Capture Point

The point on the ground where, if the robot steps right now, it would come to a complete stop.

The capture point was introduced by Pratt, Carff, Drakunov, and Goswami in a 2006 Humanoids conference paper to answer the question of where to step, after being pushed, in order to stop. In the linear inverted pendulum model — which treats the robot as a point mass at constant height, balanced on a single support point — the capture point is ξ = x + ẋ/ω: x is the center of mass's horizontal position, ẋ is its horizontal velocity, and ω = √(g/h), with g the gravitational acceleration and h the center-of-mass height. It is precisely the part of the motion that diverges in this model: placing the zero moment point at the capture point brings the center of mass gradually to rest, while a capture point that falls outside the foot means the robot must take a step. Later work developed it into biped walking controllers and into the broader framework of 'capturability' analysis.

ExampleSuppose the center-of-mass height is 0.9 m, so ω ≈ 3.3 /s; if the robot is pushed and its center of mass moves forward at 0.5 m/s, the capture point lands roughly 0.15 m ahead of the center of mass's ground projection. If that point already lies beyond the supporting foot, the robot has to step forward and place its foot near the capture point.

Also called

CP, Instantaneous Capture Point, ICP

Related

Linear Inverted Pendulum Model (LIPM) · Divergent Component of Motion · Zero Moment Point · Push Recovery · Support Polygon · Centroidal Moment Pivot

Sources

Pratt et al.: Capture Point: A Step toward Humanoid Push Recovery (Humanoids 2006)
Stéphane Caron: Capture point