Robotics
Support polygon
Definition
The support polygon is the convex hull of a robot’s active contact points or contact patches projected onto a common support plane. It describes the available support region in planar contact models.
Also known as: Support polygons
Updated
Which contacts count
With both feet flat on a level floor, the support polygon encloses the two contact patches and the space between them. With one foot lifted, only the supporting foot contributes. A foot hovering just above the floor provides no support.
For contacts that can push but not pull, MIT's contact-force derivation shows that the center of pressure must lie within the convex hull of the contact points. The available polygon therefore changes as the robot makes and breaks contact.
Using it for standing and walking
For static equilibrium under gravity on a horizontal plane, the vertical projection of the center of mass must lie within the support region, assuming the contacts can supply the needed forces. A standing humanoid can widen its feet to increase that region.
Dynamic walking instead involves acceleration and momentum. A planner often constrains the zero-moment point, rather than simply keeping the center-of-mass projection inside the feet.
A polygon cannot describe every constraint
A large support polygon does not prevent sliding on a low-friction floor. Contact forces must also satisfy their friction cones. Contacts on stairs or against a wall need a more general analysis of feasible forces and moments; a flat drawing of the feet loses relevant geometry.
Sources
Related terms
Zero-moment point
The zero-moment point is a point on a chosen support plane where the net moment associated with the ground reaction wrench has zero components parallel to that plane. In flat-ground walking with the usual contact assumptions, it coincides with the center of pressure.
Center of mass
The center of mass is the mass-weighted average position of a body or a collection of bodies. For an articulated robot, its position changes as the links move.
Friction cone
A friction cone is the set of contact forces permitted by a Coulomb friction model at a contact that pushes but does not pull. The allowable tangential force magnitude is bounded by the normal force multiplied by a friction coefficient.
Bipedal locomotion
Bipedal locomotion is movement using two legs, with body motion coordinated through changing contacts between the feet and the environment. It includes walking and running.