on the ground, the gait is conservative, and it cannot be used in moments of running or jumping when both feet leave the ground. It also uses a lot of energy, since the joint motors must constantly correct the robot’s posture.
To get past these limits, researchers have explored other paths as well.
- Passive Dynamic Walking: a method demonstrated by Tad McGeer in 1990, in which a machine walks down a gentle slope with no motors, using only the swing of its legs and gravity.
- Capture Point: a concept proposed in 2006 by Jerry Pratt’s research team that tells where a robot must step to come to a stop after being pushed.
- Reinforcement Learning: by letting a robot fall countless times in a virtual space as it learns to walk, it finds gaits that keep balance even on rough ground.
The Zero Moment Point is a concept that let us see walking as an endless tug-of-war against falling. Robots today walk and run in many more ways, but the idea of working out where balance converges beneath the soles still remains the starting point of research on bipedal walking.
Knowing exactly where the force of falling is headed and holding that force within the soles: that is the first step for a robot that walks on two legs.
