The Zero tipping Moment Point (ZMP) is useful in determining if a bipedal robot is in a stable configuration or not. It has been used extensively in a number of biped control algorithms, most notably at Honda. The ZMP is the point on the ground where the sum of all the moments of the active forces is equal to zero. It helps to clarify this with equations and diagrams:
Given a robot we can write:
F = m.g - m.a
Where m is the robots mass, g is gravity and a is the acceleration of the center of mass.
The moment on any point is:
Mp = p.COM x m.g - p.COM x m.a - H
Where p is the point in question, COM is the center of mass, and H is the rate of angular momentum at the center of mass.
If we can find a point on the ground that balances the motion of the robot then we have the ZMP.
P.zmp = n x MP / F.n
Where P is the projection of the ankle to the ground, and n is the grounds normal.
For more information refer to Honda's ASIMO history which gives a few diagrams and an overview, and Philippe Sardain and Guy Bessonnet article Forces Acting on a Biped Robot: Center of Pressure, Zero Moment Point.
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