Zero Moment Point

Post Date : December 4, 2022

From Newton’s Law, to be at rest or not accelerating, the net sum of external forces acting on a body must be countered with the net sum of reactions in equal magnitude and opposite driection. In 2D, this is true for all three axis, which are the movement in x and y axes and rotation about z axis, which are all perpendicular to each other (x and y axes are the axes of the screen plane and z axis is the 3rd dimension perpendicular to the screen, but the rotation around it still falls on the screen plane so evberything is in 2D). In 3D, we again have x y and z axes but this time we have translation (movement on a line) and rotation about all axes.

To keep a robot stable during its movement, in other words not accelerate (by moving or rotating around a point) the law above therefore applies.

The zero moment point (ZMP) is the point on the robot where the reaction from the ground acts such that, in that given instant, by acting from a particular point at the robots base in a particular magnitude, it cancels out the effects of forces from robots weight plus any inertial forces of the robots mass.

Walking robot for example, will need to move its leg such that, this reaction force can fall on the area of the foot, otherwise the robot will start to fall, since the effects of gravity and inertial forces cannot be countered with an equal and opposing reaction. Needless to say, this becomes a key criteria to achieve for an android’s bipedal walking.

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