Static Stability

The robot's center of mass projects straight down inside its support polygon, so it stays balanced even standing still.

Static stability means a robot can hold its balance on its own support whenever its velocity and acceleration are both near zero. The test is simple: project the center of mass (the robot's overall center of gravity) straight down onto the ground, and check whether that point falls inside the support polygon — the convex region enclosed by all the ground-contact points. The farther the projection sits from the boundary, the more stable the robot is; that shortest distance is often called the stability margin. The advantage is that the robot can stop at any instant without a controller correcting it in real time, which is why early multi-legged robots and slow-walking humanoids were designed around it — a quadruped walking slowly, for example, lifts only one leg at a time and always keeps the other three planted in a triangle. The cost is speed: moving fast or running requires letting the center of mass leave the support region briefly, which calls for dynamic-stability criteria like the zero moment point or the capture point instead.

ExampleWhen a hexapod robot uses a tripod gait, it lifts three legs at a time while the other three form a triangle on the ground; as long as the center-of-mass projection stays inside that triangle, the robot could stop at any instant without falling.

Also called

Static Balance, Statically Stable

Related

Support Polygon · Dynamic Stability · Center of Mass (CoM) · Zero Moment Point · Quasi-Static Assumption · Quadruped Robot

Sources

Legged robot - Wikipedia
Support polygon - Wikipedia