Glossary · Robotics and control
Support polygon
Also called base of support, support region
The outline on the floor around all the points where the body touches the ground. Standing still, the body balances if its centre of mass is above it.
Take every point where the body touches the floor and stretch an imaginary rubber band around them. The shape inside is the support polygon. Mathematically, it’s the convex hull of the contact points.
With two feet flat and apart, it’s roughly the shape that encloses both feet. Lift a heel and it shrinks to the ball of that foot. Stand on one foot and it’s just that foot.
Static balance
A body standing still is balanced when its centre of mass, projected straight down, is inside the support polygon. The further inside, the bigger the push it can absorb before it starts to tip.
That’s why fighters widen and lengthen their stance against pushes. A long stance gives a long polygon front to back, so shoves from the front or back are easy to absorb. A narrow stance is weak to the side.
Dynamic balance
When the body is moving, the projected COM isn’t enough. The test becomes whether the capture point is inside the polygon. If it is, the body can stop without stepping. If it isn’t, it has to move its feet and make a new polygon around the capture point. That’s a step, a hop or a fall.
In this project
The support polygon is built each step from the parts of the feet touching the mat. Recovery mode starts when the capture point leaves it, or sits within 2 cm of its edge while moving outward. A long, narrow stance (0.51 m by 0.16 m) explains why front and back shoves of 150 N were absorbed while sideways shoves of 100–150 N started a slow drift the stance couldn’t stop.