Support Polygon

The convex region enclosed by all of a robot's ground-contact points; balance criteria are measured against this boundary.

The support polygon is the convex region on the horizontal plane enclosed by every point where a robot touches the ground. For a humanoid balanced on one foot it's roughly the outline of that foot; standing on both feet, it's the outer boundary connecting the two footprints; for a quadruped with three legs down, it forms a triangle, which is why it's also called the support triangle. It serves as the boundary for balance criteria: static stability requires the center-of-mass projection to land inside it, and dynamic walking requires the center of pressure — where the resultant ground-reaction force acts, equivalent to the zero moment point — to stay inside it, since the center of pressure can never geometrically leave the contact region. The larger the support polygon, the wider the range of center-of-mass acceleration it can tolerate, which is why slow quadruped walking keeps three legs down at all times and why humanoid feet are made large enough to matter.

ExampleWhen a quadruped trots, only the two diagonal legs touch the ground at once, so the support polygon collapses into a line segment; the center-of-mass projection can almost never land exactly on that line, so trotting isn't statically stable — balance has to be maintained by continuously adjusting the gait instead.

Also called

Support Region, Base of Support, Support Triangle

Related

Static Stability · Zero Moment Point · Center of Pressure (CoP) · Center of Mass (CoM) · Double Support Phase · Trot Gait

Sources

Support polygon - Wikipedia
Underactuated Robotics (Tedrake), Ch. Simple Models of Walking: CoP and ZMP